Consider laminar flow of a fluid with Pr = 4 that undergoes a combined entrance process within a con- stant surface temperature tube of length L xfd,t with a flow rate of m. An engineer suggests that the total heat transfer rate can be improved if the tube is divided into N shorter tubes, each of length LN = L/N with a flow rate of m/N.
Determine an expression for the ratio of the heat transfer coefficient averaged over the N tubes, each experiencing a combined entrance process, to the heat transfer coefficient averaged over the single tube, hD,N /hD,1.