# Heat Transfer – Conduction of Heat

Conduction of heat in a solid wall is expressed using Fourier's equation for heat conduction,

T : Temperature at a point in wall
θ : Time
k : Thermal Conductivity of wall material
A : Cross sectional area of the element around the point
x : Distance perpendicular to area element

For steady state heat transfer this equation becomes,

Q : Heat transfer rate

This equation can be further developed to express temperature profiles in various geometries with one dimensional heat transfer.

### Heat conduction across flat wall

Assuming that thermal conductivity 'k' is independent of temperature and location and A is independent of location, as is the case for a solid wall with constant cross sectional area.

### Radial heat conduction across a hollow cylinder

For radial geometry of a hollow cylinder, following equation expresses the heat transfer rate.

Integral of this equation from inner radius r1 to outer radius r2 represents the total heat transfer across the cylindrical wall.

N = length of the hollow cylinder

T1 and T2 are inner and outer wall temperature of the hollow cylinder.