Fundamentals of Heat and Mass Transfer, 8th edition

If you design anything that gets hot or cold — electronics, buildings, engines, heat exchangers — this is the standard reference. It teaches a discipline: estimate the Biot number before trusting a shortcut, check the Reynolds number before picking a correlation, draw the thermal circuit before computing. Engineers keep it on the shelf for the property tables and the correlations alone. Best for mechanical and chemical engineering students and practicing designers.

1. 1Chapter 1

   Heat flows through resistance, just like current

   Open Chapter 1 and you're handed the whole game in miniature: a composite wall of layers (brick, insulation, plaster). Each layer resists heat differently, and instead of wrestling with coupled equations you draw a thermal circuit — conduction resistance R = L/kA and convection resistance R = 1/hA — and read the heat rate off like current through a resistor. The rate equations come first: Fourier's law q'' = -k dT/dx for conduction, Newton's law of cooling q'' = h(Ts - T∞) for convection, where h sweeps in every effect influencing convection. Then the first law closes the loop: the rate of energy storage in a control volume equals the rate of energy inflow minus the rate of energy outflow plus the rate of energy generation.

   The idea

   The electrical analogy is the book's master key. Once a wall, a fin, or a furnace shell becomes a network of resistances, complicated multi-mode problems collapse into series and parallel arithmetic you can do on a napkin. The surprise is how much physics hides inside h — it isn't a property of the fluid but a summary of everything happening in the boundary layer. And the control-volume energy balance, storage = in - out + generation, is the skeleton every later chapter hangs equations on.

   Try this: Sketch a thermal circuit for the wall of the room you're in: convection outside, conduction through each layer, convection inside, and estimate which resistance dominates.

2. 2Chapter 1/2

   Copper conducts 15,000 times better than air

   At 300 K the property tables tell a dramatic story: pure copper carries heat at about 400 W/m·K (401 W/m·K), aluminum at 237, steel at 14.9, glass at 1.4, and air at a whisper-thin 0.026. The book explains the mechanism: thermal conductivity arises from lattice vibrations (phonons) and free-electron transport in metals.

   The idea

   Choosing a material is often choosing your heat transfer rate outright.

   Try this: Look up the k values of two materials in your kitchen — a metal pot and its plastic handle — and compute the resistance ratio.

3. 3Chapter 2

   The heat diffusion equation, in every coordinate system

   Chapter 2 builds the machinery: apply the energy balance to a differential control volume and out pops the heat diffusion equation in Cartesian coordinates, ∂²T/∂x² + ∂²T/∂y² + ∂²T/∂z² + q̇/k = (1/α) ∂T/∂t, for a homogeneous, isotropic material with constant k. Here q̇ is volumetric heat generation and α = k/ρcp is the thermal diffusivity. The chapter then translates the same physics into cylindrical and spherical forms, because pipes and spheres don't care about your Cartesian bias.

   The idea

   Thermal diffusivity is the ratio of heat conducted to heat stored.

   Try this: Compute α = k/ρcp for copper and for glass and note how much faster temperature changes travel through the metal.

4. 4Chapter 3

   Radial resistance and the insulation that backfires

   Chapter 3 starts tame — the plane wall with no generation, R = L/k, the overall coefficient U, series and parallel composites — then goes round. For a hollow cylinder the resistance becomes ln(r2/r1)/(2πkL); for a hollow sphere, (1/r1 - 1/r2)/(4πk). Then the trap: add insulation to a cylinder and the conduction resistance grows, but the outer area grows too, cutting convection resistance. Below the critical radius rcrit = kins/h, adding insulation actually increases heat transfer. The chapter also solves the wall with uniform generation, where the parabolic profile T(x) = q̇L²/(2k)(1 - x²/L²) + Ts peaks at the centerline, Tmax = Ts + q̇L²/(2k).

   The idea

   Resistance is geometry-dependent, not just material-dependent.

   Try this: For a 5 mm diameter electrical wire, estimate rcrit with rubber insulation and check whether you're below it.

