Heat and Mass Transfer




3L-0T-1P-0A (10 Credits)



ME 231.

Course content:

Introduction. One-dimensional and Two-dimensional Steady and Transient Conduction. Forced Convection over a flat plate and inside tubes. Natural Convection over a vertical flat plate. Mass Transfer. Boiling and Condensation. Heat Exchangers. Thermal Radiation. Heat Transfer Applications.

Lecture-wise break-up:

I. Introduction: (1 Lecture)

II. Conduction: (11 Lectures)

III. Forced Convection: (9 Lectures)

IV. Natural Convection: (2 Lectures)

V. Mass Transfer: (3 Lectures)

VI. Boiling and Condensation: (3 Lectures)

VII. Heat Exchangers: (3 Lectures)

VIII. Thermal Radiation: (6 Lectures)

IX. Heat Transfer Applications: (2 Lectures)

Laboratory sessions:

I. Pin Fin Apparatus.

II. Unsteady State Heat Conduction.

III. Measurement of Critical Heat Flux in Pool Boiling.

IV. Emissivity Measurement Apparatus.

V. Natural Convection over a Vertical Cylinder.

VI. Calibration of Thermocouples.


  1. Fundamentals of Heat and Mass Transfer by Frank P. Incropera and David P. Dewitt (4th ed.,  John Wiley & Sons, New York, 1998).

  2. Heat Transfer by J.P.Holman (9th ed., Tata McGraw-Hill Edition, New Delhi, 2004).

  3. Heat Transfer by P.S.Ghoshdastidar (Oxford University Press India, New Delhi, 2004).

  4. Heat and Mass Transfer by Yunus A. Cengel (3rd ed., Tata McGraw-Hill Edition, New Delhi, 2007).

  5. Solar Energy by S. P.Sukhatme (2nd ed., Tata McGraw-Hill, New Delhi, 1996).

Sub-total in Conduction: (11 lectures)

Introduction: Definitions of heat and heat transfer.  Difference between heat transfer and thermodynamics.  Basic Modes and Laws of Heat Transfer.  Importance of Convective Heat Transfer Coefficient.  Examples of Heat and Mass Transfer.  Engineering  Applications of Heat Transfer. (1 Lecture)

Conduction: Fourier’s law of heat conduction for homogeneous, isotropic media in Cartesian coordinates and its extension to heterogeneous, isotropic media (differential form). Vectorial form of Fourier’s law for heterogeneous, isotropic continua. Fourier’s law in cylindrical and spherical coordinates. (1 Lecture)

Derivation of heat conduction equation in Cartesian coordinates for heterogeneous, isotropic materials. Heat conduction equation in Cartesian coordinates for homogeneous, isotropic materials (Case of constant thermal conductivity). Significance of thermal diffusivity. Heat conduction equations in cylindrical and spherical coordinates for constant thermal conductivity. Simple One-dimensional Steady Heat Conduction Problems: Plane Wall. Temperature distribution and heat transfer. Concepts of conductive and convective resistances. Conductive and Convective Resistances in Series. (1 Lecture)

Hollow Cylinder: Temperature distribution and heat transfer. Conductive resistance. Composite Cylindrical shell. Hollow Spherical Shell: Temperature distribution and heat transfer. Conductive resistance. Composite Plane Walls: Series Resistance Network. Series-Parallel Resistance Network. (1 Lecture)

Composite Cylindrical Walls. Overall heat transfer coefficient: Expressions for plane wall and cylindrical shell. Critical Thickness of Insulation: Applications to Steam/Hot Water Pipes and Electrical Wires. Basic Concept. Derivation of the expression of critical radius of insulation. Small Pipe and Large Pipe Cases. (1 Lecture)

Heat Generation: Applications. Analysis of Steady 1D heat conduction with heat generation in Plane wall. Temperature distribution and heat transfer. Heat Generation in Solid Cylinder. Heat Generation in Solid Sphere. Extended Surfaces (Fins): Derivation of heat conduction equation for a variable cross-sectional area fins using control system approach. (1 Lecture)

Special case of constant cross-sectional area fins. Case (a): Infinitely long fin; Case (b): Fin of finite length having insulated tip. Temperature distribution and heat transfer. Evaluation of fin performance: Fin efficiency. Fin effectiveness. Relationship between fin effectiveness and fin efficiency. Total efficiency of a finned surface. (1 Lecture)

