K13THT Laboratory Guide

Architectural Environmental Engineering Topics of Heat Transfer (K13THT) Laboratory Measurement of the Heat transfer Coefficient and Nusselt Number using G.U.N.T WL314 Heat Transfer Bench

Prepared by Siegfried Yeboah

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Table of Contents Introduction........................................................................................................................................................................................................ 3 Safety Symbols................................................................................................................................................................................................... 3 Important Safety Information ..................................................................................................................................................................... 3 Aim ......................................................................................................................................................................................................................... 3 Objectives ............................................................................................................................................................................................................ 4 Theory ................................................................................................................................................................................................................... 4 Apparatus ............................................................................................................................................................................................................ 8 Experimental ................................................................................................................................................................................................... 10 Procedure ......................................................................................................................................................................................................... 10 Results and Calculations............................................................................................................................................................................. 11 Discussion and Conclusion ........................................................................................................................................................................ 12 Assessment Criteria...................................................................................................................................................................................... 12 References ........................................................................................................................................................................................................ 12

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Introduction Our present standard of living is made possible by the energy available in the form of heat from various sources like fuels. The process by which this energy is converted for everyday use is studied under thermodynamics, leaving out the rate at which the energy is transferred. In all applications, the rate at which energy is transferred as heat, plays an important role. The design of all equipment involving heat transfer require the estimate of the rate of heat transfer. The driving potential or the force which causes the transfer of energy as heat is the difference in temperature between systems. In addition to the temperature difference, physical parameters like geometry, material properties like conductivity, flow parameters like flow velocity also influence the rate of heat transfer.

Safety Symbols

Important Safety Information A key requirement in the use of ALL UNNC laboratories is the use of Personal Protective Equipment (PPE). Students for this laboratory session should ensure they have the following on whilst in the laboratory: 

Laboratory Coat (Student should bring their own along)



Fully covered shoes(Student should ensure)



Safety glasses (provided in lab)



Gloves (provided in lab)



Protective ear muffs (provided in lab)

Those with long hair are expected to tie it for health and safety reasons (so bring a hair band if you need one).

Aim To investigate the convective heat transfer phenomena of a flowing medium on tube banks. Page 3 of 12 Prepared by Siegfried Yeboah

Objectives 

To measure the Heat Transfer Coefficient and Nusselt number using G.U.N.T WL314 Heat Transfer Bench



To become familiar with the complex area of convective heat transfer with its many variants.

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To develop skills in analysis and academic report writing

Theory Conduction is the mode of heat transfer due to temperature difference within a body or between bodies in thermal contact without the involvement of mass flow and mixing. This is the mode of heat transfer through solid barriers and is encountered extensively in heat transfer equipment design as well as in heating and cooling of various materials as in the case of heat treatment. The rate equation in this mode is based on Fourier’s law of heat conduction which states that the heat flow by conduction in any direction is proportional to the temperature gradient and area perpendicular to the flow direction and is in the direction of the negative gradient. The proportionality constant obtained in the relation is known as thermal conductivity, k, of the material. Heat flow, Q = −kA

𝑑𝑇 𝑑𝑥

The integration of the equation for a plane wall of thickness, L between the two surfaces at temperatures 𝑇1 𝑎𝑛𝑑 𝑇2 under steady condition leads to Q=

𝑇1 − 𝑇2 (𝐿⁄𝑘𝐴)

Fig. 1 Conduction, Plane Wall Convection heat transfer occurs where energy is transferred as heat to a flowing fluid at the surface over which the flow occurs. This mode is basically conduction in a very thin fluid layer at the surface and then mixing caused by the flow (Fig. 2a&b). The energy transfer is by combined molecular diffusion and bulk flow. The heat flow is Page 4 of 12 Prepared by Siegfried Yeboah

independent of the properties of the material of the surface and depends only on the fluid properties. However the shape and nature of the surface will influence the flow and hence the heat transfer. Convection is not a pure mode as conduction or radiation and hence involves several parameters. If the flow is caused by external means like a fan or pump, then the mode is known as forced convection. If the flow is due to the buoyant forces caused by temperature difference in the fluid body, then the mode is known as free or natural convection. In most applications heat is transferred from one fluid to another separated by a solid surface. So heat is transferred from the hot fluid to the surface and then from the surface to the cold fluid by convection. The rate equation is due to Newton’s law of cooling called convective heat transfer coefficient (h) as given in equation Heat flow, Q = hA(𝑇1 − 𝑇2 )

Fig. 2a. Analogy for Convection Heat Transfer 2b. Conduction Nusselt Number: Due to the large number of heat exchanger shapes and conditions, the thickness of the thermal boundary layer would need to be determined in each case. Applying similitude theory a dimensionless number, the Nusselt number, can be developed that takes into account the thermodynamic and fluid mechanic related conditions. Nu = h ∙

𝑥 𝑘

Here 𝑥 is a length similar to that for the Reynolds’ number (Re). For a single body in a flow, a flow length L’ is defined. For a plate in a flow, this is the same as the length of the plate 𝐿′ = L For a cylinder or pipe in a transverse flow, this is equal to half the circumference:

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𝐿′ = d ∙

𝜋 2

This yields for the Nusselt number 𝐿′ Nu = h ∙ 𝑘 The Nusselt number can be calculated from the Reynolds’ and Prandtl number. The Reynolds’ number represents the flow state (laminar-turbulent) Re =

𝑐 ∙ 𝐿′ 𝜈

The velocity can then be determined with the aid of the density, 𝜌;

𝑐 = √2 ∙

∆𝑃 𝜌

The Prandtl number defines the relationship between flow and thermal boundary layer. 𝑃𝑟 =

