It is desired to develop a simple model for predicting the temperature-time history of a plate during the drying cycle in a dishwasher. Following the wash cycle the plate is at Tp(t) = Tp(0) = 65°C and the air in the dishwasher is completely  saturated  (¢oo  = 1.0)  at  Too  = 55°C. The values of the plate surface area As, mass M, and specific heat c are such that Mc/As = 1600 J/m2 · K.

(a) Calculate the average mass transfer convection coefficient hm for the evaporation process.

(b) Calculate the average heat transfer convection coefficient h.

(c) Do the values of hm and h satisfy the heat-mass analogy?

(d) If the relative  humidity  of  the  ambient  air  at 295 K were increased from 0 (dry) to 0.50, but

(a) Assuming the plate is completely covered by a thin film of water and neglecting the thermal resistances of the film and plate, derive a differential equation for predicting the plate temperature as a function of time.

(b) For the initial conditions (t = 0) estimate the change in plate temperature with time, dT/dt (°C/s), assuming that the average heat transfer coefficient on the plate is 3.5 W/m2 · K.