Boiling Heat Transfer

July 6, 2019 | Author: Andi Ishaka | Category: Heat Transfer, Thermal Conduction, Heat, Convection, Boiling
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Boiling Heat Transfer  The formation of steam bubbles along a heat transfer surface has a significant effect on the overall heat transfer rate.

Boiling In an industrial facility, convective heat transfer is used to remove heat from a heat transfer surface. The liquid used for cooling is usually in a compressed state, (that is, a subcooled fluid) at  pressures higher than the normal saturation pressure pressure for the given temperature. temperature. Under certain conditions, some type of boiling (usually nucleate boiling) can tae place. !ore than one type of boiling can tae place "ithin an industrial facility. # discussion of the  boiling processes, specifically specifically local and bul boiling, boiling, "ill help the student student understand these  processes and provide provide a clearer picture of "hy bul boiling (specifically (specifically film boiling) is to be avoided.

 $ucleate Boiling Boiling The most common type of local boiling encountered in industrial facilities is nucleate boiling. In nucleate boiling, steam bubbles form at the heat transfer surface and then brea a"ay and are carried into the main stream of the fluid. %uch movement enhances heat transfer because the heat generated at the surface is carried directly into the fluid stream. &nce in the main fluid stream, the  bubbles collapse because because the bul temperature temperature of the fluid is not as as high as the heat transfer transfer surface temperature "here the bubbles "ere created. This heat transfer process is sometimes desirable because the energy created at the heat transfer surface is quicly and efficiently 'carried' a"ay.

Bul Boiling #s system temperature increases or system pressure drops, the bul fluid can reach saturation conditions. #t this point, the bubbles entering the coolant channel "ill not collapse. The bubbles "ill tend to oin together and form bigger steam bubbles. This phenomenon is referred to as bul  boiling. Bul boiling can provide adequate adequate heat transfer provided provided that the steam bubbles bubbles are carried a"ay from the heat transfer surface and the surface is continually "etted "ith liquid "ater. hen this cannot occur film boiling results.

*ilm Boiling hen the pressure of a system drops or the flo" decreases, the bubbles cannot escape as quicly from the heat transfer surface. +ie"ise, if the temperature of the heat transfer surface is increased, more bubbles are created. #s the temperature continues to increase, more bubbles are formed than can be efficiently carried a"ay. The bubbles gro" and group together, covering small areas of the heat transfer surface "ith a film of steam. This is no"n as partial as partial film boiling . %ince steam has a lo"er convective heat transfer coefficient than "ater, the steam patches on the heat transfer surface act to insulate the surface maing heat transfer more difficult. #s the area of

the heat transfer surface covered "ith steam increases, the temperature of the surface increases dramatically, "hile the heat flu from the surface decreases. This unstable situation continues until the affected surface is covered by a st able blanet of steam, preventingcontact bet"een the heat transfer surface and the liquid in the center of the flo" channel. The condition after the stable steam blanet has formed is referred to as as film  film boiling . The process of going from nucleate boiling to film boiling is graphically represented in *igure -. The figure illustrates the effect of boiling on the relationship bet"een the heat flu and the temperature difference bet"een the heat transfer surface and the fluid passing it.

Figure 1 Boiling Heat Transfer Curve *our regions are represented in *igure -. The first and second regions sho" that as heat flu increases, the temperature difference (surface to fluid) does not change very much. Better heat transfer occurs during nucleate boiling than during natural convection. #s the heat flu increases, the bubbles become numerous enough that partial film boiling (part of the surface being  blaneted "ith bubbles) bubbles) occurs. This region is characteried by an an increase in temperature difference and a decrease in heat flu. The increase in temperature difference thus causes total film boiling, in "hich steam completely blanets the heat transfer surface.

/eparture from $ucleate Boiling and 0ritical Heat *lu In practice, if the heat flu is increased, the transition from nucleate boiling to film boiling occurs suddenly, and the temperature difference increases rapidly, as sho"n by the dashed line in the figure. The point of transition from nucleate boiling to film boiling is called the point of departure from nucleate boiling, commonly "ritten as /$B. The heat flu associated "ith /$B is commonly called the critical heat flu (0H*). In many applications, 0H* is an important  parameter. *or eample, eample, in a boiler, if the critical critical heat flu is eceeded and /$B occurs at any any location, the temperature difference required to transfer the heat being produced increases greatly.

The amount of heat transfer by convection can only be determined after the local heat transfer coefficient is determined. %uch determination must be based on available eperimental data. #fter eperimental data has been correlated by dimensional analysis, it is a general practice to "rite an equation for the curve that has been dra"n through the data and to compare eperimental results "ith those obtained by analytical means. In the application of any empirical equation for forced convection to practical problems, it is important for the student to bear in mind that the  predicted values of heat heat transfer coefficient are not not eact. The values values of heat transfer coefficients coefficients used by students may differ considerably from one student to another, depending on "hat source 'boo' the student has used to obtain the information. In turbulent and laminar flo", the accuracy of a heat transfer coefficient predicted from any available equation or graph may be no better than 123.

0onduction Heat Transfer  0onduction heat transfer is the transfer of thermal energy by interactions bet"een adacent atoms and molecules of a solid. 0onduction 0onduction involves the transfer of heat by the interaction  bet"een adacent molecules molecules of a material. Heat transfer transfer by conduction is dependent dependent upon the driving 'force' of temperature difference and the resistance to heat transfer. The resistance to heat transfer is dependent upon the nature and dimensions of the heat transfer medium. #ll heat transfer problems involve the temperature difference, the geometry, and the physical properties of the obect being studied. In conduction heat transfer problems, the obect being studied is usually a solid. 0onvection  problems involve a fluid fluid medium. 4adiation heat heat transfer problems involve involve either solid or fluid surfaces, separated by a gas, vapor, or vacuum. There are several "ays to correlate the geometry,  physical properties, and and temperature difference difference of an obect "ith the rate of heat transfer through the obect. In conduction heat transfer, the most common means of correlation is through *ouriers +a" of 0onduction. The la", in its equation form, is used most often in its rectangular or cylindrical form (pipes and cylinders), both of "hich are presented belo".

