A water heating loop consists of a water tank and an electric heater of power P = 400 Watts. The tank is filled with m=20 kg of water whose specific heat is C p = 4200 J/kg K. Water from the tank outlet flows through a PVC pipe(well insulated) to the electric heater at a rate of q = 0.1 kg per second.. The electric heater supplies energy to the water and hence the water heats up. This hot water again flows back to the tank through another PVC pipe to complete the cycle. There is some energy loss through the tank. The process continues for a long time until the water temperature in the tank reaches a steady state. The room temperature is T = 25 o C. The overall heat transfer coefficient for the tank is U = 5 W/m 2 K and the surface area of the tank is A = 0.3 m 2 . (a) Write the energy balance equation for calculating the tank water temperature T o that varies with time t . (Assume that both inlet and outlet water temperatures only vary with time. ) [ Do not solve, just write the equation] (b) If the flow rate increases, will the time taken for temperature to reach steady state be less, more or the same ? (Answer logically without calculating). (c) If the heater power increases, will the time taken for temperature to reach steady state be less, more or the same ? (Answer logically without calculating). [6 + 2 + 2 = 10]

A water heating loop consists of a water tank and an electric heater of power P = 400 Watts. The tank is filled with m=20 kg of water whose specific heat is C_p = 4200 J/kg K. Water from the tank outlet flows through a PVC pipe(well insulated) to the electric heater at a rate of  q = 0.1 kg per second.. The electric heater supplies energy to the water and hence the water heats up. This hot water again flows back to the tank through another PVC pipe to complete the cycle. There is some energy loss through the tank. The process continues for a long time until the water temperature in the tank reaches a steady state. The room temperature is T = 25^o C. The overall heat transfer coefficient for the tank is U = 5 W/m²K and the surface area of the tank is  A = 0.3 m^{2 .}

 

(a) Write the energy balance equation for calculating the tank water temperature T_o that varies with time t .  (Assume that both inlet and outlet water temperatures only vary with time. )  [ Do not solve, just write the equation]

 

(b) If the flow rate increases, will the time taken for temperature to reach steady state be less, more or the same ? (Answer logically without calculating).  

 

(c) If the heater power increases, will the time taken for temperature to reach steady state be less, more or the same ? (Answer logically without calculating).  

                                                                                       [6 + 2 + 2 = 10]