\#4. Consider a water tank subjected to an internal heating by a hot wire of heat generation rate per unit volume, S. Assume that the tank is well-stirred and has an unknown temperature Ttank(t) that will grow with time t due to S. To prevent overheating, there is also a heat exchanger to cool off this water tank under a continuous supply of a cold water at a constant volumetric flow rate Q. The entry cold water stream is kept at temperature Tcold. Once it is in contact with the tank, a heat flux q (you figure out what it is) is transferred from the tank to the heat exchanger. The water temperature inside the heat exchanger thus becomes T hor (t) which is also unknown, so does the exit stream. In other words, the heat exchanger acts much like a Continuous Stirred Tank Reactor (CSTR). The goal here is to determine Tlank(t) and Thor(t). (i) Carry out the respective energy balances for the water tank and the heat exchanger under the unsteady state condition. You assume whatever variables and physical properties you need in your derivation. (ii) Assume that the heat exchanger is at steady state. Using this condition, you can relate Thor(t) to Tiamk(t) and then solve for Tramk(t) using (i). (iii) Determine Trank at steady state. Discuss how it is influenced by S and Tcold