In a residential heating system (see figure below), a storage tank containing 200 liters of water at a constant pressure is used as a thermal energy storage device. There is a negligible change in the volume of the water. The residential space is maintained at a constant 293 K temperature. Stored water is initially at 370 K temperature. A heater with 2 m2surface area is utilized to transfer energy from tank to the room. The overall convective heat transfer coefficient between the water inside the heater and the room is 30 W/(m2K) and it is constant. Energy in the storage tank is used until its temperature reaches 310 K. The water inside the tank is stirred to maintain a uniformly distributed temperature inside the tank. The stirrer uses 0.2 kW of power, which at the end, dissipates to the stored water as heat. Storage tank is insulated, but there is still heat loss to the surroundings over a surface area of 5 m2subject to an overall heat transfer coefficient of 2.0 W/(m2K). The outside temperature is 283 K. The heat rate from the residential space (room) to the outside may not be constant, and it is always equal to or greater than that supplied from the storage tank. The residential space remains at a constant temperature of 293 K. If the energy from storage tank is insufficient, a backup heating unit is used to maintain room temperature, which is not part of this problem, neither heat from room to outside. Neglect radiative heat transfer in all parts.
A. How long will the thermal energy storage unit provide energy to the residential space?
B. What is the steady state temperature of the tank when it transfers energy to the residential space and to the outside (heat loss)? HINT: There is a power input from the stirring work.
C. Plot the heat rate from the tank as a function of time until stored water reaches 310 K.
D. Calculate the total heat in Joules that were added to the residential space from the thermal energy storage device until stored water reaches 310 K
E. Determine the rate of heat as a function of time and the total energy added to the room from the storage tank if stored water is initially raised to a temperature of 370 K, is not used for 12 hours for residential space heating, then heating continues until stored water temperature becomes 310 K. What does your result imply about thermal energy storage?