Combined Heat transfer process

In most of the engineering applications, however, heat is transferred in successive steps by similar or different mechanisms.

For instance, let us consider the case of heating of water in a tube laid in a heat exchanger (or cooling of hot fluid in shell by CW). The water will receive heat from the products of combustion that emit and absorb radiation. The heat will flow by combination of different modes through successive steps as indicated below (fig 1).

It may be clarified here that the tube wall surface temperatures are different than the fluid temperatures on the respective sides. This can be explained by assuming that a thin layer of fluid adheres to the wall on both sides. The temperature gradient exits only within this thin layer.

Considering the temperatures at each step and resistance to heat flow through each step (R) where R1, R2 and R3 are resistances through step 1, 2 & 3 respectively. Since the same quantity of heat is flowing through each step we obtain:

This equation represents the heat flow from the hot fluid to water. Here U is known as the Overall unit conductance or the Overall coefficient of heat transfer.