Heat transfer: conduction, convection and radiation

In short

Heat transfer is the study of the rate at which thermal energy crosses a boundary because of a temperature difference. Thermodynamics tells you how much energy moves between two states; heat transfer tells you how fast, and therefore how big the wall, fin, radiator, insulation or furnace must be. It happens by three modes - conduction through matter by molecular and electron interaction, convection by a moving fluid, and radiation by electromagnetic waves needing no medium. It is one of the heaviest-weighted sections in GATE Mechanical and in university Heat and Mass Transfer papers, and it is asked in design and plant interviews at BHEL, NTPC, L&T, Thermax, Tata Steel, ISRO, Godrej, Voltas, Blue Star, Cummins and every HVAC, boiler and automotive thermal-systems role.

Explained

Modes, Fourier's law and thermal conductivity

• Conduction: energy diffuses through a stationary medium down the temperature gradient - lattice vibrations (phonons) in solids, free electrons in metals (which is why good electrical conductors are good thermal conductors), molecular collisions in still fluids.
• Fourier's law (1822, empirical): Q = −kA dT/dx. The minus sign satisfies the second law - heat flows from hot to cold. Heat flux q = Q/A in W/m².
• Thermal conductivity k (W/m·K) is a material property; it varies with temperature, so handbooks quote it at a mean temperature. Metals: k falls slightly with temperature; gases and most insulators: k rises with temperature.
• Thermal diffusivity α = k/ρc (m²/s) governs how fast a temperature *change* travels, not how much heat flows steadily. High α (metals) means the body equalises quickly.
• Convection: conduction at the wall plus bulk transport by fluid motion. Free (natural) convection is driven by buoyancy from density differences; forced convection by a pump, fan or wind. The coefficient h is *not* a property - it depends on geometry, fluid, velocity and even surface orientation.
• Radiation: every surface above 0 K emits electromagnetic energy (mainly 0.1-100 µm, the thermal band). It needs no medium, travels at light speed, and goes as T⁴ - so it dominates at high temperature and in vacuum (spacecraft, furnaces, incandescent surfaces).
• All three usually act together: a hot pipe loses heat by conduction through the wall and insulation, then by convection *and* radiation from the outer surface in parallel.

Steady conduction: resistance networks, generation, critical radius

• Electrical analogy: Q = ΔT/R. Resistances in series add; in parallel, 1/R = Σ1/Rᵢ. This single idea solves most exam problems.
• Plane wall R = L/kA; hollow cylinder R = ln(r₂/r₁)/(2πkL); hollow sphere R = (r₂−r₁)/(4πk r₁r₂); convection film R = 1/hA.
• Composite wall: add film, wall and insulation resistances; the temperature drop across each layer is proportional to its resistance. In a plane wall the profile is linear per layer (for constant k), logarithmic in a cylinder.
• Overall coefficient: Q = UAΔT with 1/UA = ΣR. For a cylinder, U must be quoted with the reference area (inside or outside).
• Thermal contact resistance: real joints touch only at asperities, so a finite ΔT appears across a "perfect" interface. Reduced by higher contact pressure, softer/thermal-grease interstitial material, machined flatness - important in electronics heat sinks and bolted flanges.
• With internal generation q̇ (W/m³): slab of thickness 2L cooled on both faces, T_max − T_wall = q̇L²/2k; solid cylinder, T_centre − T_wall = q̇R²/4k; sphere, q̇R²/6k. Used for nuclear fuel rods, current-carrying conductors, resistance heaters.
• Variable k: if k = k₀(1 + βT), use the mean k at the mean temperature; the profile curves convex or concave depending on the sign of β.
• Critical radius of insulation: adding insulation to a small cylinder increases the outer surface area while adding conduction resistance. The two compete, and heat loss is *maximum* at r_cr = k/h (cylinder) and 2k/h (sphere). Insulating above r_cr reduces loss; below it, insulation *increases* loss. This matters for thin electric cables and small-bore tubing (small r, low h) - for steam pipes r_cr is a few millimetres and is already exceeded.