The use of 5quations 678 and 679 in determining the amount of heat transferred by conduction is demonstrated in the follo"ing eamples.

0onduction74ectangular 0oordinates 5ample: -222 Btu;hr is conducted through a section of insulating material sho"n in *igure 6 that measures - ft6 in cross7sectional area. The thicness is - i n. and the thermal conductivity is 2.-6 Btu;hr7ft7< *. 0ompute the temperature difference across the material.

Figure 2 Conduction Through a Slab

5ample: # concrete floor "ith a conductivity of 2.= Btu;hr7ft7< * measures 12 ft by 82 ft "ith a thicness of 8 inches. The floor has a surface temperature of >2< * and the temperature beneath it is ?2< *. hat is the heat flu and the heat transfer rate through the [email protected] %olution: Using 5quations 67- and 678:

Using 5quation 671:

5quivalent 4esistance !ethod It is possible to compare heat transfer to current flo" in electrical circuits. The heat transfer rate may be considered as a current flo" and the combination of thermal conductivity, thicness of material, and area as a resistance to this flo". The temperature difference is the potential ordriving function for the heat flo", resulting in the *ourier equation being "ritten in a form similar to &hms +a" of 5lectrical 0ircuit Theory. If the thermal resistance term A; is "rittenas a resistance term "here the resistance is the reciprocal of the thermal conductivity divided by the thicness of the material, the result is the conduction equation being analogous to electrical systems or net"ors. The electrical analogy may be used to solve comple problems involving  both series and parallel thermal resistances. The student is referred to *igure 1, sho"ing the equivalent resistance circuit. # typical conduction problem in its analogous electrical form is given in the follo"ing eample, "here the 'electrical' *ourier equation may be "ritten as follo"s.

Figure 3 Equivalent Resistance

5lectrical #nalogy 5ample: # composite protective "all is formed of a - in. copper plate, a -;= in. layer of asbestos, and a 6 in. layer of fiberglass. The thermal conductivities of the materials in units of Btu;hr7ft7o* are as follo"s:  0u  682,  asb  2.28=, and  fib  2.266. The overall temperature difference across the "all is 922C*. 0alculate the thermal resistance of each layer of the "all and the heat transfer rate  per unit area (heat flu) through the composite structure.

0onduction70ylindrical 0oordinates Heat transfer across a rectangular solid is the most direct application of *ouriers la". Heat transfer across a pipe or heat echanger tube "all is more complicated to evaluate. #cross a cylindrical "all, the heat transfer surface area is continually increasing or decreasing. *igure 8 is a cross7sectional vie" of a pipe constructed of a homogeneous material.

Figure 4 Crosssectional Surface !rea of a C"lindrical #i$e

The surface area (#) for transferring heat through the pipe (neglecting the pipe ends) is directly  proportional to the radius (r) of the pipe and the length (+) of the pipe. #  6Dr+ #s the radius increases from the inner "all to the outer "all, the heat transfer area increases. The development of an equation evaluating heat transfer through an obect "ith cylindrical geometry begins "ith *ouriers la" 5quation 679.

*rom the discussion above, it is seen that no simple epression for area is accurate. $either the area of the inner surface nor the area of the outer surface alone can be used in the equation. *or a  problem involving cylindrical geometry, it is necessary to define a log mean cross7sectional area (#lm).

%ubstituting the epression 6Dr+ for area in 5quation 67> allo"s the log mean area to be calculated from the inner and outer radius "ithout first calculating the inner and outer area.

This epression for log mean area can be inserted into 5quation 679, allo"ing us to calculate the heat transfer rate for cylindrical geometries.

5ample: # stainless steel pipe "ith a length of 19 ft has an inner diameter of 2.E6 ft and an outer diameter of -.2= ft. The temperature of the inner surface of the pipe is -66< * and the temperature of the outer surface is --=< *. The thermal conductivity of the stainless steel is -2= Btu;hr7ft7< *. 0alculate the heat transfer rate through the pipe. 0alculate the heat flu at the outer surface of the pipe.

5ample: # -2 ft length of pipe "ith an inner radius of - in and an outer radius of -.69 in has an outer surface temperature of 692< *. The heat transfer rate is 12,222 Btu;hr. *ind the interior surface temperature. #ssume   69 Btu;hr7ft7< *.

The evaluation of heat transfer through a cylindrical "all can be etended to include a composite  body composed of several concentric, cylindrical layers, as sho"n in *igure 9.

Figure % Co&$osite C"lindrical 'a"ers

5ample: # thic7"alled coolant pipe (s  -6.9 Btu;hr7ft7< *) "ith -2 in. inside diameter (I/) and -6 in. outside diameter (&/) is covered "ith a 1 in. layer of asbestos insulation (a  2.-8 Btu;hr7ft7< *) as sho"n in *igure ?. If the inside "all temperature of the pipe is maintained at 992< *, calculate the heat loss per foot of length. The outside temperature is -22< *.

Figure ( #i$e )nsulation #roble&

0onvection Heat Transfer   Heat transfer by the motion and mixing of the molecules of a liquid or gas is called convection.

