January 9, 2018 | Author: Narayana Swamy G | Category: Heat Transfer, Thermal Conduction, Thermal Conductivity, Convection, Solid
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MEL242 HEAT AND MASS TRANSFER Prabal Talukdar Associate Professor Department p of Mechanical Engineering g g IIT Delhi [email protected]


Course Coordinator: Dr. Prabal Talukdar Room No: III, 368 E-mail: [email protected] Course webpage: http://web.iitd.ac.in/~prabal/courses.html Pre-requisite: Fluid Mechanics (AML 160)

Lectures: Tue, Wed, Fri: 9-9.50 a.m. (Room No: IV LT1) Tut: 1-1.50 p.m. (Tentative Room no: III352

MEL 242: Heat and Mass Transfer (3-1-0) •Syllabus (for total 42 lectures) Introduction and basics of to heat transfer: Modes of heat transfer, Fourier’s law, conductivity, diffusivity. Heat conduction equation: q 1D Heat conduction,, General heat conduction equation, q , Boundary y and initial conditions, Heat generation. Steady heat conduction: Heat conduction in plane wall, cylinder, sphere, network analysis, critical radius of insulation, heat transfer from fins. Transient heat conduction: Lumped system analysis, transient heat conduction in large plane walls, long cylinders li d and d spheres h with ith spatial ti l effect, ff t Heisler H i l and d Grober G b charts h t Numerical methods of heat conduction: Finite difference formulation, numerical methods for 1D and 2D steady state heat conduction. (≈ 10 lectures) Introduction to convection: Fundamentals, Velocity and thermal boundary layer, laminar, turbulent flows, conservation equations for mass, momentum and energy, solution of boundary layer equations, Analogy between heat and momentum transfer, Non-dimensional numbers External heat transfer: Drag and heat transfer, parallel flow over flat plates, flow across cylinders and spheres Internal heat transfer: Mean velocity and mean temperature, entrance region, constant heat flux and temperature condition in pipe flow, flow Hagen–Poiseuille Hagen Poiseuille flow, flow Turbulent flow and heat transfer Natural/free convection: Equation of motion of Grashof number, natural convection over surfaces and inside enclosures (≈ 13 lectures)

Boiling and condensation: Boiling heat transfer, pool boiling, flow boiling, condensation heat transfer, film condensation, heat transfer correlations. ((≈ 4 lectures) Heat Exchangers: Types of heat exchangers, overall heat transfer coefficient, analysis of heat exchangers, the log mean temperature method, ε-NTU method. (≈ 4 lectures) Introduction to radiation: Fundamentals, radiative properties of opaque surfaces, Intensity, emissive power, radiosity, di i Planck’s Pl k’ law, l Wien’s Wi ’ displacement di l law, l Black Bl k andd Gray G surfaces, f Emissivity, E i i i absorptivity, b i i Spectral S l andd directional variations, Stephan Boltzmann law, Kirchhoff’s law View factors: Definitions and relations, radiation heat transfer between two black surfaces, between diffuse gray surfaces, network method above two surfaces, re-radiating surface, radiation shield, radiation effects on temperature p measurements. (≈ 7 lectures) Mass Transfer: Introduction, analogy between heat and mass transfer, mass diffusion, Fick’s Law, boundary conditions, steady mass diffusion through a wall, cylinder and sphere, water vapour migration in buildings, transient mass diffusion, mass transfer in a moving medium, diffusion of vapor through a stationary gas: Stefan Flow (≈ 4 lectures) Evaluation: Tuts and Quiz (2 nos): 20% (Closed note, book) Minor Test I: 20% (Open note, note closed book) Minor Test II: 25% (Open note, closed book) Major Test: 35% (Open note, closed book) Total: 100% Textbook: Fundamental of Heat and Mass Transfer: F. P. Incropera and D. P. Dewitt Heat Transfer: Yunus A. Cengel Heat Transfer: J.P. Holmann


Quiz Tentative Date

Quiz 1 August 27

Quiz 2 November 5

Heat Transfer as a Course • Has a “reputation” for being one of the most challenging, fundamental, conceptual courses in ME. It is the “heart” of thermal h l engineering i i • Why?? – Physically diverse: thermodynamics, thermodynamics material science science, diffusion theory, fluid mechanics, radiation theory – Higher-level math: vector calculus, ODEs, PDEs, numerical methods – Physically elusive: heat is invisible; developing intuition takes time – Appropriate assumptions: required i d to simplify i lif andd solve l most problems

• However, Heat Transfer is interesting, fun, and readily applicable to the real world P.TALUKDAR/IITD

Heat Transfer Applications • Heat transfer is commonly encountered in engineering systems and other aspects of life, and one does not need to go very far to see some application areas of heat transfer. transfer


Human body y


Heat Transfer - Thermodynamics y • Thermodynamics is concerned with the amount of heat transfer as a system y undergoes g a process p from one equilibrium q state to another, and it gives no indication about how long the process will take. • A thermodynamic analysis simply tells us how much heat must be transferred to realize a specified change of state to satisfy the conservation of energy principle. We are normally interested in how long it takes for the hot coffee in a thermos to cool to a certain temperature, which cannot be determined from a thermodynamic analysis alone alone.

