Table Of Content

HEATA NDM ASST RANSFER (SUIN ITS) (For B.E./ B. Tech., I.E.S. and I.A.S. Examinations) (Fifth Edition) R.YADAV B.Sc. Engg., M.E., Ph.D., F.I.E., M.I.S.T.E. Emeritus Professor of Mechanical Engineering MNNIT Allahabad -211004 Former Professor and Head, Mechanical Engineering Department M.N.R.Engineering College (N.ow MNNIT) Allahabad Former Principal, Rl(Tno w NIT) Jamshedpur AND SANJAY B.E. (MECH.) M.E. Assistant Professor of Mechanical Engineering NIT Jamshedpur AND RAJAY B.TECH. (MECH.), Senior Engineer, B.H.E.L., HARDWAR CENTRPAULB LISHHIONUGS E 18C ,S AROJNJANIIDMA UR G ALLAlfA-B2A/D1 001 -- --r- - © COPYRI1G9H9T8 PubialinAsduh tehro r ISB8N2 -85444-38-2 SecRoenvdi Esdeidt1 i9o9n2 ThiRredv iEsdeidtI9 i 9o6n FouRretvhiE sdeidt2 i0o0n1, FifRtehv iEsdeidt 2i0o0n4, Publbi:ysC heendtP ruballi HsohuiAsnlegl, a habad FiguDreessib gynS:eu dGn r apAhlilcash,0a5 3b2a-d2;54945 17546473,7 43 anPdr ibnytH:ea dl cPyroe1ns8 s-S,Ca ,r oNjaiiMndai�r Agl,ta habad !f;!Je'iJ-ictatoth e@lite'iJ-e mm:oy� @!Uy c£ovin9 @/Uothe@/l;in 8 �athe•i - ----- NOMENCLATURE A = Area Ae = Cross Sectional Area As = Surface Area B = Constant b = Width C = Constant, Concentration C = Sound Velocity, Specific Heat D = Diameter, Diffusion Coefficient a = Diameter E = Energy, Emmissive Power F = Shape Factor f = Frequency· h = Heat Transfer Coefficient I = Intensity of Radiation ] = Total Radiation Energy k = Thermal Conductivity L = Length, Thickness m = Mass, Mass Flow Rate N, n = Normal p = Pressure q = Heat Transfer Rate Q = Heat Transfer R = Thermal Resistance s = Length T = Absolute Temperature = Temperature u = Overall Heat Transfer Co�fficient u = Velocity V = Velocity, Voltage, Volume w = Width X,y , Z = Directions PREFACTEO F IFfH REVIS(ESD.E ID.I)T ION In the present edition, a revisi�n has bean made and printing mistakes have been removed. Many figures havl;been replaced for better understanding. I hope this edition will serve better to students appearing for B.E./B.Tech, I.E.S. and i.A.S. Examinations. . - R.YADAV Allahabad SANJAY Godess Swarswati Puja Day, '2004 RAJAY / • I PREFATCOEF IRS(TS EID)I TION Heat and mass transfer processes are the integral parts of the technology and environment. During the recent past, its importance has been recognised and a full course on this topic was introduced in almost all the engineering and technological institutions of the world. Most of the engineering institutions in India and abroad . have switched over from MKS or FPS to SI (System Internationale) system of units and the rest are in the transition stage. Though there are many books availabie on this topic in the international market but there is a scarcity of good books written i:1 SI units covering all the aspects of the subject matter. This book has been written to fill this gap. This book will suit the courses followed in the engineering colleges leading to B.E. degrees. It will also suit the courses of A.M.I.E. and U.P.S.C. examinations. I have attempted to present the matter iri a simple, lucid and precise manner. A large number of good practical and typical problems have been solved in all the nineteen chapters of the book and I hope the book will meet the requirements of the students, teachers and practical engineers. Sincere acknowledgement are due to the authors listed in the references whose books/papers have been consulted during the preparation of this work. Finally, the author wishes to thank his wife Meera and sons Sanjay and Rajay for the hardships which they had to face due to the authors engagement in the v.enture. R. YADAV CONTENTS Chapters 1. INTRODUCTION: -Importance of Heat Transfer; Basic Modes of Heat Transfer; Conduction Mechanism; Convection Mechanism; Radiation Mechanism; Steady and Unsteady Heat Transfer; Conservation or Energy; Basic Law of Heat Conduction; General Heat Conduction Mechanism and Law; Basic Law of Convection; Basic Law of Radiation; Thermal Resistance and Conductance; Combined Heat Transfer Mechanisms; Thermal Conductivity. 