0onvection 0onvection involves the transfer of heat by the motion and miing of 'macroscopic' portions of a fluid (that is, the flo" of a fluid past a solid boundary). The term natural convection is used if this motion and miing is caused by density variations resulting from temperature differences "ithin the fluid. The term forced convection is used if t his motion and miing is caused by an outside force, such as a pump. The transfer of heat from a hot "ater radiator to a room is an eample of heat transfer by natural convection. The transfer of heat from the surface of a heat echanger to the bul of a fluid being pumped through the heat echanger is an eample of forced convection. Heat transfer by convection is more difficult to analye than heat transfer by conduction because no single property of the heat transfer medium, such as thermal conductivity, can be defined to describe the mechanism. Heat transfer by convection varies from situation to situation (upon the fluid flo" conditions), and it is frequently coupled "ith the mode of fluid flo". In practice, analysis of heat transfer by convection is treated empirically (by direct observation). 0onvection heat transfer is treated empirically because of the factors that affect t he stagnant film thicness: • • • • •

*luid velocity *luid viscosity Heat flu %urface roughness Type of flo" (single7phase;t"o7phase) 0onvection involves the transfer of heat bet"een a surface at a given t emperature (Ts) and fluid at a bul temperature (T b). The eact definition of the bul temperature (T b) varies depending on the details of the situation. *or flo" adacent to a hot or cold surface, Tb is the temperature of the fluid 'far' from the surface. *or boiling or condensation, T b is the saturation temperature of the fluid. *or flo" in a pipe, T b is the average temperature measured at a particular cross7section of the pipe. The basic relationship for heat transfer by convection has the same form as that for heat transfer  by conduction:

The convective heat transfer coefficient (h) is dependent upon the physical properties of the fluid and the physical situation. Typically, the convective heat transfer coefficient for laminar flo" is relatively lo" compared to the convective heat transfer coefficient for turbulent flo". This is due to turbulent flo" having a thinner stagnant fluid film l ayer on the heat transfer surface. Falues of h have been measured and tabulated for the commonly encountered fluids and flo" situations occurring during heat transfer by convection. 5ample: # 66 foot uninsulated steam line crosses a room. The outer diameter of the steam line is -= in. and the outer surface temperature is 6=2< *. The convective heat transfer coefficient for the air is -= Btu;hr7ft67< *. 0alculate the heat transfer rate from the pipe into the room if the room temperature is >6< *.

!any applications involving convective heat transfer tae place "ithin pipes, tubes, or some similar cylindrical device. In such circumstances, the surface area of heat transfer normally given in the convection equation varies as heat passes through the cylinder. In addition, the temperature difference eisting bet"een the inside and the outside of the pipe, as "ell as the temperature differences along the pipe, necessitates the use of some average temperature value in order to analye the problem. This average temperature difference is called the log mean temperature difference (+!T/), described earlier. It is the temperature difference at one end of the heat echanger minus the temperature difference at the other end of the heat echanger, divided by the natural logarithm of the ratio of these t"o temperature differences. The above definition for +!T/ involves t"o important assumptions:

(-) the fluid specific heats do not vary significantly "ith temperature, and (6) the convection heat transfer coefficients are relatively constant throughout the heat echanger.

&verall Heat Transfer 0oefficient !any of the heat transfer processes encountered in nuclear facilities involve a combination of  both conduction and convection. *or eample, heat transfer in a steam generator involves convection from the bul of the reactor coolant to the steam generator inner tube surface, conduction through the tube "all, and convection from the outer tube surface to the secondary side fluid. In cases of combined heat transfer for a heat echanger, there are t"o values for h. There is the convective heat transfer coefficient (h) for the fluid film inside the tubes and a convective heat transfer coefficient for the fluid film outside the tubes. The thermal conductivity () and thicness (A) of the tube "all must also be accounted for. #n additional term (U o), called the overall heat transfer coefficient, must be used instead. It is common practice to relate the total rate of heat transfer to the cross7sectional area for heat transfer (# o) and the overall heat transfer coefficient (Uo). The relationship of the overall heat transfer coefficient to the individual conduction and convection terms is sho"n in *igure >.

Figure * +verall Heat Transfer Coefficient

4ecalling 5quation 671:

"here Uo is defined in *igure =. #n eample of this concept applied to cylindrical geometry is illustrated by *igure =, "hich sho"s a typical combined heat transfer situation.

Figure , Co&bined Heat Transfer Using the figure representing flo" in a pipe, heat transfer by convection occurs bet"een temperatures T- and T6G heat transfer by conduction occurs bet"een temperatures T 6 and T1G and heat transfer occurs by convection bet"een temperatures T 1 and T8. Thus, there are three  processes involved. 5ach has an associated heat transfer coefficient, cross7sectional area for heat transfer, and temperature difference. The basic relationships for these three processes can be epressed using 5quations 679 and 67E.

ATo can be epressed as the sum of the AT of the three individual processes.

If the basic relationship for each process is solved for its associated temperature difference and substituted into the epression for AT o above, the follo"ing relationship results.

This relationship can be modified by selecting a reference cross7sectional area # o.

5quation 67-2 for the overall heat transfer coefficient in cylindrical geometry is relatively difficult to "or "ith. The equation can be simplified "ithout losing much accuracy if the tube that is being analyed is thin7"alled, that is the tube "all thicness is small compared to the tube diameter. *or a thin7"alled tube, the inner surface area (# -), outer surface area (# 6), and log mean surface area (# -m), are all very close to being equal. #ssuming that #-, #6, and #-m are equal to each other and also equal to # o allo"s us to cancel out all the area terms in the denominator of 5quation 67--. This results in a much simpler epression that is similar to the one developed for a flat plate heat echanger in *igure >.