𝜈 𝜈 = 𝑐𝑝 ∙ 𝛼 𝑘

As both are material properties, the Prandtl number is often given directly. For gases the Prandtl number is in the range around 1 while for liquids it is around 10. For the cylinder in a transverse flow, the Nusselt number can be given as follows: 𝐿𝑎𝑚𝑖𝑛𝑎𝑟(1 > 𝑅𝑒 > 103 ) 𝑁𝑢𝑙𝑎𝑚 = 0.644 ∙ √𝑅𝑒 ∙ 𝑃𝑟 0.33 𝑇𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡 (105 < 𝑅𝑒 < 107 ) 𝑁𝑢𝑡𝑢𝑟𝑏 = 0.037 ∙ 𝑅𝑒 0.8 ∙ 𝑃𝑟 0.48 For transition turbulent area(103 < 𝑅𝑒 < 105 ) a geometric mean from 𝑁𝑢𝑡𝑢𝑟𝑏 and 𝑁𝑢𝑙𝑎𝑚 is formed 𝑇𝑎𝑖𝑟 0.12 𝑁𝑢 = (0.3 + √𝑁𝑢𝑡𝑢𝑟𝑏 2 + 𝑁𝑢𝑙𝑎𝑚 2 ) ∙ ( ) 𝑇𝑤 The temperature dependence is taken into account by a correction factor with the quotients of the Kelvin temperatures of the air 𝑇𝑎𝑖𝑟 and wall 𝑇𝑤 . In an experiment on the dependence of the Nusselt number on the Reynolds’ number, a profile per is shown in Fig 3.

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Fig. 3. Nusselt number versus Reynolds’ number The dimensionless ratio of the Nu⁄𝑅𝑒𝑃𝑟 is known as the Stanton number St. This allows the determination of the heat transfer coefficient for fluids with 𝑃𝑟 ≈ 1from a friction coefficient. Where 

c is the flow velocity



𝜈 is the kinematic viscosity.



L’ again reflects a characteristic length.

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𝛼 is the thermal diffusivity (m2/s)

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Apparatus

Fig. 4. Layout of the Heat Transfer Bench

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Fig. 5 Switch Cabinet

Fig.6 Barometer Page 9 of 12 Prepared by Siegfried Yeboah

Experimental The individual heater is inserted in the duct above the fan as shown in Fig. 7. The temperature of the air is measured at bottom of the duct below the fan. It is assumed that the temperature of the air is only changed slightly by the fan.

Fig. 7. Measurement at Individual Heaters

Procedure 1. Switch on fan using pushbutton (21). 2. The flow rate can be regulated using the adjusting flap (9). 3. Check pressure display for velocity measurement. 4. Displays (17, 20) at the switch cabinet must indicate the current temperatures. 5. Switch on heater (22). The temperature of the heater must increase. 6. The heater power can be adjusted using adjusting knob (24). 7. The heater power is displayed on the digital display (16). 8. The measurement can be started when the temperature no longer changes. 9. Record the results as shown on Table 1. 10. Repeat the experiment for different power inputs.

Pressure Measurement 1. Connect one end of a tube to the measuring connection in Figure 6 to measure the static pressure at the measuring point is measured. 2. Connect another tube, one end to the measuring connection of the Pitot tube and the other to the manometer to measure the total pressure. 3. To obtain a pressure profile, move the Pitot tube across the entire cross-section.

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Figure 6 Measuring the Pressure NOTE 

A complete experimental series with recording of measured values requires a large amount of time, as it is necessary to wait for a steady-state condition for each point measured.

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Approx. five minutes should be planned for the measurement of a point. For this reason the experiment should be carefully planned to avoid unnecessary delays.

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The temperature cut-out shuts down the heater element at approx. 85°C.

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Ensure you take all other relevant data such as the dimensions of the heat exchanger etc.

Table. 1. Table of Results Parameter

Value

Unit

Pressure at the flow nozzle ∆p

Pa

Air temperature, 𝑇𝑎𝑖𝑟

°C

Heater surface temperature 𝑇ℎ𝑒𝑎𝑡

°C

Electrical heater power, 𝑃𝑒𝑙

W

Results and Calculations 1. Determine the experimental and numerical coefficient of heat transfer 2. Determine the flow type 3. Calculate the experimental and numerical Nusselt number for the flow 4. Plot the relationship between the following Page 11 of 12 Prepared by Siegfried Yeboah

a. Re and Nu (both experimental and numerical) b. Re and St (both experimental and numerical) c. Re and Pr (both experimental and numerical) 5. Provide table of results for the experimental and numerical data

Discussion and Conclusion 1. Compare and discuss the numerical and the experimental coefficient of heat transfer determined 2. Analyse the relationship between the following 

Nu and Re (both experimental and numerical)

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St and Re (both experimental and numerical)

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Re and Pr (both experimental and numerical)

3. Discuss key findings of the experimental and numerical tasks 4. Discuss any possible sources of errors in your results and how they could be corrected. 5. Provide a concluding summary of key findings

Assessment Criteria Abstract

[5%]

Introduction

[5%]

Methodology

[10%]

Results and Calculation

[40%]

Discussion and Conclusion (Word Limit - 1500)

[30%]

Presentation and Communication

[5%]

References

[5%]

References 

Kothandaraman, C.P. Fundamentals of Heat and Mass Transfer (3). Daryaganj, IN: New Age International, 2006. ProQuest ebrary. Web. 9 October 2016. Copyright © 2006. New Age International. All rights reserved.



Kreith, Frank. Manglik, Raj. M. and Bohn, Mark. S. (2011) Principles of Heat Transfer. 7th Edition. CENGAGE Learning.



Cengal, Yunus. A. and Ghajar, Afshin. J. (2011) Heat and Mass Transfer: Fundamental Applications. McGraw Hill.

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