Answer Happy

1. Hot water at a temperature of Th is supplied to the jacket of a tank, shown in Figure-1 below. Heat is transferred at a rate of UA(Th - T(t)) from the jacket to the tank content. This input causes a change in the liquid temperature, T (t). Qin T(t) Figure-1: Water jacket heating system where Qin is the heat transfer from jacket to the tank, T(t) is liquid temperature in the tank. The tank is insulated and therefore the energy balance over the system is governed by: UA(Th – T(t)) = mcp Answer the following questions: dT (t) dt (a) Use Laplace transform to find T(t) with an initial condition of T(0) = 0 °C in terms of the variables given in this problem. (17 marks) (b) How long does it take for 500 kg of liquid from 0 °C to reach 55 °C if hot water at 90 °C circulates around the tank? The heat surface area (A) and overall heat transfer coefficient (U) are 20 m² and 1.7 kWm-²K-¹, respectively (Cp = 0.7 kJkg-¹K-¹). (8 marks)