The convection heat transfer process is strongly dependent upon the properties of the fluid being considered. 0orrespondingly, the convective heat transfer coefficient (h), the overall coefficient (Uo), and the other fluid properties may vary substantially for the fluid if it eperiences a large temperature change during its path through the convective heat transfer device. This is especially true if the fluids properties are strongly temperature dependent. Under such circumstances, the temperature at "hich the properties are 'looed7up' must be some type of average value, rather than using either the inlet or outlet temperature value. *or internal flo", the bul or average value of temperature is obtained analytically through the use of conservation of energy. *or eternal flo", an average film temperature is normally calculated, "hich is an average of the free stream temperature and the solid surface temperature. In any case, an average value of temperature is used to obtain the fluid properties to be used in the heat transfer problem. The follo"ing eample sho"s the use of such principles by solving a convective heat transfer problem in "hich the bul temperature is calculated. 5ample: # flat "all is eposed to the environment. The "all is covered "ith a layer of insulation - in. thic "hose thermal conductivity is 2.= Btu;hr7ft7< *. The temperature of the "all on the inside of the insulation is ?22< *. The "all loses heat to the environment by convection on the surface of the insulation. The average value of the convection heat transfer coefficient on the insulation

surface is E92 Btu;hr7ft67< *. 0ompute the bul temperature of the environment (T b) if the outer surface of the insulation does not eceed -29< *. %olution:

Heat 5changers  Heat exchangers are devices that are used to transfer thermal energy from one fluid to another without mixing the two fluids. The transfer of thermal energy bet"een fluids is one of the most important and frequently used  processes in engineering. The transfer of heat is usually accomplished by means of a device no"n as a heat echanger. 0ommon applications of heat echangers in an industrial facility include boilers, fan coolers, cooling "ater heat echangers, and condensers.

The basic design of a heat echanger normally has t"o fluids of different temperatures separated  by some conducting medium. The most common design has one fluid flo"ing through metal tubes and the other fluid flo"ing around the tubes. &n either side of the tube, heat is transferred  by convection. Heat is transferred through the tube "all by conduction. Heat echangers may be divided into several categories or classifications. In the most commonly used type of heat echanger, t"o fluids of different temperature flo" in spaces separated by a tube "all. They transfer heat by convection and by conduction through the "all. This type is referred to as an 'ordinary heat echanger,' as compared to the other t"o types classified as 'regenerators' and 'cooling to"ers.' #n ordinary heat echanger is single7phase or t"o7phase. In a single7phase heat echanger, both of the fluids (cooled and heated) remain in their initial gaseous or liquid states. In t"o7phase echangers, either of the fluids may change its phase during the heat echange process. The steam generator and main condenser are of the t"o7phase, ordinary heat echanger classification. %ingle7phase heat echangers are usually of the tube7and7shell typeG that is, the echanger consists of a set of tubes in a container called a shell (*igure E). #t the ends of the heat echanger, the tube7side fluid is separated from the shell7side fluid by a tube sheet. The design of t"o7phase echangers is essentially the same as that of single7phase echangers.

Figure - T"$ical Tube and Shell Heat E.changer

arallel and 0ounter7*lo" /esigns #lthough ordinary heat echangers may be etremely different in design and construction and may be of the single7 or t"o7phase type, their modes of operation and effectiveness are largely determined by the direction of the fluid flo" "ithin the echanger. The most common arrangements for flo" paths "ithin a heat echanger are counter7flo" and  parallel flo". # counter7flo" heat echanger is one in "hich the direction of the flo" of one of

the "oring fluids is opposite to the direction to the flo" of the other fluid. In a parallel flo" echanger, both fluids in the heat echanger flo" in the same direction. *igure -2 represents the directions of fluid flo" in the parallel and counter7flo" echangers. Under comparable conditions, more heat is transferred in a counter7flo" arrangement than in a  parallel flo" heat echanger.

Figure 1/ Fluid Flo0 irection The temperature profiles of the t"o heat echangers indicate t"o maor disadvantages in the  parallel7flo" design. *irst, the large temperature difference at the ends (*igure --) causes large thermal stresses. The opposing epansion and contraction of the construction materials due to diverse fluid temperatures can lead to eventual material failure. %econd, the temperature of the cold fluid eiting the heat echanger never eceeds the lo"est temperature of the hot fluid. This relationship is a distinct disadvantage if the design purpose is to raise the temperature of the cold fluid.

Figure 11 Heat E.changer Te&$erature #rofiles The design of a parallel flo" heat echanger is advantageous "hen t"o fluids are required to be  brought to nearly the same temperature. The counter7flo" heat echanger has three significant advantages over the parallel flo" design. *irst, the more uniform temperature difference bet"een the t"o fluids minimies the thermal stresses throughout the echanger. %econd, the outlet temperature of the cold fluid can approach the highest temperature of the hot fluid (the inlet temperature). Third, the more uniform temperature difference produces a more uniform rate of heat transfer throughout the heat echanger.

hether parallel or counter7flo", heat transfer "ithin the heat echanger involves both conduction and convection. &ne fluid (hot) convectively transfers heat to the tube "all "here conduction taes place across the tube to the opposite "all. The heat i s then convectively transferred to the second fluid. Because this process taes place over the entire l ength of the echanger, the temperature of the fluids as they flo" through the echanger is not generally constant, but varies over the entire length, as indicated in *igure --. The rate of heat transfer varies along the length of the echanger tubes because its value depends upon the temperature difference bet"een the hot and the cold fluid at the point being vie"ed.

 $on74egenerative Heat 5changer  #pplications of heat echangers may be classified as either regenerative or non7regenerative. The non7regenerative application is the most frequent and involves t"o separate fluids. &ne fluid cools or heats the other "ith no interconnection bet"een the t"o fluids. Heat that is removed from the hotter fluid is usually reected to the environment or some other heat sin (*igure -6).

