Heat Transfer Calculator: Conduction, Convection, Radiation

How does heat move?

Heat moves from hot to cold in three ways: conduction, convection and radiation. Real problems usually involve all three, but each has its own relation.

Conduction: Fourier's law

If the two faces of a solid wall are at different temperatures, heat is conducted through it: Q = k × A × (T₁ − T₂) / L, where k is the thermal conductivity of the material, A the area and L the thickness.

Example: a wall 3 m × 5 m and 30 cm thick with a conductivity of 0.9 W/(m·K) and faces at 16 °C and 2 °C passes Q = 0.9 × 15 × 14 / 0.3 = 630 W.

With several layers, each acts as a thermal resistance (R = L / (k × A)) and the resistances add like electrical resistors in series. Convection at the surfaces joins the same chain as 1 / (h × A). The tool handles up to three layers and gives the interface temperatures.

For cylindrical walls such as pipes the area grows with radius, so the relation is logarithmic: Q = 2πkL × (T₁ − T₂) / ln(D₂ / D₁).

Convection: Newton's law of cooling

Heat transfer between a surface and the air or water touching it is Q = h × A × (T_s − T_∞). The coefficient h depends on the flow, not the material: small in still air and very large in fast flowing water.

Radiation: the Stefan-Boltzmann law

Every surface emits radiation in proportion to the fourth power of its temperature. The net exchange with its surroundings is Q = ε × σ × A × (T_s⁴ − T_surr⁴). Temperatures are in kelvin, σ = 5.670374 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant and ε the emissivity of the surface.

Example: a person with a surface area of 1.4 m², emissivity 0.95 and surface temperature 30 °C loses 152 W by radiation in a room whose walls are at 10 °C. With walls at 25 °C the loss falls to about 41 W. That is why we feel colder in winter at the same air temperature.

Limits

The relations are for steady state, one dimensional heat flow. Transient heating and cooling, finned surfaces, view factors between two surfaces and the calculation of convection coefficients are outside this tool.