Steady-State Tubular Flow with Heat Loss

1 Steady-State Tubular Flow with Heat Loss 

Here a steady-state formulation of heat transfer is considered (Pollard, 1978). A hot fluid flows with linear velocity v, through a tube of length L, and diameter D, such that heat is lost via the tube wall to the surrounding atmosphere. It is required to find the steady-state temperature profile along the tube length. 

Consider an element of tube of length AZ, distance Z from the tube inlet as shown in Fig. 4.24. If the temperature at the inlet to the tube element is T, then the temperature at the outlet of the element can be written as T + (dT/dZ) AZ. 

The energy balance for the element of tube length can be stated as 

As shown in Sec. 1.2.5, the heat balance equation, assuming constant fluid properties, becomes 

---