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 (ϕ∞ = 1.0) at T∞ = 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) 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 (oC/s), assuming that the average heat transfer coefficient on the plate is 3.5 W/m2 ∙ K.