## The Composite Bar

A composite bar is a bar made of two materials of thermal conductivitiesandjoined end to end, so that heat is allowed to pass from one end of one bar to the other end of the other. The cross sectional are of each material is the same, and the temperatures of each end of the bar and the intersection are steady and are as in the diagram.

The sides of the bar are perfectly lagged, so that no heat flows out of the sides of the bar. All the heat that flows in through the end A flows through the intersection of the two bars, B, and out through the end C.

This means that the heat flow out of bar AB at the intersection of the two bars, B,

equals the rate of inflow of heat into the bar BC at the intersection B,

We can write

The temperature gradient, the rate of temperature drop per unit length is inversely proportional to the thermal conductivity, so that good conductors, with higherwill experience a lower temperature drop along their length. This is illustrated foin the graph below.