Figure 12 onRegenerative Heat E.changer

4egenerative Heat 5changer  # regenerative heat echanger typically uses the fluid from a different area of the same system for both the hot and cold fluids. The primary coolant to be purified is dra"n out of the primary system, passed through a regenerative heat echanger, non7regenerative heat echanger, demineralier, bac through the regenerative heat echanger, and returned to the primary system (*igure -1). In the regenerative heat echanger, the "ater returning to the primary system is pre7heated by the "ater entering the purification system. This accomplishes t"o obectives. The first is to minimie the thermal stress in the primary system piping due to the cold temperature of the purified coolant  being returned to the primary system. The second is to reduce the temperature of the "ater entering the purification system prior to reaching the non7regenerative heat echanger, allo"ing use of a smaller heat echanger to achieve the desired temperature for purification. The primary advantage of a regenerative heat echanger application is conservation of system energy (that is, less loss of system energy due to the cooling of the fluid).

Figure 13 Regenerative Heat E.changer

0ooling To"ers The typical function of a cooling to"er is to cool the "ater of a steam po"er plant by air that is  brought into direct contact "ith the "ater. The "ater is mied "ith vapor that diffuses from the condensate into the air. The formation of the vapor requires a considerable removal of internal energy from the "aterG the internal energy becomes 'latent heat' of the vapor. Heat and mass echange are coupled in this process, "hich is a steady7state process lie the heat echange in the ordinary heat echanger. ooden cooling to"ers are sometimes employed in factories of various industries. They generally consists of large chambers loosely filled "ith trays or similar "ooden elements of construction. The "ater to be cooled is pumped to the top of the to"er "here it is distributed by spray or "ooden troughs. It then falls through the to"er, splashing do"n from dec to dec. #  part of it evaporates into the air that passes through the to"er. The enthalpy needed for the evaporation is taen from the "ater and transferred to the air, "hich is heated "hile the "ater cools. The air flo" is either horiontal due to "ind currents (cross flo") or vertically up"ard in counter7flo" to the falling "ater. The counter7flo" is caused by the chimney effect of the "arm humid air in the to"er or by fans at the bottom (forced draft) or at the top (induced flo") of the to"er. !echanical draft to"ers are more economical to construct and smaller in sie than natural7 convection to"ers of the same cooling capacity.

+og !ean Temperature /ifference #pplication To Heat 5changers In order to solve certain heat echanger problems, a log mean temperature difference (+!T/ or Tlm) must be evaluated before the heat removal from the heat echanger is determined. The follo"ing eample demonstrates such a calculation. 5ample: # liquid7to7liquid counterflo" heat echanger is used as part of an auiliary system at an industrial facility. The heat echanger is used to heat a cold fluid from -62< * to 1-2< *.

#ssuming that the hot fluid enters at 922< * and leaves at 822< *, calculate the +!T/ for the echanger. %olution:

The solution to the heat echanger problem may be simple enough to be represented by a straight7for"ard overall balance or may be so detailed as to require integral calculus. # steam generator, for eample, can be analyed by an overall energy balance from the feed"ater inlet to the steam outlet in "hich the amount of heat transferred can be epressed simply as ṁ Ah, "here ṁ is the mass flo" rate of the secondary coolant and Ah is the change in enthalpy of the fluid. The same steam generator can also be analyed by an energy balance on the primary flo" stream "ith the equation ṁ c p AT "here ṁ, c p, and AT are the mass flo" rate, specific heat capacity, and temperature change of the primary coolant. The heat transfer rate of the st eam generator can also be determined by comparing the temperatures on the primary and secondary sides "ith the heat transfer characteristics of the steam generator using the equation Uo #o ATlm. 0ondensers are also eamples of components found in industrial facilities "here the concept of +!T/ is needed to address certain problems. hen the steam enters the condenser, it gives up its latent heat of vaporiation to the circulating "ater and changes phase to a liquid. Because condensation is taing place, it is appropriate to term this the latent heat of condensation. #fter the steam condenses, the saturated liquid "ill continue to transfer some heat to the circulating "ater system as it continues to fall to the bottom (hot"ell) of the condenser. This continued cooling is called subcooling and is necessary to prevent cavitation in the condensate pumps. The solution to condenser problems is approached in the same manner as those for steam generators, as sho"n in the follo"ing eample.

&verall Heat Transfer 0oefficient hen dealing "ith heat transfer across heat echanger tubes, an overall heat transfer coefficient, Uo, must be calculated. 5arlier in this module "e looed at a method for calculating U o for both rectangular and cylindrical coordinates. %ince the thicness of a condenser tube "all is so small and the cross7sectional area for heat transfer is relatively constant, "e can use 5quation 67-- to calculate Uo.

5ample: 4eferring to the convection section of this manual, calculate the heat rate per foot of tube from a condenser under the follo"ing conditions. T  6165*. The outer lm diameter of the copper condenser tube is 2.>9 in. "ith a "all thicness of 2.- in. #ssume the inner convective heat transfer coefficient is 6222 Btu;hr7ft675*, and the thermal conductivity of copper is 622 Btu;hr7 ft75*. The outer convective heat transfer coefficient is -922 Btu;hr7ft675*.

Heat Transfer Terminology To understand and communicate in the thermal science field, certain terms and expressions must be learned in heat transfer.

