Thermal conduction, convection, and radiation explain how energy moves because of temperature differences. This cheat sheet helps students choose the correct heat transfer model, substitute units correctly, and solve worked-problem style questions. It is useful for physics, engineering, and environmental science problems involving insulation, cooling, heating, and energy loss.
Key Facts
- Conduction through a flat wall is modeled by , where is thermal conductivity, is area, and is thickness.
- Thermal resistance for conduction is , so heat transfer rate can be written as .
- For layers in series, total thermal resistance is and the same heat rate passes through each layer at steady state.
- Convective heat transfer is estimated by Newton's law of cooling, , where is the convection coefficient.
- Radiation from an object is given by the Stefan-Boltzmann law , where .
- Net radiation between an object and large surroundings is , with all temperatures measured in kelvin.
- Temperatures must be converted using before using any radiation formula.
- When conduction, convection, and radiation act together, the total heat transfer rate is often found by adding parallel contributions, such as .
Vocabulary
- Conduction
- Conduction is heat transfer through direct particle interactions, usually strongest in solids with high thermal conductivity.
- Convection
- Convection is heat transfer between a surface and a moving fluid such as air or water.
- Radiation
- Radiation is heat transfer by electromagnetic waves and can occur through empty space.
- Thermal Conductivity
- Thermal conductivity measures how easily a material conducts heat, with larger giving a larger heat transfer rate.
- Emissivity
- Emissivity is a number from to that describes how effectively a surface emits thermal radiation.
- Steady State
- Steady state means temperatures at each point are constant in time, even though heat continues to flow.
Common Mistakes to Avoid
- Using Celsius in radiation formulas is wrong because requires absolute temperature in kelvin.
- Forgetting the thickness in conduction changes the physics because thicker materials reduce heat flow according to .
- Adding conductivities instead of thermal resistances for layered walls is wrong because layers in series combine as .
- Using the wrong area gives an incorrect heat rate because all three main formulas depend directly on surface area .
- Ignoring the sign of the temperature difference can confuse direction because heat flows from higher temperature to lower temperature, even when the calculated rate is written as a positive magnitude.
Practice Questions
- 1 A glass window has , , , and inside and outside temperatures of and . Find the conductive heat loss rate .
- 2 A metal plate of area is at in air at with . Calculate the convective heat transfer rate.
- 3 A black surface with and is at in surroundings at . Use to find the net radiated power.
- 4 A house wall loses heat by conduction through insulation and then by convection from the outer surface to the air. Explain why adding insulation reduces heat loss more effectively than simply painting the wall a different color in many winter heating situations.
Understanding Thermal Conduction, Convection & Radiation Worked Problems
Conduction starts at the particle level. In a solid, neighbouring atoms vibrate and pass energy along. Metals conduct especially well because mobile electrons carry energy too.
Wood, foam, and trapped air conduct poorly because their structure slows this transfer. A worked problem often treats a wall as uniform, but real walls have joints, screws, window frames, and small air gaps. These can create thermal bridges.
A thermal bridge is a route where heat crosses much more easily than through the insulation around it. This explains why a building can lose heat even when most of its wall has thick insulation.
Thermal resistance is useful because it turns a complicated material stack into a simple comparison. A large resistance means a small heat transfer rate for the same temperature difference. At steady state, each layer carries the same rate of energy per second.
The temperature drop is not usually shared equally. The layer with the greatest resistance has the largest temperature drop. This is a good check on answers involving brick, insulation, plaster, or glass.
Separate routes through a system behave differently. Heat moving through insulation and through a metal support has two parallel paths. The path with lower resistance carries more energy, much like electric current prefers a lower electrical resistance.
Convection needs careful interpretation because the convection coefficient is not a fixed property of a material. It depends on the fluid, its speed, its density, and the shape and orientation of the surface. Air flowing past a cyclist removes energy faster than still air.
A fan increases cooling because it continually replaces warmed air near a surface with cooler air. In most questions, the relevant temperature is the surface temperature compared with the temperature of the surrounding moving fluid. Radiation has no need for air or any other medium.
Every ordinary object emits it. Dull dark surfaces usually emit and absorb radiation well, while shiny metal surfaces usually do both poorly.
Radiation calculations need absolute temperature because the emitted power depends very strongly on temperature. A hot object can radiate far more energy than expected from a simple Celsius temperature comparison.
A reliable solution begins by drawing the object and marking every boundary where energy enters or leaves. Decide whether the situation is steady state. If temperatures are changing with time, some energy may be warming or cooling the object itself, so the incoming and outgoing rates do not have to match.
Keep area units in square metres, thickness in metres, and energy transfer rates in watts. Use kelvin only for radiation expressions involving temperature raised to the fourth power. Check the direction of every result.
A negative net radiation value means the object gains energy by radiation. In real situations such as a thermos flask, a house wall, a radiator, or a laptop heat sink, several transfer routes operate at once. Good modelling means including the important routes without counting the same energy transfer twice.