Laminar Flow Heat Transfer with Axial Conduction in a Circular Tube: a Finite Difference Solution

A finite difference technique is developed for evaluating the rate of heat transfer in the thermal entrance region of ducts with axial conduction. The pipe is assumed to extend from minus to plus infinity, while the velocity profile is fully developed. The boundary condition selected is a uniform heat flux for z greater than or equal to 0, while the wall temperature is kept uniform and equal to its minus infinity value for z less than 0. The results show that axial conduction and heat losses from the unheated section of the pipe significantly affect the temperature profile at the inlet of the heated part lower than the local mixed mean temperatures immediately downstream from the start of the heating. It is found that the performance of this type of heat exchanger can be described by a new parameter as an alternative to the usual Nusselt number.