• Determining the rates of heat transfer to or from a system and thus the times of cooling or heating, heating as well as the variation of the temperature, is the subject of heat transfer P.TALUKDAR/IITD

Definition • Heat transfer is energy transfer due to a temperature difference in a medium or between two or more media • Different types of heat transfer processes are called different modes of heat transfer • Conduction heat transfer is due to a temperature gradient in a stationary medium or media • Convection heat transfer occurs between a surface and a moving fluid at different temperatures • Radiation heat transfer occurs due to emission of energy in the f form off ele electromagnetic t eti waves e by b all ll bodies b die above b e absolute b l te zero e temperature – Net radiation heat transfer occurs when there exists a temperature difference between two or more surfaces emitting radiation energy P.TALUKDAR/IITD

Conduction • Conduction heat transfer is due to random molecular and atomic vibrational, rotational and translational motions – High temperature and more energetic molecules vibrate more and transfer energy to less energetic particles as a result of molecular collisions or interactions

• The heat flux (a vector)

& ′′ (W / m2) Q x

is characterized by a transport property know as the – Thermal Conductivity, y k ((W / m · K)) – W = watts


m = Meters

K = temperature in Kelvin

• Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles. • Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons • The rate of heat conduction through a medium depends on the geometry of the medium, its thickness, and the material of the medium, as well as the temperature difference across the medium


Fourier’s Law T2 − T1 ΔT & = − kA Q cond = − kA Δx Δx


• In the limiting case of x →0, the equation above reduces to the differential form Fourier’s law of heat

dT & Q cond = −kA dx


• The negative sign ensures that heat transfer in the positive x direction is a positive quantity


conduction after J. Fourier, who expressed it first in his heat transfer text in 1822 T1=

T2 =

Thermal Conductivity y • Specific heat Cp is a measure of a material’s ability to store thermal energy. gy For example, p , Cp = 4.18 kJ/kg·°C g for water and Cp = 0.45 kJ/kg·°C for iron at room temperature, which indicates that water can store almost 10 times the energy that iron can per unit mass. • Likewise Likewise, the thermal conductivity k is a measure of a material material’ss ability to conduct heat. For example, k = 0.608 W/m·°C for water and k = 80.2 W/m·°C for iron at room temperature, which indicates that iron conducts cond cts heat more than 100 times faster than water ater can. can • Thus water is a poor heat conductor relative to iron, although water is an excellent medium to store thermal energy


Range g of Thermal Conductivity y • The thermal conductivities of gases such as air vary by a factor of 104 from those of pure metals such as copper. • Note that pure crystals and metals have the highest thermal conductivities and gases and conductivities, insulating materials the lowest.


A simple experimental setup to determine the thermal conductivity of a material material.


The range of thermal conductivity of various materials at room temperature


• The thermal conductivity of a substance is normally highest in the solid phase and lowest in the gas phase. • Unlike gases, the thermal conductivities of most liquids li id decrease d with i h increasing i i temperature, with water being a notable exception. • In solids, heat conduction is due to two effects: the lattice vibrational waves induced by tthee vvibrational b at o a motions ot o s oof tthee molecules o ecu es positioned at relatively fixed positions in a periodic manner called a lattice, and the energy transported via the free flow of electrons in the solid . The thermal conductivity of a solid is obtained by adding the lattice and electronic components. components The relatively high thermal conductivities of pure metals are primarily due to the electronic component. P.TALUKDAR/IITD

• The lattice component of thermal conductivity strongly depends on the way the molecules are arranged • Unlike metals, which are good electrical and heat conductors, crystalline lli solids lid suchh as diamond di d andd semiconductors i d suchh as silicon are good heat conductors but poor electrical conductors. As a result, such materials find widespread use in the electronics industry. For example, diamond, which is a highly ordered crystalline solid, has the highest known thermal conductivity at room temperature.

