Mechanical
Heat Transfer
Conduction, convection, radiation — three modes of thermal energy flow
Heat transfer is the movement of thermal energy from hot to cold. Three modes. Conduction through solids by molecular vibration (Fourier's law q = -k dT/dx). Convection by fluid motion (Newton's cooling q = h delta T). Radiation by electromagnetic waves (Stefan-Boltzmann q = epsilon sigma T to the fourth). Real systems combine all three. Critical to engines, electronics cooling, buildings, spacecraft thermal control, food processing, and climate.
- ConductionFourier's law — q = -k dT/dx
- ConvectionNewton's cooling — q = h delta T
- RadiationStefan-Boltzmann — q = epsilon sigma T to the fourth
- Conductivity rangeAir 0.026, copper 400 W/(m K)
- Modes coexistReal systems combine all three
- Driving forceTemperature difference
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Why heat transfer matters
- Energy efficiency. Building insulation, HVAC, water heaters.
- Electronics cooling. Heatsinks, fans, liquid loops, vapor chambers.
- Engines. Combustion temperatures, cooling jackets, exhaust.
- Manufacturing. Heat treatment, casting, welding, drying.
- Aerospace. Re-entry shields, satellite thermal control.
- Food. Cooking, refrigeration, freezing, pasteurization.
- Climate. Atmospheric circulation, ocean currents, ice dynamics.
Common misconceptions
- One mode dominates. Most real situations combine conduction, convection, radiation.
- Cold flows. Heat flows; cold is the absence of heat.
- Conductivity is constant. Varies with temperature, especially gases.
- Insulator stops heat. Slows it. No perfect insulator at finite temperature.
- Radiation needs hot surface. All objects above 0 K radiate.
- Black equals hot. Black surfaces emit and absorb well; color is wavelength-dependent.
Frequently asked questions
What are the three modes?
Conduction transfers heat through a stationary medium by molecular collisions and electron motion. Convection transfers via bulk fluid motion (natural buoyancy or forced flow). Radiation transfers by electromagnetic waves and needs no medium — it's how Earth receives solar energy through space. All three operate simultaneously in most real systems.
How does conduction work?
Fourier's law. Heat flux q equals minus thermal conductivity k times temperature gradient dT/dx. Negative sign indicates flow from hot to cold. Conductivity varies enormously: air ~0.026, water ~0.6, glass ~1, stainless steel ~16, copper ~400 watts per meter-kelvin. Insulators have low k; conductors have high k.
What's natural vs forced convection?
Natural convection arises from density differences caused by heating: warm fluid rises, cold sinks (Rayleigh-Benard cells). Forced convection uses fans, pumps, or wind to drive flow. Forced convection coefficients (h ~10 to 10000 W/m²K) far exceed natural (h ~5 to 25). CPU heatsinks rely on fan-forced convection across fins.
How does radiation work?
Every object above absolute zero emits thermal radiation. Stefan-Boltzmann law: power per area equals emissivity times sigma (5.67e-8) times T to the fourth, with T in kelvin. Doubles in flux when T rises 19%. Hot objects radiate strongly; sun's surface at 5800 K, room-temperature surfaces emit infrared. Vacuum doesn't stop radiation.
What is thermal resistance?
Analog of electrical resistance for heat. R = thickness / (k times area) for conduction. R = 1/(h times area) for convection. Resistances in series add (composite walls). Resistances in parallel use reciprocal sum (heat flowing through two paths). Total heat flow q = delta T / R_total. Used heavily in building thermal design and electronics cooling.
How is electronics cooling designed?
Junction-to-ambient resistance budget. Chip junction temperature must stay below maximum (often 125 C). Path: junction-to-case (chip package), case-to-heatsink (thermal interface material), heatsink-to-air (convection). Thermal grease, heat pipes, and forced air or liquid cooling reduce stages. Maximum power dissipation determines cooling solution.
What is emissivity?
Fraction of blackbody radiation actually emitted by a surface, between 0 and 1. Polished metals are very low (~0.05). Painted or oxidized surfaces are high (~0.9). Selectivity matters: solar absorbers want high emissivity in solar wavelengths, low in IR. White paint reflects sunlight but emits IR readily — passive cooling exploits this.