Extended surfaces (fins) and transient conduction

• Why fins: when h is small (air side), Q = hAΔT is raised by increasing A. Hence fins on motorcycle cylinders, transformers, radiators, air-cooled condensers, heat sinks and economiser tubes.
• Fin equation for a uniform-section fin: d²θ/dx² − m²θ = 0 with θ = T − T∞ and m = √(hP/kA_c).
• Standard solutions: infinitely long fin Q = √(hPkA_c)·θ_b; insulated (adiabatic) tip Q = √(hPkA_c)·θ_b·tanh(mL) - the usual exam case; convecting tip handled by a corrected length L_c = L + t/2.
• Fin efficiency η = actual heat/heat if the whole fin were at base temperature = tanh(mL)/mL. Fin effectiveness ε = Q_with fin/Q_from the bare base area; a fin is worthwhile only if ε > 1, i.e. high k, high P/A_c (thin), low h.
• Fins are made of aluminium or copper because high k keeps the fin near base temperature; fins are useless in a high-h liquid stream and are therefore put on the gas side of a gas-liquid exchanger.
• Transient (unsteady) conduction - lumped capacitance: valid when Bi = hL_c/k < 0.1 (internal resistance negligible, body essentially uniform), with L_c = V/A_s. Then θ/θ₀ = exp(−t/τ), τ = ρVc/hA_s. A 20 mm steel ball (k = 45) quenched in oil at h = 300 has Bi = 0.022, so lumping is legitimate.
• Exponent can be written −Bi·Fo, where Fourier number Fo = αt/L_c² is dimensionless time.
• Bi > 0.1: use one-term approximations or Heisler/Grober charts for an infinite slab, long cylinder and sphere, with the product solution for finite shapes (e.g. a short cylinder = infinite cylinder × infinite slab).
• Semi-infinite solid (a thick wall for a short time, ground, a quenched large block): (T−Tᵢ)/(T_s−Tᵢ) = erfc[x/(2√(αt))]; penetration depth grows as √(αt).
• Thermocouple response: the time constant τ sets the lag; a fine bead (small L_c) responds faster. Standard interview question on measurement error.

Convection: boundary layers, dimensionless groups, correlations

• Newton's law of cooling: Q = hA(T_s − T∞). All the physics hides in h, found from experiment-based correlations in dimensionless form.
• Velocity boundary layer (thickness δ) carries the shear; thermal boundary layer (δ_t) carries the temperature drop. Their ratio is set by Pr = ν/α = µc_p/k: Pr ≈ 0.7 for air (δ ≈ δ_t), ≈ 2-7 for water, ≫1 for oils (δ ≫ δ_t), ≪1 for liquid metals.
• Groups to know: Re = ρVL/µ (inertia/viscous), Nu = hL/k (ratio of convection to pure conduction across the same layer), Pr, Gr = gβΔTL³/ν² (buoyancy/viscous), Ra = Gr·Pr, St = h/ρVc_p, Pe = Re·Pr, Bi, Fo.
• Transition: flat plate Re_x ≈ 5×10⁵; tube flow Re ≈ 2300 (laminar below), fully turbulent above about 10⁴; free convection on a vertical plate Ra ≈ 10⁹.
• Entrance effects: h is highest at the leading edge/tube inlet and falls to a fully-developed value; hydrodynamic and thermal entry lengths differ, and short tubes have higher average h.
• Property evaluation: external flow at the film temperature T_f = (T_s + T∞)/2; internal flow at the bulk mean temperature. Getting this wrong is a classic error.
• Analogies: Reynolds analogy St = C_f/2 (valid for Pr = 1); Colburn analogy St·Pr^2/3 = C_f/2 links measured friction to heat transfer - the basis of "augment turbulence to augment h, at the cost of pressure drop".
• Free convection in practice: h ≈ 5-25 W/m²K for air, 2-10 for a vertical wall in a room; forced air 10-200; forced water 500-10,000; boiling water 3,000-50,000; condensing steam 5,000-20,000. Quoting the right order of magnitude impresses interviewers.
• Boiling (pool boiling curve): free convection → nucleate boiling (the useful regime, very high h) → critical heat flux / burnout point → partial film → stable film boiling. Exceeding CHF on a heat-flux-controlled surface causes a sudden jump in wall temperature and tube failure - the limiting design criterion in boilers and reactors.
• Condensation: film condensation (continuous liquid film, Nusselt's 1916 analysis, h ∝ (1/L)^¼) or dropwise condensation (h up to an order of magnitude higher, but hard to sustain). Non-condensable gases drastically reduce h - hence air vents on condensers and steam coils.

