Heat Transfer
Conduction, convection and radiation, fins, heat exchangers, transient heating and cooling, cooling electronics and the heat loss of buildings and pipes, with worked numbers.
Heat always flows from hot to cold, and engineering is largely about controlling how fast: keeping a building warm, an engine cool, a processor below its limit, a pipe from freezing, a process stream at the right temperature. Heat moves in three ways (conduction through solids, convection into a moving fluid, and radiation across space) and one idea ties them together: a heat flow is a temperature difference divided by a thermal resistance, so every problem becomes a chain of resistances. This guide takes you from the basics through each mode to fins, heat exchangers, transient heating and cooling, cooling electronics and the heat loss of buildings and pipes. Every worked number is computed, and a small set of examples (a cavity wall, a hot pipe, an oil cooler, a power device) runs through the pages. The fluid side of convection is in Fluid Mechanics and Pipe Flow.
Start here: what do you need?
| I need to… | Go to |
|---|---|
| understand heat, temperature, specific heat and the three modes | Heat, Temperature and the Three Modes |
| find the heat loss through a wall or insulate a pipe | Conduction: Walls, Pipes and Insulation |
| find a heat transfer coefficient for air or water | Convection and Heat Transfer Coefficients |
| estimate radiation, solar heating or use a radiation shield | Thermal Radiation |
| design a fin or a heat sink | Fins and Extended Surfaces |
| size or rate a heat exchanger or oil cooler | Heat Exchangers: LMTD and NTU |
| find how long a part takes to heat or cool | Transient Heating and Cooling |
| keep a chip or power device within its temperature limit | Cooling Electronics and Thermal Design |
| estimate heating energy, insulation payback or condensation | Insulation, Heat Loss and Troubleshooting |
A suggested order
Start with Heat, Temperature and the Three Modes, then the three modes in turn (Conduction: Walls, Pipes and Insulation, Convection and Heat Transfer Coefficients and Thermal Radiation). Fins and Extended Surfaces, Heat Exchangers: LMTD and NTU and Transient Heating and Cooling build on them, and Cooling Electronics and Thermal Design and Insulation, Heat Loss and Troubleshooting apply everything to two of the commonest jobs.
- Heat, Temperature and the Three Modes: Energy and power, specific heat, conduction, convection and radiation, thermal resistance and the numbers to remember.
- Conduction: Walls, Pipes and Insulation: Fourier’s law, composite walls and U-values, cylinders, insulation thickness, the critical radius and contact resistance.
- Convection and Heat Transfer Coefficients: Newton’s law of cooling, Reynolds, Prandtl and Nusselt numbers, forced flow in pipes and over surfaces, and natural convection.
- Thermal Radiation: Stefan–Boltzmann, emissivity and absorptivity, view factors, radiation between surfaces, shields and solar heating.
- Fins and Extended Surfaces: The fin equation, fin efficiency, heat sinks and finned tubes, with a worked aluminum fin.
- Heat Exchangers: LMTD and NTU: Types of exchanger, the log-mean temperature difference, the effectiveness–NTU method, fouling and a complete oil-cooler example.
- Transient Heating and Cooling: The lumped-capacitance method, the Biot number, time constants, quenching and warming up a part.
- Cooling Electronics and Thermal Design: Junction-to-ambient resistance, heat sinks, interface materials, forced air, PCB copper and derating.
- Insulation, Heat Loss and Troubleshooting: Wall and roof heat loss, pipe insulation economics, condensation, heating energy and a table of common thermal problems.
One idea, three examples
Worked example: the same method on three problems
- A wall (Conduction: Walls, Pipes and Insulation): resistances in series, R″ = 3.112 m²K/W, U = 0.321 W/m²K, a flux of 8.0 W/m² for 25 K.
- A heat exchanger (Heat Exchangers: LMTD and NTU): Q̇ = U A ΔTlm; the oil cooler with U A = 3 500 W/K transfers 142.0 kW in counterflow.
