Answer Happy

(4) Consider the pellet tank system shown below. The fluid volume is small and its temperature change cannot be neglected. Pellets A and B have the same values for area A, mass M, heat capacity C and heat transfer coefficient h. The bath fluid has mass Mr and heat capacity Cf. At time zero, pellet A is dropped into the bath with a temperature of 250 °C. Pellet B was already in the bath and is at the same initial temperature as the bath fluid (25 °C). (a) Letting TA, TB and T₁ represent the temperatures of pellet A, pellet B, and the bath fluid respectively as functions of time, write the differential equations and initial conditions for the thermal behavior of this system. Neglect any heat transfer between the bath and surroundings. (b) Draw a block diagram for this system. Separate scopes should be indicated to plot TA, TB and Tr.