Radiation: laws, properties and surface exchange

• Black body: a perfect absorber and emitter, diffuse emitter. Planck's law gives the spectral distribution; Wien's displacement law λ_max·T = 2898 µm·K (the sun at ~5800 K peaks at ~0.5 µm, visible; a 300 K surface at ~9.7 µm, far infrared). Stefan-Boltzmann law: E_b = σT⁴ with σ = 5.67×10⁻⁸ W/m²K⁴, T in kelvin.
• Surface properties: absorptivity α, reflectivity ρ, transmissivity τ with α + ρ + τ = 1 (opaque: α + ρ = 1). Emissivity ε = ratio of actual to black-body emission.
• Kirchhoff's law: α = ε for a surface in thermal equilibrium with its surroundings and, more generally, monochromatically and directionally (α_λ = ε_λ). A grey body has ε independent of wavelength; a diffuse surface has it independent of direction. Real surfaces are selective - white paint has low α for sunlight but ε ≈ 0.9 in the infrared, which is why cool roofs work.
• Lambert's cosine law: a diffuse surface has the same intensity in every direction, I = E_b/π; the energy it emits per unit solid angle then varies as cos θ with the normal.
• View (shape, configuration) factor F₁₂ = fraction of radiation leaving surface 1 that strikes 2. Rules: reciprocity A₁F₁₂ = A₂F₂₁; summation ΣF_ij = 1 over an enclosure; F₁₁ = 0 for a plane or convex surface, nonzero for a concave one. Two large parallel plates: F₁₂ = 1. A small body in a large enclosure: F₁₂ = 1.
• Radiosity network: each grey surface contributes a surface resistance (1−ε)/(εA), each pair a space resistance 1/(A₁F₁₂), driven by the potential difference σT⁴. Solve like a resistance circuit. A re-radiating (adiabatic, refractory) surface is a floating node that carries no net heat.
• Radiation shields: thin, low-ε sheets inserted between surfaces add large surface resistances. With n shields of the same emissivity as the plates, q falls to q₀/(n+1); with low-ε shields, by one to two orders of magnitude. Used in cryogenic (multi-layer) insulation, furnace peepholes and satellite blankets.
• Linearised radiation coefficient: h_r = εσ(T_s² + T_sur²)(T_s + T_sur) lets radiation be added in parallel with convection, h_total = h_c + h_r - the standard practical trick for pipes, walls and electronics.
• Gas radiation: air, N₂, O₂ are effectively transparent; CO₂, H₂O vapour, SO₂ and CO emit and absorb in bands, which is why furnace and boiler radiation calculations use gas emissivity charts (Hottel) based on partial pressure × beam length. The same selectivity is the greenhouse effect. Solar irradiance outside the atmosphere ≈ 1367 W/m²; about 1000 W/m² reaches a clear-sky horizontal surface at noon in India.

Indian standards, codes and practice

• Energy Conservation Act, 2001 and the Bureau of Energy Efficiency (BEE) drive thermal design limits: the Energy Conservation and Sustainable Building Code (ECSBC 2024), successor to ECBC 2017 and adopted by States in their own versions, sets maximum U-values/assembly R-values for roofs, walls and fenestration (plus SHGC) by climate zone, and ECO-Niwas Samhita 2018 sets RETV for residences. Exact numbers differ by climate zone and code version - check the current edition.
• National Building Code (NBC) 2016, Part 11, covers thermal performance and sustainability of the envelope; SP 41 is the BIS handbook on functional requirements of buildings including thermal design.
• Insulation material standards: IS 8183 (bonded mineral wool), IS 3677 (unbonded rock/slag wool), IS 9742/related standards for calcium silicate and other preformed insulation. IS 14164 is the code of practice for industrial application and finishing of thermal insulation (roughly −80 °C to 700 °C).
• Property measurement: IS 3346 - determination of thermal conductivity of insulating materials by the guarded hot-plate method; guarded hot box and heat-flow-meter methods are used for assemblies.
• Boilers and pressure parts: the Indian Boiler Regulations, 2026 (in force from October 2026, superseding the 1950 Regulations; framed under the Boilers Act, 2025, which replaced the 1923 Act from 1 May 2025) govern construction and inspection; design heat-transfer and allowable-stress practice follows IBR with ASME Section I/VIII references.
• Appliances and equipment: BEE star labelling uses ISEER for room air conditioners; solar flat-plate collectors are covered by the IS 12933 series; MNRE specifications apply to solar thermal systems. The PAT (Perform, Achieve and Trade) scheme makes furnace and boiler heat losses a compliance and money issue for designated consumers.