5. 5Chapter 3

   Fins: fighting area against resistance

   A long rod of diameter D sticks out from a base at Tb into air at T∞. Heat conducts down the rod while leaking out the sides, and the fin equation captures the duel. For an infinitely long fin the solution decays exponentially, θ/θb = e^(-mx), with m = √(hP/kAc), and the heat rate is qf = √(hPkAc)(Tb - T∞). Since real fins end, the book defines fin efficiency ηf and fin effectiveness εf to judge whether a fin earns its metal.

   The idea

   Fins trade added surface area against the falling tip temperature.

   Try this: Feel the temperature drop along a metal spoon left in hot soup; the tip stays cool because the fin solution decays exponentially.

6. 6Chapter 4

   Separation of variables and the shape factor shortcut

   Two-dimensional conduction gets serious in Chapter 4. For a rectangular plate with prescribed boundary temperatures, separation of variables yields a temperature distribution written as an infinite series of sine functions — elegant, exact, laborious. Then the escape hatch: for multidimensional bodies, conduction shape factors reduce everything to q = Sk(T1 - T2). The tables give S for standard geometries, like an isothermal sphere buried in a semi-infinite medium, S = 4πr, and a horizontal isothermal cylinder of length L buried the same way.

   The idea

   The shape factor absorbs the two-dimensional field into one geometry-dependent number.

   Try this: Estimate the heat loss from a buried spherical tank using S = 4πr before looking up anything else.

7. 7Chapter 5

   Lumped capacitance: when a body has one temperature

   Drop a hot part into cool air and Chapter 5 asks the first question: does the inside matter? If the Biot number Bi = hLc/k is below about 0.1, conduction inside beats convection out, and the whole body cools as one temperature, following θ/θi = exp(-Bi·Fo), with Fo = αt/Lc² the Fourier number — equivalently (T - T∞)/(Ti - T∞) = exp(-t/τ) with time constant τ = (ρVc)/(hAs). When Bi is larger, internal gradients are real, and the Heisler charts — now often replaced by computational tools — supply graphical solutions for the plane wall, infinite cylinder, and sphere.

   The idea

   The Biot number decides whether your problem is algebra or partial differential equations.

   Try this: Estimate Bi for a roasting chicken (h ≈ 15 W/m²·K, Lc ≈ 0.05 m) and decide whether the lumped method would lie to you.

8. 8Chapter 6

   Boundary layers: where convection actually happens

   Chapter 6 zooms into the thin film where all the action is. Air flows over a plate; velocity climbs from zero at the wall to 0.99u∞ at the edge of the velocity boundary layer of thickness δ, while a thermal boundary layer of thickness δt grows alongside, their ratio set by the Prandtl number Pr = ν/α. The convection coefficient is pinned to the surface temperature gradient: h = -kf (∂T/∂y)|y=0 / (Ts - T∞). The cast of dimensionless characters appears: Reynolds number Re = ρu∞L/μ, Prandtl number Pr, Nusselt number Nu = hL/kf, Grashof number for buoyancy, Stanton number St = h/(ρVcp). At 300 K, air has Pr = 0.71, water 5.83, engine oil 6,400.

   The idea

   The Prandtl number compares momentum diffusion to thermal diffusion.

   Try this: Blow on your hand slowly, then fast: you're changing Re and thinning the boundary layer, which is why faster air feels cooler.

9. 9Chapter 6/7

   Blasius, transition, and the flat plate

   For laminar flow over a flat plate, the Blasius solution gives the boundary layer thickness δ ≈ 5x/√Rex and the local friction coefficient Cf,x = 0.664/√Rex. Heat follows: the local Nusselt number Nux = 0.332 Rex^(1/2) Pr^(1/3) for Pr ≥ 0.6. Then the flow trips — around a critical Reynolds number near 5 × 10⁵ — and turbulence rewrites the rules: Nux = 0.0296 Rex^0.8 Pr^(1/3). Notice the exponent: 0.5 becomes 0.8, and heat transfer climbs much faster with velocity.

   The idea

   The transition at Re ≈ 5 × 10⁵ changes the law of heat transfer on either side of it.

   Try this: Compute h for air at 5 m/s over a 1 m plate assuming laminar, then turbulent, and see the penalty of guessing the wrong regime.