Even small amounts in a pure metal of “foreign” molecules that are good conductors themselves seriously i l disrupt di t the th flow fl off heat h t iin that th t metal. t l For example, the thermal conductivity of steel containing just 1 percent of chrome is 62 W/m·°C, while the thermal conductivities of iron and chromium are 83 and 95 W/m·°C, P.TALUKDAR/IITD

• The variation of the thermal conductivity of various solids, liquids and gases liquids, with temperature (from White)


Thermal Diffusivity y • The product ρCp, which is frequently encountered in heat transfer y is called the heat capacity p y of a material. Both the analysis, specific heat Cp and the heat capacity ρCp represent the heat storage capability of a material. •

But Cp expresses it per unit mass whereas ρCp expresses it per unit volume, as can be noticed from their units J/kg·°C and J/m3·°C, respectively.

• Another material property that appears in the transient heat conduction analysis is the thermal diffusivity, which represents how fast heat diffuses through a material and is defined as


The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of tthermal e a d diffusivity us v ty means ea s tthat at heat eat is mostly absorbed by the material and a small amount of heat will be conducted further

• Note that the thermal diffusivity ranges from 0.14 x 10-6 m2/s for water to 174 x 10-6 m2/s for silver, which is a difference of more than a thousand times. • Also note that the thermal diffusivities of beef and water are the same. This is not surprising, since meat as well as fresh vegetables and fruits are mostly water, water and thus they possess the thermal properties of water.


Forced Convection

Natural Convection

B ili Boiling

C d Condensation i


Convection • Convection heat transfer involves both energy transfer due to random molecular motions and by bulk motion of the fluid – Convection heat transfer includes both forced convection and natural convection

• IIn convection i heat h transfer, f the h transfer f off heat h is i between b a surface f and a moving fluid (liquid or gas), when they are at different temperatures. The rate of transfer is given by Newton’s Law of Cooling.

q '' = h (Ts − T∞ ) T∞


Moving fluid

Ts Ts > T∞


Typical values of convection h t ttransfer heat f coefficient ffi i t Process

h (W / m2 K)

Free Convection Gases



50 -1000

Forced Convection Gases

35 -250 250


50 -20,000

with Phase Change Boiling or Condensation


2500 -100,000

Radiation • • •

All surfaces of finite temperature emit energy in the form of electromagnetic waves In the absence of an intervening medium, there is a heat transfer by radiation between two surfaces at different temperatures The maximum flux, E (W / m2), at which radiation may be emitted from a bl kb d surface blackbody f is i given i by: b – Stefan Boltzmann Law

E b = σT

4 s

where Eb or E = Surface emissive power (W / m2) T = absolute temperature (K) σ = Stefan-Boltzmann constant = 5.67 x 10-8 (W / m2 ּ◌ K4) P.TALUKDAR/IITD

Eb Ts

• For a real surface:

E = εσTs4 • For a surface with absorptivity p y α,, the incident radiation (G, ( , W/m2) that is absorbed by the surface is given by: Gabs = α ⋅ G

where G = incident radiation (W / m2) T = absolute temperature (K) ε = surface emissivity (0 ≤ ε ≤ 1) α = surface absorptivity (0 ≤ α ≤ 1) P.TALUKDAR/IITD



• For a gray surface α = ε • When radiant energy is incident on a transparent surface, it can be absorbed, reflected, or transmitted through the material. Hence,

G = G absorbed + G transmitted + G reflected = (α + τ + ρ) G α + τ+ρ =1 where

ρ = materials surface reflectivity τ = materials transmissivity


• Consider a small gray surface at temperature Ts that is completely enclosed by the surroundings at temperature Tsur. • The net rate of radiation heat transfer from the surface is: Tsur

' 4 q 'rad = E s − αG sur = εσTs4 − ασTsur

qsur’’ qs’’

' q 'rad =


q 4 = εσTs4 − ασTsur = h r (Ts − Tsur ) A

• Where hr is the radiation heat transfer coefficient, W / m2 K


2 hr = ε ⋅ σ(Ts + Tsur ) Ts2 + Tsur



Conduction example


Convection example Calculate the heat flux from your hand when it is exposed to moving air and water, assuming the surface temperature of your hand is 30°C.


Radiation ex. An instrumentation package has a spherical outer surface of diameter D = 100 mm and emissivity ε = 0.25. 0 25 The package is placed in a large space simulation chamber whose walls are maintained at 77 K. Iff the operation off the electronic components is restricted to the temperature range of 40 ≤ T ≤ 85 85°C, C, what is the range of acceptable power dissipation for the package?


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