Key points

• Conduction - diffusion of heat through matter, Q = −kA dT/dx; needs a medium, no bulk motion.
• Convection - transport by a moving fluid, Q = hA(T_s − T∞); h is a coefficient, not a property.
• Radiation - electromagnetic emission, E = εσT⁴ with T in kelvin; needs no medium and dominates at high temperature.
• Thermal resistance - R = L/kA, ln(r₂/r₁)/2πkL, (r₂−r₁)/4πkr₁r₂, 1/hA; series and parallel like electrical circuits.
• Thermal diffusivity α = k/ρc - governs transient response; conductivity governs steady flow.
• Critical radius r_cr = k/h - heat loss is maximum here; insulating a thin cable can increase loss.
• Biot number Bi = hL_c/k - internal vs surface resistance; Bi < 0.1 permits lumped (uniform-temperature) analysis.
• Fourier number Fo = αt/L_c² - dimensionless time; θ/θ₀ = exp(−Bi·Fo) for a lumped body.
• Fin efficiency = tanh(mL)/mL, m = √(hP/kA_c); fins pay only where h is low and k is high.
• Nusselt number Nu = hL/k - dimensionless temperature gradient at the wall; Nu = 1 means pure conduction.
• Prandtl number Pr = µc_p/k = ν/α - momentum vs thermal diffusivity; it sets δ/δ_t ≈ Pr^1/3; ~0.7 air, ~7 water at 20 °C, ≪1 liquid metals.
• Grashof/Rayleigh numbers - replace Re in natural convection; Ra = Gr·Pr decides laminar or turbulent plumes.
• Dittus-Boelter: Nu = 0.023 Re⁰·⁸Prⁿ - the workhorse turbulent in-tube correlation (n = 0.4 heating, 0.3 cooling).
• Kirchhoff's law α = ε - a good emitter is a good absorber at the same wavelength.
• View factor rules - reciprocity A₁F₁₂ = A₂F₂₁ and summation ΣF = 1 solve most enclosure problems.
• Radiation shields - n identical shields cut exchange to 1/(n+1); low-ε foil does far better.
• Film vs bulk temperature - external flow properties at T_f = (T_s+T∞)/2, internal flow at bulk mean temperature.
• Critical heat flux - the burnout limit of nucleate boiling; exceeding it destroys boiler and reactor tubes.

Formulas and examples

Example 1 - Composite furnace wall (series resistances, per m²). Flue gas at 900 °C, h_i = 30; firebrick 200 mm (k = 1.2); insulating block 100 mm (k = 0.08); steel casing 10 mm (k = 45); ambient air 30 °C, h_o = 10.

• R_i = 1/30 = 0.03333; R₁ = 0.2/1.2 = 0.16667; R₂ = 0.1/0.08 = 1.25; R₃ = 0.01/45 = 0.00022; R_o = 1/10 = 0.10 → ΣR = 1.5502 m²K/W
• q = ΔT/ΣR = (900 − 30)/1.5502 = 561 W/m²
• Interface temperatures: inner face 900 − 561×0.03333 = 881 °C; firebrick/insulation 881 − 561×0.16667 = 788 °C; insulation/steel 788 − 561×1.25 = 86 °C; outer skin 86 °C (check: 86 − 561×0.10 ≈ 30 °C ✓)
• The 100 mm insulation carries 81% of the total resistance; the steel casing is negligible. An 86 °C skin is still a burn hazard - IS practice for personnel protection targets about 60 °C, so more insulation or cladding is needed.

Example 2 - Critical radius on an electric cable. Bare conductor radius 5 mm, surface held at 70 °C, ambient 25 °C, insulation k = 0.2, h = 10 (per metre length).

• r_cr = k/h = 0.2/10 = 0.02 m = 20 mm > 5 mm, so insulation will *increase* loss at first.
• Bare: Q = h(2πrL)ΔT = 10 × 2π × 0.005 × 45 = 14.1 W/m
• With insulation to r = 20 mm: R_cond = ln(20/5)/(2π×0.2) = 1.3863/1.2566 = 1.1032; R_conv = 1/(10×2π×0.02) = 0.7958 → ΣR = 1.8990 → Q = 45/1.8990 = 23.7 W/m (+68%)
• At r = 50 mm: R_cond = ln10/1.2566 = 1.8326, R_conv = 1/(10×2π×0.05) = 0.3183 → Q = 45/2.1509 = 20.9 W/m - still above bare. Useful when cable cooling is wanted; a disaster if the aim was to save heat.

