A rigid tank of cold fluid sits in a room at (300 K = T..). The fluid is initially at (180 K = T.). THe luis temperature is observed to vary with time as: Tfluid(t) = T..-(T..-T.)exp[-t/time constant(3600s). The energy absorbed by the tank wall is negligible. Assume the tank wall thickness is constant and that the tank inner surface temperature is the same as the fluid temperature. Plot Ffluid(t), Tsurface(t) and Q(t). Given: Tank surface area = 2.2 m^2, wall thickness =.11m, wall thermal conductivity = .0014 kW/m-K, and the surface convection coefficient = .0005 kW/m^2-K.
a) Find the fluid Tfluid and outer surface Tsurface and the heat transfer rate versus time for t= 30 minutes and t = 3 hours.
b) Determine the total amount of heat transferred over the period of 0-->3 hours, Q (kJ)