1-29 2. GENERAL HEAT CONDUCTION EQUATION :- General Heat Conduction Equation in Rectangular Co-ordinates; General Heat Conduction Equation in Cylindrical Co-ordinates; General Heat Conduction Equation in Spherical Co-ordinates; Solutions of Equations 30-41 3. ONE-DIMENSIONAL STEADY-STA TE HEAT CONDUCTION WITHOUT HEAT GENERATION:- Plane Wall or Slab; Hollow Cylinder or Tube; Spherical Shells; Conduction Shape Factor; Heat Flow through Composite Structures; Series Composite Wall; Critical Thickness of Insulation for Pipes; Composite Spherical Shells; Critical Thickness of Insulation for Spheres; Effect of Variable Thermal Conductivity; Heat Flow Through Plain Wall with Non-Upiform Thermal Conductivity; Heat Flow Through Cylinder at Non Uniform Conductivity; Heat Flow Through Sphere with Non Uniform Conductivity; Heat Flow From a Long Tube Through_ which the Hot Fluid is Flowing. 42-104 4. ONE DIMENSIONAL STEADY STATE HEAT CONDUCTION WITH HEAT GENERATION:'- Plane Wall with Uniform Heat Generation; Hollow Cylinder with Uniform Heat Generation; Solid Cylinder with Uniform Heat Generation; Electric Wire Carrying Electric current; Solid Sphere with Uniform Heat Generation; Heat Flow Through Pis- ton Crown; The Buried Cable; Variable Distributed Generation as a Function of Temperature; Dielectric Heating 105-152 5. HEAT TRANSFER FROM EXTENDED SURFACES : Straight Fin of Rectangular and Circular profile; Conduction Cooling of Turbine Bladings; Efficiency of Straight Rectangular Fins; Effectiveness of the Fin; Optimum Dimensions for Straight Rectangular Fins; Errors of Measurement of Temperature of Thermometer Well; Heat Flow Form a Bar Maintained at Different Temperatures; Gene:;alised Equations for Fios or Spines; Straight Fin of Triangular Profile; Optimum Dimensions for Straight Triangular Fin; Straight Fin of Concave Parabolic Profile; Optimum Dimension of Concave Parabolic �V 1 1)1 Profii.e; Straight Fin of Convex Parabolic Profile; Straight Fin of Least Material; Selection and Design of Straight Fins . . . 153-205 6. T\VO AND THREE DIMENSIONAL STEADY S'{'ATE HEAT CONDUCTION :- Conduction in a Semi-infinite Strip; Coi1ducuon in a Long Rectangular Rod; Graphical Method; Analogical Solution; ?inite Difference Method; The Nodal Network and Finite Difference Form; Finite Difference method; The Relaxation Method; The Gauss-Seidel Iteraction; The Matrix Inversion Method; Three Dimensional Heat Conduction. . . . 206-232 7. UNSTEADY STATE (TRANSIENT) HEAT CONDUCTION :- Non-periodic Heating and Cooling; Heating or Cooiings with Known Temperature Distribution; Newtonian Heating or Cooling with negligible Internal Resistance; Temperature-Time Response of Thermocouple; Heating or Cooling with negligible Surface Resistance; Transient Heat Conduction in Semi-infinite Solids; Heating or Cooling of Infinite Plate with Finite Internal and Surface Resistance; Infinitely Long Cylinder and Sphere with Finite Internal and Surface Resistance; Graphical Method (Temperature Time Charts) for Finite Internal and Surface Resistance; Periodic Heat Flow; Periodic Heat Flow in Semi infinite Thick Solid; Transient Conduction with Given Temperature Distribution; Multi-dimensional Effect. . . . 