Example 3 - Aluminium fin. k = 200, fin 100 mm wide × 50 mm long × 1 mm thick, base 100 °C, air 25 °C, h = 25, insulated tip.

• A_c = 0.1 × 0.001 = 1×10⁻⁴ m²; P ≈ 2 × 0.1 = 0.2 m; θ_b = 75 K
• m = √(hP/kA_c) = √(25×0.2 / (200×10⁻⁴)) = √(5/0.02) = √250 = 15.81 m⁻¹; mL = 0.791; tanh(0.791) = 0.659
• √(hPkA_c) = √(5 × 0.02) = 0.3162 → Q = 0.3162 × 75 × 0.659 = 15.6 W
• η = 0.659/0.791 = 83%; bare base would give hA_cθ_b = 25×10⁻⁴×75 = 0.188 W, so effectiveness ≈ 83 - the fin moves 83 times the heat its footprint would.

Example 4 - Forced convection of water in a tube. Water, bulk mean 40 °C, V = 1 m/s, D = 25 mm; ρ = 992, µ = 653×10⁻⁶, k = 0.631, Pr = 4.32. Wall at 80 °C (water being heated).

• Re = 992×1×0.025/653×10⁻⁶ = 37,980 → turbulent, L/D long, so Dittus-Boelter applies with n = 0.4
• Re⁰·⁸ = 4,609; Pr⁰·⁴ = 1.796 → Nu = 0.023 × 4,609 × 1.796 = 190
• h = Nu·k/D = 190 × 0.631/0.025 = 4,800 W/m²K
• For a 3 m length at a mean ΔT of 40 K (approximation - the bulk temperature really rises along the tube): Q = hπDLΔT = 4,800 × π × 0.025 × 3 × 40 ≈ 45 kW

Example 5 - Radiation between plates, and a shield. Large parallel plates, T₁ = 800 K, ε₁ = 0.8; T₂ = 500 K, ε₂ = 0.6.

• σ(T₁⁴ − T₂⁴) = 5.67×10⁻⁸ × (4.096×10¹¹ − 6.25×10¹⁰) = 5.67×10⁻⁸ × 3.471×10¹¹ = 19,680 W/m²
• Denominator 1/0.8 + 1/0.6 − 1 = 1.9167 → q = 19,680/1.9167 = 10,270 W/m² (10.3 kW/m²)
• Insert one polished shield, ε_s = 0.05 both faces: ΣR = (1.25 + 20 − 1) + (20 + 1.6667 − 1) = 40.92 → q = 19,680/40.92 = 481 W/m², a 95% cut.
• Equivalent radiation coefficient for the unshielded case: h_r = q/ΔT = 10,270/300 = 34 W/m²K - comparable to forced air convection, which is why radiation cannot be ignored above ~200 °C.

Where it is used

• Power and process plant: boiler furnace and waterwall heat absorption, superheaters, economisers, air preheaters, condensers and cooling towers at NTPC, BHEL, Thermax, L&T Power; refractory and insulation design for reheating furnaces at Tata Steel, JSW and SAIL, where PAT-scheme targets make surface heat loss a costed item.
• HVAC and building envelope: U-value and heat-gain calculations against ECBC/ECO-Niwas Samhita, cool roofs and radiant barriers, duct and chilled-water pipe insulation thickness, cold-room and cold-chain design - Voltas, Blue Star, Daikin, Godrej, Danfoss, consulting roles.
• Automotive and off-highway thermal systems: radiators, intercoolers, EGR coolers, brake-disc cooling, cylinder-head fins, battery-pack thermal management in EVs - Maruti, Tata Motors, Mahindra, Cummins, Subros, Banco Aluminium.
• Electronics and telecom cooling: heat sinks, thermal interface materials, heat pipes, vapour chambers and data-centre airflow - junction-temperature limits set product life.
• Aerospace and space: multi-layer insulation, radiators and selective α/ε coatings for satellite thermal control at ISRO; ablative and re-entry heat shields; cryogenic stage insulation.
• Solar thermal and energy: flat-plate and evacuated-tube collectors (selective absorbers with high α, low ε), solar water heaters under MNRE schemes, concentrated-solar receivers, and furnace/kiln waste-heat recovery projects.