Heat and Temperature In describing heat transfer problems, students often mae the mistae of interchangeably using the terms heat and temperature. #ctually, there is a distinct difference bet"een the t"o. Temperature is a measure of the amount of energy possessed by the molecules of a substance. It is a relative measure of ho" hot or cold a substance is and can be used to predict the direction of heat transfer. The symbol for temperature is T. The common scales for measuring temperature are the *ahrenheit, 4anine, 0elsius, and Jelvin temperature scales.  Heat  is energy in transit. The transfer of energy as heat occurs at the molecular level as a result of a temperature difference. Heat is capable of being transmitted through solids and fluids by conduction, through fluids by convection, and through empty space by radiation. The symbol for heat is . 0ommon units for measuring heat are the British Thermal Unit (Btu) in the 5nglish system of units and the calorie in the %I system (International %ystem of Units).

Heat and or  /istinction should also be made bet"een the energy terms heat  and work . Both represent energy in transition. or is the transfer of energy resulting from a force acting through a distance. Heat is energy transferred as the result of a temperature difference. $either heat nor "or are thermodynamic properties of a system. Heat can be transferred into or out of a system and "or can be done on or by a system, but a system cannot contain or store either heat or "or. Heatinto a system and "or out of a system are considered positive quantities. hen a temperature difference eists across a boundary, the %econd +a" of Thermodynamics indicates the natural flo" of energy is from the hotter body to the colder body. The %econd +a" of Thermodynamics denies the possibility of ever completely converting into "or all the heat supplied to a system operating in a cycle. The %econd +a" of Thermodynamics, described by !a lanc in -E21, states that: It is impossible to construct an engine that "ill "or in a complete cycle and produce no other effect ecept the raising of a "eight and the cooling of a reservoir. The second la" says that if you dra" heat from a reservoir to raise a "eight, lo"ering the "eight "ill not generate enough heat to return the reservoir to its original temperature, and eventually the cycle "ill stop. If t"o blocs of metal at different temperatures are thermally insulated from their surroundings and are brought into contact "ith each other the heat "ill flo" from the hotter to the colder. 5ventually the t"o blocs "ill reach the same temperature, and heat transfer "il l cease. 5nergy has not been lost, but instead some energy has been transferred from one bloc to another.

!odes of Transferring Heat Heat is al"ays transferred "hen a temperature difference eists bet"een t"o bodies. There are three basic modes of heat transfer: Conduction involves the transfer of heat by the interactions of atoms or molecules of a material through "hich the heat is being transferred. Convection involves the transfer of heat by the miing and motion of macroscopic portions of a fluid.

 Radiation, or radiant heat transfer, involves the transfer of heat by electromagnetic radiation that arises due to the temperature of a body. The three modes of heat transfer "ill be discussed in greater detail in the subsequent chapters of this module.

Heat *lu The rate at "hich heat is transferred is represented by the symbol 0ommon units for heat transfer rate is Btu;hr. %ometimes it is important to determine the heat transfer rate per unit area, or heat flux, "hich has the symbol Units for heat flu are Btu;hr7ft6. The heat flu can be determined by dividing the heat transfer rate by the area t hrough "hich the heat is being transferred.

Thermal 0onductivity The heat transfer characteristics of a solid material are measured by a property called the thermal conductivity () measured in Btu;hr7ft7 < *. It is a measure of a substances ability to transfer heat through a solid by conduction. The thermal conductivity of most liquids and solids varies "ith temperature. *or vapors, it depends upon pressure.

+og !ean Temperature /ifference In heat echanger applications, the inlet and outlet temperatures are commonly specified based on the fluid in the tubes. The temperature change that taes place across t he heat echanger from the entrance to the eit is not linear. # precise temperature change bet"een t"o fluids across the heat echanger is best represented by the log mean temperature difference (+!T/ or ATlm), defined in 5quation 676.

0onvective Heat Transfer 0oefficient The convective heat transfer coefficient  (h), defines, in part, the heat transfer due to convection. The convective heat transfer coefficient is sometimes referred to as a film coefficient and represents the thermal resistance of a relatively stagnant layer of fluid bet"een a heat transfer surface and the fluid medium. 0ommon units used to measure the convective heat transfer coefficient are Btu;hr 7 ft6 7 < *.

&verall Heat Transfer 0oefficient In the case of combined heat transfer, it is common practice to relate the total rate of heat Transfer

the overall cross7sectional area for heat transfer (#o), and the overall temperature

difference using the overall heat transfer coefficient  (Uo). The overall heat transfercoefficient combines the heat transfer coefficient of the t"o heat echanger fluids and the thermal conductivity of the heat echanger tubes. U o is specific to the heat echanger and the fluids that are used in the heat echanger.

Bul Temperature The fluid temperature (T b), referred to as the bulk temperature, varies according to the details of the situation. *or flo" adacent to a hot or cold surface, T b is the temperature of the fluid that is

'far' from the surface, for instance, the center of the flo" channel. *or boiling or condensation, T b is equal to the saturation temperature.

4adiant Heat Transfer   Radiant heat transfer is thermal energy transferred by means of electromagnetic waves or  particles.

Thermal 4adiation 4adiant heat transfer involves the transfer of heat by electromagnetic radiation that arises due to the temperature of a body. !ost energy of this type is in the infra7red region of the electromagnetic spectrum although some of it is in the visible region. The term thermal radiation is frequently used to distinguish this form of electromagnetic radiation from other forms, such as radio "aves, 7rays, or gamma rays. The transfer of heat from a fireplace across a room in the line of sight is an eample of radiant heat transfer. 4adiant heat transfer does not need a medium, such as air or metal, to tae place. #ny material that has a temperature above absolute ero gives off some radiant energy. hen a cloud covers the sun, both its heat and light diminish. This is one of the most familiar eamples of heat transfer  by thermal radiation.

Blac Body 4adiation # body that emits the maimum amount of heat for its absolute temperature is called a blac  body. 4adiant heat transfer rate from a blac body to its surroundings can be epressed by the follo"ing equation.

T"o blac bodies that radiate to"ard each other have a net heat flu bet"een them. The net flo" rate of heat bet"een them is given by an adaptation of 5quation 67-6.