10. 10Chapter 7

    Cylinders, spheres, and tube banks

    Chapter 7 is the correlation catalog for external flow. Cross-flow over a cylinder: the Churchill-Bernstein correlation for the average Nusselt number, valid for ReD Pr > 0.2. Flow over a sphere: the Whitaker correlation, NuD = 2 + (0.4 ReD^1/2 + 0.06 ReD^2/3) Pr^0.4 (μ/μs)^1/4, good for 0.71 < Pr < 380 and 3.5 < ReD < 7.6 × 10⁴. Then whole arrays: banks of tubes in cross flow, handled by the Grimison and Zukauskas correlations with correction factors for the number of tube rows and whether the array is inline or staggered.

    The idea

    Every correlation is a contract with its validity range.

    Try this: Pick a correlation you use at work and read its stated validity range; check whether your last application actually fit.

11. 11Chapter 8

    Pipes, entry lengths, and Dittus-Boelter

    Inside a tube, the flow needs runway. Fully developed means the velocity profile stops changing with axial position x; for laminar flow the hydrodynamic and thermal entry lengths run xe/d ≈ 0.05 ReD, while turbulent flow settles after roughly xe/d ≈ 10 diameters. For the turbulent workhorse, the book hands you Dittus-Boelter: NuD = 0.023 ReD^4/5 Pr^n, with n = 0.4 for heating and n = 0.3 for cooling, valid for 0.6 < Pr < 160 and ReD > 10,000.

    The idea

    Entry length determines whether your tube is fully developed.

    Try this: For a 2 cm pipe with water at Re = 2,000, compute the laminar entry length and see whether your heat exchanger is even fully developed.

12. 12Chapter 9

    Buoyancy does the pumping: free convection

    No fan, no pump — just a hot vertical plate warming the air beside it until buoyancy takes over. The Grashof number GrL = gβ(Ts - T∞)L³/ν² measures the driving force, and Ra = Gr·Pr sets the regime: for 10⁴ < RaL < 10⁹ the laminar correlation is NuL = 0.59 RaL^(1/4), while the Churchill-Chu correlation holds for all RaL. The chapter also crawls inside enclosures — the air gap of a double-pane window, where for small gaps the Nusselt number sits close to 1 — and cites the Globe and Dropkin correlation for a horizontal enclosure between two plates.

    The idea

    The Rayleigh number decides laminar versus turbulent in free convection.

    Try this: Hold your hand a few centimeters above a radiator, then beside it: above, buoyant flow is strong; beside it, the vertical-plate regime is weaker.

13. 13Chapter 10

    The boiling curve and its cliff

    Turn up the heat under a pot of water and the story unfolds on the Nukiyama curve — heat flux versus excess temperature ΔTe = Ts - Tsat. First natural convection, then nucleate boiling where bubbles churn the surface and heat flux soars, then the critical heat flux marking departure from nucleate boiling, then the dangerous transition and film boiling regimes where vapor blankets the surface. The Rohsenow correlation handles nucleate pool boiling. On the other side of the chapter, film condensation on a vertical plate gets the classical Nusselt theory, NuL = 0.943 [ρl g hfg L³ / (μl kl (Tsat - Ts))]^1/4, plus a Reynolds number for the condensate film.

    The idea

    The critical heat flux marks departure from nucleate boiling.

    Try this: Watch a pot on the stove: the shift from gentle bubbles to vigorous nucleate boiling is you moving along the boiling curve toward CHF.

14. 14Chapter 11

    LMTD and effectiveness-NTU: sizing and rating exchangers

    Two fluids, one metal wall, endless industrial duty. Chapter 11 sorts exchangers into parallel-flow, counterflow, and cross-flow, then offers two calculators. The LMTD method defines ΔTlm = (ΔT1 - ΔT2)/ln(ΔT1/ΔT2) for the parallel and counterflow cases, with a correction factor F for multipass and cross-flow designs. The effectiveness-NTU method flips it: ε = q/qmax and NTU = UA/Cmin, with effectiveness relations for parallel-flow, counterflow, and shell-and-tube geometries. And because real surfaces foul, the book tabulates fouling factors — extra resistance for deposits — for various fluids.

