Conjugate heat transfer in laminar tube flow with convective boundary conditions is considered analytically.
The steady state problem involving two-dimensional wall and axial fluid conduction is solved
using separation of variables for a thick walled cylindrical pipe. The effects of the wall thickness, external
Biot number and wall-to-fluid thermal conductivity ratio are investigated on the heat flux, fluid bulk and
wall temperatures. Results are presented for the cases when the wall thickness is between 0.1 and 2, Biot
number ranging between 0.1 and 10, and the ratio of wall-to-fluid thermal conductivity between 3 and
100. These parameters are found to significantly affect the heat transfer characteristics at the thermal
entrance region, for instance, increase in wall thickness results in reduced heat flux while increase in Biot
number and the ratio of the wall-to-fluid thermal conductivity result in increased heat flux. Decrease in
wall thickness, increase in both Biot number and the ratio of the wall-to-fluid thermal conductivity
correspond to decreased fluid bulk and wall temperature profiles.