Heat Transfer Calculator

Heat Transfer Explained

Heat can transfer into or out of a material in a few distinct ways, each with its own formula: raising or lowering temperature, changing phase (like melting or boiling), or flowing through a material from a hot side to a cold side.

Specific heat: $$Q = mc\Delta T$$

Latent heat: $$Q = mL$$

Conduction (Fourier's law): $$\frac{Q}{t} = \frac{kA\Delta T}{d}$$

Worked Example: Heating Water

Using the specific-heat mode's defaults — 2 kg of water (c = 4186 J/(kg·°C)) heated by 20°C — the energy required is $Q = 2 \times 4186 \times 20 = 167{,}440$ J, or about 167.4 kJ. For comparison, heating the same 2 kg of aluminum (c ≈ 900 J/(kg·°C)) by the same 20°C would take only about 36 kJ — water needs roughly 4.6 times more energy for the same temperature change, which is exactly why it's such an effective coolant.

Why the Three Modes Use Different Formulas

Specific heat and latent heat both describe fixed amounts of energy, but for fundamentally different processes — one raises temperature, the other breaks or forms bonds during a phase change without changing temperature at all. Conduction is different in kind: it's a rate law, describing how quickly heat flows continuously through a material as long as a temperature difference is maintained, which is why its answer comes out in watts (energy per second) instead of joules.

Thermal Conductivity of Common Materials

For the conduction mode, k spans an enormous range — good insulators trap heat by conducting it thousands of times more slowly than metals do. The table below covers typical room-temperature values for materials you'll commonly run into, ordered from the best insulator to the best conductor.

Material	k, W/(m·°C)
Air (still)	0.024
Glass Wool (insulation)	0.04
Expanded Polystyrene	0.033
Wood	0.13
Water	0.6
Brick	0.72
Glass	0.8
Concrete	1.7
Ice	2.18
Stainless Steel	16
Iron	80
Aluminum	205
Copper	401
Silver	429

A Brief History of Heat Transfer Theory

Joseph Fourier developed his law of heat conduction in 1822, building a mathematical theory of heat flow that remains essentially unchanged in engineering use today. The concept of specific heat capacity traces back further, to Joseph Black's calorimetry experiments in the 1760s, where he first distinguished the amount of heat from temperature itself — a crucial conceptual split that made it possible to define latent heat as a separate quantity from sensible (temperature-changing) heat.

Common Heat Transfer Mistakes

Using the wrong latent heat value — fusion instead of vaporization, or vice versa — is a common error, since the two differ by nearly a factor of seven for water. Forgetting that temperature stays constant during a phase change, and mistakenly trying to apply Q = mcΔT across a melting or boiling point, is another frequent mistake. Mixing up thermal conductivity units (W/(m·°C) vs. W/(m·K), which are numerically identical since both scales share the same degree size) rarely causes an actual error but often causes confusion when cross-checking a value from a different source.

Heat Transfer Terms You Should Know

Specific Heat Capacity (c) — the energy needed to raise 1 kg of a material by 1°C.

Latent Heat (L) — the energy needed to change 1 kg of a material's phase without changing temperature.

Thermal Conductivity (k) — how readily a material conducts heat; higher values mean faster heat flow.

Sensible Heat — heat that changes temperature (as opposed to latent heat, which doesn't).

Specific heat and thermal conductivity values vary somewhat with temperature and purity; the presets here are typical room-temperature values.