    The idea

    LMTD sizes an exchanger when both outlet temperatures are known; effectiveness-NTU predicts performance when they aren't.

    Try this: For your car's radiator, sketch whether coolant and air flow mostly parallel or cross to each other and where the thermal resistance sits.

15. 15Chapter 12

    Blackbodies, gray surfaces, and the sky's temperature

    Radiation gets its own chapter and its own physics. The blackbody emits according to the Planck spectral distribution, summarized by Wien's displacement law λmax T = 2897.8 μm·K and the Stefan-Boltzmann law E = σT⁴. Real surfaces fall short, characterized by spectral and hemispherical emissivity ελ and ε; a gray surface keeps ε independent of wavelength, and Kirchhoff's law ties absorption to emission: αλ = ελ at thermodynamic equilibrium. Then the atmosphere enters: the solar constant S ≈ 1367 W/m², an effective sky temperature Tsky to model atmospheric radiation, and flat-plate collectors whose absorptivity decides how much sun they keep.

    The idea

    Kirchhoff's law ties absorption to emission at each wavelength.

    Try this: On a clear night, compare how cold a metal railing feels versus grass — radiative exchange with a cold effective sky temperature at work.

16. 16Chapter 13

    View factors and the radiation network

    Two surfaces stare at each other; the view factor Fij is the fraction of radiation leaving i that lands on j. Chapter 13 builds the algebra: the reciprocity relation AiFij = AjFji, the summation rule, and tricks like the crossed-strings method for two-dimensional geometries. For black surfaces, radiosities track the exchange; for diffuse-gray surfaces in an enclosure, Oppenheim's network method defines a surface resistance (1-εi)/(εi Ai) and a space resistance 1/(Ai Fij), and you solve radiation like a circuit. The two-surface enclosure follows: q12 = σ(T1⁴ - T2⁴)/[(1-ε1)/(ε1A1) + 1/(A1F12) + (1-ε2)/(ε2A2)], and a radiation shield slashes the net transfer.

    The idea

    The two-surface enclosure reduces to three resistances in series: surface, space, surface.

    Try this: Wrap a hot drink cup in shiny foil: you're raising its surface resistance (1-ε)/εA and slowing radiative loss.

17. 17Chapter 14

    Mass transfer: the heat equation's twin

    The final chapter swaps temperature for concentration and reruns the whole book. Fick's law of diffusion for a binary mixture sets species flux proportional to the concentration gradient, j''A = -DAB dCA/dx (or in molar form), with DAB the binary diffusion coefficient in m²/s. The species conservation equation mirrors the heat equation in steady and transient forms, solved for diffusion through a plane wall and a membrane. The analogies get names: the Sherwood number Sh = hm L/DAB plays Nusselt's role, the Schmidt number Sc = ν/DAB plays Prandtl's, and evaporation of water into air becomes a worked case.

    The idea

    The heat transfer tools transfer to mass transfer through a dictionary of substitutions.

    Try this: Note how a puddle evaporates faster on a windy day — you're raising the mass transfer coefficient hm, the Sh number's gift.

18. 18Appendices A and B

    The appendices: tables that earn the book's shelf space

    Behind the theory sits the machinery. Appendix A tabulates thermophysical properties: metallic solids like aluminum, copper, and iron; nonmetallic solids like brick, glass, and wood; common liquids; and gases at atmospheric pressure — each with density, specific heat, thermal conductivity, and viscosity at various temperatures. Appendix B supplies the mathematics the solutions lean on: the error function and its complement, Bessel functions for cylindrical coordinate problems, and the roots of transcendental equations that appear in series solutions for transient conduction.

    The idea

    The property tables and mathematical functions are the machinery behind the chapters.

    Try this: Bookmark the property table for the one material you work with most; you'll use it more than any equation in the book.

Mechanical and chemical engineering students taking heat transfer, and practicing engineers who size exchangers, insulation, or cooling systems. Also ideal for anyone preparing for the FE/PE exams who wants the correlations and property tables in one place.

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