Difference between 1D and 2D heat conduction in terms of nature of heat flux lines. Steady State Two-dimensional Heat Conduction Problems (with no internal sources): Solution in Cartesian coordinates: Heat conduction in a rectangular bar with Dirichlet Boundary Conditions: Solution by method of separation of variables. The basic methodology. Concept of orthogonal functions and Fourier series. Final series solution. (1 Lecture)

Isotherms and Heat Flux Lines. Method of Superposition. Unsteady State Heat Conduction: Definitions of Lumped and Distributed systems. Definition of Biot number and its physical implication. Biot number limit for lumped system. Lumped System Transients: Derivation of Governing Differential Equation. Solution of T vs. t. Plot of T vs. t as a function of hA/ρcV. Importance of the parameter hA/ρcV. Time constant (or response time). (1 Lecture)

Heisler Charts: Its origin and basic methodology of its use. Multi-dimensional transient conduction problems expressible in terms of one-dimensional ones: 2D Transient Problem in a long rod of rectangular cross-section: Solution in terms of the product of solution of two 1D transient problems-the basis. Use of Heisler Charts in solution of such problems. Extension of this concept to 3D transient conduction in Cartesian coordinates (T(x, y, z, t)) and to finite cylinder (T(r, z, t)). (1 Lecture)

Semi-infinite Solids: Definition. Solution of a semi-infinite body problem when the surface temperature is suddenly changed: Governing equation. Initial and boundary conditions. Temperature Distribution (Error function solution). Calculation of Heat Flux at the Surface (x = 0). Penetration depth: Definition. Expression for penetration depth as a function of time. (1 Lecture)

Sub-total in Forced Convection: (9 lectures)

Forced Convection: Fundamentals. No-slip condition. No Temperature-Jump Condition. Implication of no-slip and no temperature-jump condition: Defining relation for h. Local and average heat transfer coefficients. Nusselt number: Local and average. Its physical significance. Forced convection over a flat plate: Velocity (or Momentum) boundary layer: Laminar, transition and turbulent boundary layers. Velocity or momentum boundary layer thickness, δ. Definition of Reynolds number for a flat plate. Critical Reynolds number. Thermal boundary layer. Thermal boundary layer thickness, δt. Prandtl number: Definition and physical significance. Prandtl number range for various fluids. (1 Lecture)

Momentum Boundary Layer Equations: DefinitiBoundary layer assumptions. Derivation of energy equation in thermal boundary layer. When can viscous dissipation be neglected?. (1 Lecture)

Solution of thermal boundary layer on an isothermal flat plate: Similarity analysis of Pohlhausen. Derivation of correlations for local and average Nusselt numbers as functions of Re and Pr (for Pr > 0.5 fluids). Correlation of Nu = f(Re, Pr) for Liquid Metals (0.001 <= Pr <= 0.01)  for isothermal flat plate. (1 Lecture)

Solution of Thermal Boundary Layer on a flat plate by Integral Analysis of von Karman: Energy Integral. Basic Solution Methodology. Derivation of Nu = f (Re, Pr, L/x) for forced convection on a constant temperature plate with a starting insulated length, L for Pr 0.5 fluids. Integral analysis for Low Pr fluids (Liquid Metals): Eckert’s Correlation. Uniform Heat Flux at the Plate: Nusselt number correlations for laminar flow for Pr fluids. Nu-Correlation for liquid metals for laminar flow. (1 Lecture)

Turbulent Heat Transfer on a Flat Plate: Introduction. Time-averaged Boundary Layer Equations. Eddy diffusivity of momentum and heat. Prandtl’s Mixing Length hypothesis. Wall Friction. (1 Lecture)

Derivation of Reynolds analogy between wall friction and heat transfer. Reynolds-Colburn analogy. Correlation for turbulent heat transfer on a plate at constant temperature (Pr 0.5). Mixed Boundary Layer: Expression for average Nusselt number for constant wall temperature (Pr 0.5). (1 Lecture)

Heat Transfer in Tube Flow: Definition of heat transfer coefficient. Mean Velocity. Mean Temperature. Critical Reynolds number. The entrance regions for laminar flow and heat transfer: Hydrodynamic and thermal entry lengths. Definitions of fully developed velocity and temperature profiles. Expressions for entry lengths. First implication of fully developed temperature profile (Constant wall temperature gradient): Derivation of h = constant in the thermally fully developed region. Comparison of hydrodynamic and thermal entry lengths for Pr = 1, Pr >>1 (Oils), Pr<(1 Lecture)