#ll bodies above absolute ero temperature radiate some heat. The sun and earth both radiate heat to"ard each other. This seems to violate the %econd +a" of Thermodynamics, "hich states that heat cannot flo" from a cold body to a hot body. The parado is resolved by the fact that each  body must be in direct line of sight of the other to receive radiation from it. Therefore, "henever the cool body is radiating heat to the hot body, the hot body must also be radiating heat to the cool body. %ince the hot body radiates more heat (due to its higher temperature) than the cold  body, the net flo" of heat is from hot to cold, and the second la" is still satisfied.

5missivity 4eal obects do not radiate as much heat as a perfect blac body. They radiate less heat than a  blac body and are called gray bodies. To tae into account the fact that real obects are gray  bodies, 5quation 67-6 is modified to be of the follo"ing form.

5missivity is simply a factor by "hich "e multiply the blac body heat transfer to tae into account that the blac body is the ideal case. 5missivity is a dimensionless number and has a maimum value of -.2.

4adiation 0onfiguration *actor  4adiative heat transfer rate bet"een t"o gray bodies can be calculated by the equation stated  belo".

"here: f a  is the shape factor, "hich depends on the spatial arrangement of the t"o obects(dimensionless) f e  is the emissivity factor, "hich depends on the emissivities of both obects (dimensionless) The t"o separate terms f a and f e can be combined and given the symbol f. The heat flo" bet"een t"o gray bodies can no" be determined by the follo"ing equation:

The symbol (f) is a dimensionless factor sometimes called the radiation configuration factor , "hich taes into account the emissivity of both bodies and their relative geometry. The radiation configuration factor is usually found in a tet boo for the given situation. &nce the configuration factor is obtained, the overall net heat flu can be determined. 4adiant heat flu should only be included in a problem "hen it is greater than 623 of the problem. 5ample: 0alculate the radiant heat bet"een the floor (-9 ft  -9 ft) of a furnace and the roof, if the t"o are located -2 ft apart. The floor and roof temperatures are 6222< * and ?22< *, respectively. #ssume that the floor and the roof have blac surfaces. %olution:

Tables from a reference boo, or supplied by the instructor, give:

Calculation of overall heat transfer coefficient

roblem %tatement /etermine the overall heat transfer coefficient KUL for heat transfer occurring from superheated steam in a steel pipe to atmosphere, "ith the follo"ing conditions. ipe nominal sie  =M  pipe schedule  %T/ #verage steam temperature over the pipe length  622 20 #mbient air temperature  6620 heat transfer coefficient on steam side  h %  2.2= ; 20m6 heat transfer coefficient on air side  h #  2.28 ; 20m6 conductivityKL of steel  ?2 ;mJ (at given temperature range)

%olution The sample problem can be solved by follo"ing the steps given here. *irst an equation is developed to determine the overall heat transfer coefficient for this pipe as a function of the individual heat transfer coefficients on both sides as "ell as the conductivity and then the overall heat transfer coefficient is calculated using the developed equation.

%tep4efer to 5ngg0yclopediaLs article about heat transfer coefficients, for relation bet"een heat transfer rate and the individual heat transfer coefficients on inside and outside of the pipe.

  h%N#%N(T%7T-) O steam side heat transfer  (T%7T-)  ;(h%N#%) P (-)   h#N##N(T67T#) O steam side heat transfer  (T#7T6)  ;(h#N##) P (6) *or conductive heat transfer across the pipe "all,

Hence, (T-7T6)   N ln(r 6;r -) ; (6D$) P (1) (-) Q (6) Q (1) gives, (T%7T#)  (T %7T-) Q (T#7T6) Q (T-7T6) (T%7T#)   N (-;h%N#% Q -;h#N## Q ln(r6;r-);6D$) %ince   U#N##N(T%7T#), U#  -;(##;h%#% Q -;h# Q ##ln(r6;r-);6D$) 0onsider unit length of the pipe, i.e. $-m Then, ##  6Dr 6 and #%  6Dr U#  -;(r 6;h%r - Q -;h# Q r 6Nln(r6;r-);) P (8)

%tep6 "here $ is the tube length and KrL stands for tube radius. The subscripts - and 6 stand for inner and outer tube "all respectively. Tube metal conductivity is epressed as KL. *rom 5ngg0yclopediaLs standard piping dimensions calculator, for =M %T/ schedule pipe,  pipe inner diameter  d-  626.>6 mm  2.62 m  pipe outer diameter  d6  6-E.2= mm  2.66 m r -2  2.- m and r 6  2.-- m Using the given data and equation (8), U#  -;(2.--;(2.2=N2.-2) Q -;2.28 Q 2.--Nln(-.-);?2) U#  -;(-1.>9 Q 69 Q 2.222-=) R -;1=.>9 U# 2.26? ; 20m6

%tep1 It should be noted that the terms L-;h%K, L-;h#K and Kr 6Nln(r6;r-);L represent the heat transfer resistance for convection inside and outside the pipe and for conduction across the pipe "all, respectively. %maller magnitude of the heat transfer resistance indicates higher ease of heat transfer.

Thus it can be noted that heat transfer is most easy for conduction across the pipe "all and is represented by a negligible heat transfer resistance value. &n the other hand heat transfer resistance is higher for the convective heat transfer and inversely  proportional to the related heat transfer coefficient. Hence it can be seen that most of the heat transfer resistance is contributed by heat transfer on air side of the pipe, "hich has the lo"est heat transfer coefficient. *inally it can be observed that the overall heat transfer coefficient is lo"er than heat transfer coefficients on both sides of the pipe. This is eplained simply by the definition of the overall heat transfer coefficient "hich associates it "ith the largest temperature difference in the heat transfer system.