233-289 8. CONVECTION AND FLUID FLOW PROCESSES :- Mean Bulk Temperature and Mean Film Temperature; The Ideal Fluid; Viscous Fluid The Stream Function; The Velocity Potential; Newtonian and Non-Newtoniav Fluids;.Laminar Flow; Turbulent Flow; The Hydrodynamic (Velocity) Boundary Layer Concept; Methods of Boundary Layer Control; Thermal Boundary Layer; Convection Boundary Conditions and Their Applications; General Momentum Conservation Equations; Navier-Stoke� Equation; Flow Regimes and Simple.Flow Solutions of Navier Stokes Equation; Velocity Distribution in Fully Developed Laminar Flow in Tube: Flow Loss in Passages. ... 290-318 9. DIMENSIONAL ANALYSIS :- Criteria for Similitude; Dimensions; Dimensionless Numbers and Their Physical Significance; Characteristics Length or Equivalent Diameter; Buckingham Theorem Frictional Loss in Pipes; Forced Convection Heat Transfer; Naturai or Free Convection; Forced Convection in High Speed Flow; Model Similitude for Heat Transfer Equipment. . . . 319-33 4 iO. LAMINAR FLOW FORCED CONVECTIVE HEAT TRANSFER :- Equation of Motion for Hydrodynamic Boundary Layer Over a Flat Plate; Velocity Distrib'ution in the Boundary Layer (Exact Solution); Energy Equatibn of Thermal Boundary Layer Over a Flat Plate; The Prandtl Number; Temperatme Distribution in Boundary Layer (Exact Solution); 1; , Thickness of Thermal Boundary Layer; The Local and A veragc Heat Transfer Coefficient; The Nusselt Number; Approximate Hydrodynamic Boundary Layer Analysis (Integral Method); Approximate-Method for Temperature Distribution (Integral Method); Velocity Distribution in the Entrance Region of a Tube; Momentum Equation for Hydrodynamic Boundary Layer in a Circular Tube (Cylindrical Co-ordinates); Energy Equation for Thermal Boundary Layer in Circular Tube (Cylindrical Co ordinates); Local and Average Heat Transfer Coefficients for Laminar Flow in Tubes; Heat Transfer in Tube (Solution of Energy Equation). . . . 335-391 11. TURBULENT FLOW FORCED CONVECTIVE HEAT TRANSFER :- Turbulence; Turbulent Shearing Stress and Heat Exchange; Semi-empitj.cal Theorie� of Turbulence; Analogy between Heat and Momentum Transfer; Reynold's Analogy; General Form of Reynold's Analogy; Colburn Analogy; Prandtl Analogy; Momentum Integral Method for Turbulent Boundary Layer over Flat Plate; Turbulent Heat Flow. ... 392-421 12. EMPIRICAL CO-RELATIONS FOR CONVECTION : Laminar Flow Over Flat Plate; Laminar Flow Inside Tubes; Turbulent Flow Over Flat Plate; Mixed Boundary Conditions O\.er Flat Plate; Fully Developed Turbulent Flow in Tubes; Turbulent Flow in Non-circular Passage; Turbulent Flow Over Cylinders; Turbulent Flow Over Spheres; Turbulent Flow Across Banks of Tubes; Packed Beds; Horizontal Plates; Cylinders· and Wires; Inclined Plate; Spheres . : . 422-453 13. FREE CONVECTION :-Temperature and Velocity Distribution in a Free Convection Boundary Layer Over Vertical Plate; Similarity Relations in Free Convection; Momentum and Energy Equation in Free Convection Boundary-Layer Over a Verli.cal Plate; Velocity and Temperature Distribution in Laminar Free Convection over Vertical Flat Plate (Exact Solution); Approximate Integral Method in Laminar Flow Over Vertical Plate; Turbulent Free Convection over a Vertical Plate (Integral Method); Free Convection from Rotating Bodies. . .. 454-479 14. BOILING AND CONDENSATION:-Physical Mechanisms of Boiling; Boiling Regimes of Saturated Pool Boiling; Bubble Shape and Size Consideration; Bubble Growth and Collapse; Critical Diameter of Bubble; Factors effecting Nucleate Boiling; Forced Convection Boiling; Boiling Correlations; Physical Mechanisms of Condensation; Laminar Film Condensation on a Vertical Plate; Turbulent Filin Condensation; Film Condensation in Horizontal Tubes; Influence of the Presence of Non-condensable Gases; Enhancement of Film Condensation; Dropwise Condensation ... 480--519