Derivation of Energy Equation for Tube Flow. Dropping of axial conduction term for ReDPr > 100. Continuity and z-Momentum Equations for fully developed flow. Second implication of fully developed temperature profile (shape invariance with axial distance): Case I: Constant heat flux. Reduced form of energy equation for laminar tube flow. Derivation of NuD = 4.364 for Pr > 0.5 fluids. (1 Lecture)

Constant Wall temperature: Method of solution for derivation of NuD = 3.658 for Pr > 0.5 fluids. Derivation of expression for Tm vs. z. Correlations for laminar flow and heat transfer in tube for liquid metals. Turbulent flow and heat transfer in tube: Dittus-Boelter correlation for Pr > 0.5 fluids. Correlation for liquid metals. (1 Lecture)

Sub-total in Natural Convection: (2 lectures)

Natural Convection: Physical Mechanism. Steady laminar free convection from an isothermal vertical plate: Boussinesq approximation. Derivation of x-momentum equation. Similarity solution of Ostrach(1952): Similarity parameters. Correlations of local and average Nusselt numbers. Concept of Grashof number and Gr/Re2. (1 Lecture)

Eckert’s Integral Analysis (assuming ): Local and Average Nusselt numbers. Expression for boundary layer thickness as a function of x, Grx and Pr. Maximum u-velocity and its location in the boundary layer. Turbulent Processes: Rayleigh number. Experimental correlations for laminar and turbulent flow for constant wall temperature and constant heat flux for a vertical plate. (1 Lecture)

Mass Transfer: Fick’s law of diffusion. Derivation of various forms of equation of continuity for a binary mixture. One-dimensional steady diffusion through a stationary medium. Forced Convection with Mass Transfer over a Flat Plate Laminar Boundary Layer: Heat and Mass Transfer Analogy. Evaporative Cooling. (3 Lectures)

Boiling: Pool Boiling. Saturated Pool Boiling Curve. Rohsenow’s Nucleate boiling correlation. Critical Heat Flux correlation. Minimum heat flux and film boiling correlations.

Condensation: Dropwise and film condensation. Nusselt’s theory of laminar film condensation on a vertical plate. Transition. Turbulent film condensation. (3 Lectures)

Heat Exchangers: Introduction. Classification: Parallel Flow; Counterflow; Single Pass Crossflow. Multipass crossflow. Shell and Tube heat exchangers., Double Pipe heat exchangers. Overall Heat Transfer Coefficient. Fouling Factor. Typical temperature distributions in various types of heat exchangers. Analysis of heat exchangers: Derivation of the expression of LMTD (log mean temperature difference) for a double-pipe counterflow heat exchanger. Multipass and Crossflow heat exchangers: Correction factor approach. Correction factor charts.
Effectiveness-NTU method: Applicability. Definition of effectiveness. Expression for the effectiveness for parallel flow heat exchangers. Physical significance of NTU. Effectiveness-NTU charts for various types of heat exchangers . (3 Lectures)

Sub-total in Thermal Radiation: (6 lectures)

Thermal Radiation: Introduction. Physical Mechanism. Planck’s law. Stefan-Boltzmann law. Wien’s displacement law. Explanation for a change in colour of a body when it is heated. Intensity of Radiation: Total and Spectral. Relation to Irradiation. Relation to Radiosity. (1 Lecture)

Absorptivity, Reflectivity and Transmissivity. Monochromatic(or spectral) and Total Emissivities. Definition of a gray body. Monochromatic(or spectral) and Total Absorptivities. Diffuse and Specular surfaces. Kirchhoff’s law. Restrictions of Kirchhoff’s law. (1 Lecture)

View Factor: Definition. Derivation of View Factor Integral for diffuse surfaces. Reciprocity relationship of view factors. Summation Rule for enclosure. Fii for plane, convex and concave surfaces. (1 Lecture)

Radiation exchange in a black enclosure. Radiation exchange in a gray enclosure. Electric Circuit Analogy: Concept of surface resistance. Reradiating surface. (1 Lecture)

Concept of space resistance. A typical resistance network originating from a surface in an N-surface enclosure. Radiation heat transfer in a three-surface enclosure. (1 Lecture)

Radiation Exchange in two-surface enclosure. Radiation exchange between infinite parallel planes. Radiation exchange between two long concentric cylinders. Radiation loss from a hot object in a large room. Radiation Shields. Radiation heat transfer coefficient. (1 Lecture)

Heat Transfer Applications: 1.Electronics Cooling. 2. Solar Energy. (2 Lectures)