F!CT+RR5!'E U-Factor stands for the overall heat transfer coefficient and it is representative of a material’s ability to conduct heat. Similarly to thermal conductance, a higher U-factor value has a higher ability to conduct and transfer heat. U-factor is related to thermal conductance by the following formula.

This equation assumes that U does not vary based on temperature. For purposes of the eam, this is a safe assumption. !-"alue stands for thermal resistance and it is representative of a material’s ability to resist heat. This is opposite of the U-Factor and thermal conductance which are measures of a materials ability to conduct heat. The relationship between the !-"alue, U-Factor and thermal conductance is shown in the following formula.

This equation assumes that ! does not vary based on temperature. For purposes of the eam, this is a safe assumption.

!-values are typically used in the #"$% and !efrigeration field to describe building insulation and materials. For eample, insulation manufacturers provide product data for their various products and the &ey value shown on the product data is the !-"alue based on different thic&nesses.

'otice that the unit !-"alue is ( for )* of insulation. The corresponding !-values for various inches of thic&nesses are found by simply multiplying the thic&ness in inches by the !-value for )* of insulation, refer to the below equation.

 $ must have s&ill for the aspiring professional engineer is to be able to calculate the overall heat transfer coefficient, U-factor for a wall, roof, duct or pipe. The method in which the overall heat transfer coefficient will be described through this wall eample.

+t is important to be able to follow the flow of heat from the beginning to the end of this diagram. ) The first method of heat transfer is convection, warm outdoor air moves across the outer surface of the concrete wall causing the outer surface of the wall to heat up. There would also be radiation loads acting upon the surface of the wall, but for simplicity it is assumed that there are no radiation loads.  'et the heat travels from the outer surface of the concrete wall to the inside surface, / then to the outer surface of the insulation and through the insulation,0 then to the outer surface of the gypsum board and through the board. ( Finally the outer surface of the gypsum board transmits heat both convectively and through radiation to the indoor air.

+n order to find the overall heat transfer coefficient, all of the resistances must be summed. +t is the opinion of the author, that each method of heat transfer should be converted to its equivalent !-"alue in order to &eep it simple.

C+5ECT)+ %onvection is the second mode of heat transfer and is defined as the transfer of heat through the movement of fluids. +n the #"$% and !efrigeration field, convective heat transfer can be found in heating and air conditioning systems, whenever a moving fluid passes over a surface at a different temperature.

1ne of the most common eamples of convection is natural convection in a non-mechanically ventilation2air conditioned building. $s people enter a building, the lights get turned on and the sun heats the building, the air in the building begins to get warmer. The warm air is less dense than the air around it and begins to rise up and out of the building. The empty space left by the warm air is then replaced by cooler outside air and the cycle continues. This convective heat transfer through the movement of air is called natural convection. +t is referred to as natural because it does not rely on a mechanical source li&e a fan to move the air.

%onvective heat transfer has a similar equation to conductive heat transfer, ecept the U-Factor or !-"alue is replaced with the convective heat transfer coefficient. This convective heat transfer coefficient characteri3es the moving fluid by ta&ing into account its viscosity, thermal

conductance, temperature, velocity and it also characteri3es the surface that the fluid is moving upon.

C++')6 '+!  B!S)CS %ooling load calculations are typically one of the first calculations completed by the #"$% and !efrigeration engineer. These calculations serve as the basis for determining air conditioning equipment si3es. +n order to determine the mechanical equipment si3es, the engineer must first determine what heat is being transferred into the building and what heat is being transferred out of the building. The summation of the heat gained and lost by the building will determine the si3e of the air conditioning equipment.

The various heat gains and losses into a building can be characteri3ed as either eternal or internal loads. 4ternal loads include the conduction and radiation heat loads transferred through roofs, walls, s&ylights and windows. +n addition, outside air can be brought into a building through ventilation requirements or infiltration, which will cause a load upon the system. +nternal loads include heat loads from people, both latent and sensible, loads from lighting and miscellaneous equipment li&e computers, televisions, motors, etc.

The various heat gains can also be organi3ed into sensible and latent heat gains. Sensible heat gains are those characteri3ed by only a change in temperature and no change in state. 5atent heat gains are those characteri3ed by moisture gains. +t is important to note that in the table below, that ventilation, infiltration, people and miscellaneous equipment both have sensible and latent heat gains. These individual heat gains are discussed thoroughly in the following sections.

THERMAL MASS and TIME LAG FACTOR

6hen completing load calculations it is important to understand the time lag factor. 6hen the sun shines upon a wall face early in the morning, although the wall does eperience a heat load, the amount of heat load eperienced +' the building at that time is minimal. This is due to the thermal mass of the wall. Thermal mass is also &nown as heat capacity and is defined as the ability of a material to absorb heat.

The use of thermal mass is shown in buildings that have high thermal mass walls that absorb heat during the day, store the heat during occupied periods and release the heat during the night when it is cool.

UNCERTAINTY

%alculating heat gains and determining cooling loads has very high uncertainty. This is because of the many assumptions that must be made li&e occupant loads, occupant, schedules, outdoor weather conditions, equipment schedules and heat gains, etc. The engineer should recogni3e that the following calculations are not the most accurate ways to calculate cooling load and are only shown to highlight concepts that could be tested on the professional engineering eam. There are multiple methods used to calculate cooling load calculations li&e the !adiant Time Series, Total 4quivalent Time 7ifference and the %5T72S%52%5F methods. The %5T72S%52%5F method is shown in this section because it is the most practical method that can be tested without a computer and in a relatively short period of time 0-hours, 8 minutes per problem http922www.engproguides.com2coolingbasics.html

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