Consider laminar flow of a fluid with Pr = 4 that undergoes a combined entrance process within a constant surface temperature tube of length L< x_fd,t with a flow rate of . An engineer suggests that the total heat transfer rate can be improved if the tube is divided into N shorter tubes, each of length L_N = 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, h_D,N / h_D,1.