- A power device (Cooling Electronics and Thermal Design): Tj = Ta + P (θJC + θCS + θSA), 110 °C for 20 W at 50 °C ambient.
- In every case: find the heat flow, find the resistances, add them, and check which one dominates; that is the one to improve.
Quick reference: the equations
| What you need | Equation |
|---|---|
| Sensible heat | Q = m c ΔT |
| Conduction, plane wall | Q̇ = k A ΔT ÷ L R = L ÷ (k A) |
| Convection | Q̇ = h A (Ts − T∞) Nu = h L ÷ k |
| Radiation | Q̇ = ε σ A (T₁⁴ − T₂⁴) σ = 5.67 × 10⁻⁸ |
| Overall coefficient | 1 ÷ U = Σ resistances |
| Cylinder | R′ = ln(r₂ ÷ r₁) ÷ (2π k) |
| Fin | ηf = tanh(m L) ÷ (m L), m = √(h P ÷ (k Ac)) |
| Heat exchanger | Q̇ = U A ΔTlm ε = f(NTU, Cr) |
| Lumped transient | T = T∞ + (Ti − T∞) e−t/τ, τ = ρ c Lc ÷ h, Bi < 0.1 |
| Junction temperature | Tj = Ta + P Σ θ |
Related guides and tools
- Heat Sink and Thermal Resistance Calculator: junction temperature, allowable power and required heat sink.
- Psychrometric Calculator: dew point and moist-air properties (condensation).
- Fluid Mechanics and Pipe Flow: velocity, Reynolds number and the pressure drop that comes with a higher h.
- Thermal Design on the Board and Power Electronics: where the heat comes from.
- Material Properties, the Material Properties Table and the Energy and Temperature converters.
Safety first
- Hot surfaces burn quickly. A metal surface at 60 °C can burn skin in a few seconds; guard or insulate anything above about 55 °C that people can touch.
- Steam and hot liquids are dangerous. Never open a pressurized hot system; vent and cool first, and route relief valves to a safe place.
- Cold surfaces and cryogenic fluids can freeze skin on contact, and liquid nitrogen can displace the air in a small room.
- Fire and overheating: an overheating part can be a fire risk. Use temperature cut-outs, fuses and thermal fuses, and do not rely on a calculation alone: measure.
- The numbers here are for study and preliminary design. Pressure equipment, furnaces and safety-critical cooling need a competent engineer and the applicable codes.
FAQ
Where do I start for cooling electronics?
Read Cooling Electronics, then Fins for the heat sink, and use the Heat Sink and Thermal Resistance Calculator.
Which mode matters most?
It depends on the temperature and the fluid. Near room temperature in air, convection and radiation are about equal; in water and liquids, convection dominates; in furnaces and above about 300 °C, radiation dominates; through solids, conduction.
What is the difference between U and k?
k is a material property (W/m·K). U is the overall coefficient of an assembly (W/m²·K) that includes all the layers and the surface films: U = 1 ÷ (Σ L ÷ k + Σ 1 ÷ h).
Why do I need kelvin for radiation?
Because radiation depends on absolute temperature to the fourth power, T⁴. A temperature difference is the same in kelvin and °C, but T itself must be absolute.
Where are thermodynamics and HVAC?
They are the next guides in the Thermal and Fluids section.
References
- Incropera, F. P., et al., Fundamentals of Heat and Mass Transfer, Wiley; Çengel, Y. A. and Ghajar, A. J., Heat and Mass Transfer: Fundamentals and Applications, McGraw-Hill.
- Lienhard, J. H. IV and V, A Heat Transfer Textbook (free online); Holman, J. P., Heat Transfer, McGraw-Hill.
- ASHRAE Handbook – Fundamentals; VDI Heat Atlas, Springer; Kakaç, S., et al., Heat Exchangers, CRC Press.
- ISO 6946 and ISO 10456 (building components), JEDEC JESD51 (electronics thermal testing).
Last reviewed: November 2026. Values are typical; check the standard, the manufacturer’s data and the code that applies to your system.