Interview questions

• Q: What is the physical meaning of the Nusselt number? A: It is the ratio of convective heat transfer to pure conduction across a fluid layer of the same thickness; Nu = 1 means the fluid is effectively stagnant and conducting only.
• Q: Difference between thermal conductivity and thermal diffusivity? A: Conductivity fixes the steady heat flow for a given gradient; diffusivity α = k/ρc fixes how quickly a temperature change propagates, because it also accounts for the heat stored in the material.
• Q: Why can adding insulation increase heat loss? A: On a small cylinder or sphere, insulation adds conduction resistance but also enlarges the convecting surface; up to the critical radius r_cr = k/h the area effect wins and loss rises.
• Q: When is lumped-capacitance analysis valid, and why? A: When Bi = hL_c/k < 0.1, i.e. internal conduction resistance is far smaller than the surface convection resistance, so the body stays essentially isothermal while cooling.
• Q: Why are fins put on the air side of a radiator and not the water side? A: Fin effectiveness varies as √(kP/hA_c); the air-side h is one to two orders smaller, so that is where added area pays. On the water side the resistance is already low and fins would only add cost and fouling.
• Q: Why is radiation calculated in kelvin and never in Celsius? A: Because emission is proportional to absolute temperature to the fourth power; T⁴ is meaningless on a scale whose zero is arbitrary.
• Q: State Kirchhoff's law and one practical consequence. A: At thermal equilibrium a surface's absorptivity equals its emissivity at the same wavelength; consequently a white roof paint can reflect sunlight (low α in the visible/near-IR) while still radiating strongly at 10 µm, keeping the roof cool.
• Q: What is a radiation shield and how effective is it? A: A thin, low-emissivity sheet placed between two surfaces; it adds large surface resistances to the radiation network. With n shields of the same emissivity as the walls the exchange drops to 1/(n+1), and with polished foil by 90-98%.
• Q: Why does dropwise condensation give a higher coefficient than film condensation? A: Droplets leave much of the metal directly exposed to vapour, whereas a continuous liquid film is an added conduction resistance that thickens down the surface.
• Q: What is critical heat flux and why does it matter? A: It is the peak flux at the end of nucleate boiling; beyond it a vapour blanket forms, h collapses, and on a heat-flux-controlled surface the wall temperature jumps hundreds of degrees - tube burnout.
• Q: Where do you evaluate fluid properties - surface, bulk or film temperature? A: External flows at the film temperature (T_s+T∞)/2; internal flows at the bulk mean temperature, with a viscosity-ratio correction (Sieder-Tate) if the wall-to-bulk viscosity difference is large.
• Q: A thermocouple reads too slowly. What would you change? A: Reduce the characteristic length - a finer bead or thinner sheath - and raise h; the time constant τ = ρVc/hA_s falls with bead size, so response speeds up.

Common mistakes

• Putting temperatures in °C into T⁴ radiation terms, or forgetting to convert ΔT when linearising to h_r.
• Dropping the area from resistances: R = L/kA, not L/k; mixing per-unit-area resistance (m²K/W) with absolute resistance (K/W) in the same network.
• Using lumped capacitance when Bi > 0.1, or computing L_c from the full dimension instead of V/A_s.
• Treating h as a material property, or reusing a correlation outside its validity range (Dittus-Boelter below Re = 10⁴, free-convection correlations for forced flow).
• Evaluating properties at the wrong temperature - bulk for an external flow, or inlet instead of mean for a tube.
• Believing "more insulation always means less heat loss" without checking the critical radius for small-diameter tubing and cables.
• Taking the sphere resistance's (r₂−r₁) as a difference of diameters, or using the plane-wall formula on a thick pipe where r₂/r₁ > 1.2.
• Ignoring radiation entirely on hot surfaces above ~150-200 °C, where it is often comparable to natural convection.

Related topics

Heat exchangers: LMTD and effectiveness-NTU · Thermodynamics: laws and properties · Fluid mechanics: boundary layers and pipe flow · Refrigeration and air conditioning · Power plant engineering (boilers and condensers) · Mass transfer and diffusion.