In analyzing thermodynamic cycles involving heat exchangers, it is useful to express the heat rate in terms of an overall thermal resistance R, and the inlet temperatures of the hot and cold fluids, the heat transfer rate can also be expressed in terms of the rate equations.

(a) Derive a relation for R_1m/R, for a parallel-flow heat exchanger in terms of a single dimensionless parameter B, which does not involve any fluid temperatures but only U, A. C_b, C_c (or C _min , C _max)

(b) Calculate and plot R_1m/R, for values of B = 0.1, 1.0, and 5.0. What conclusions can be drawn from the plot?