Consider a single story $($one floor$),30ft30ft$ house with $8$ ft high walls. The house contains $6$ double pane windows. The roof and floor are well insulated. The walls are standard construction with $\frac{1}{2}"$ sheetrock, R$19$ insultation in a $26$ wall, and $\frac{1}{2}"$ plywood. On a cold, windy winter night the outside air temperature is $0F$ and the inside air temperature is $65F.$

When the inside air temperature drops to $60F,$ the heating system turns on$.$ The house is heated with baseboard hot water heaters. The supply temperature of the hot water is $150F.$ The water flows through a $\frac{3}{4}"$ diameter copper pipe with Aluminum fins and the rate of heat loss to the surroundings is $400BT\frac{U}{h}r$ per linear foot of baseboard heater at a volume flow rate of $4$ GPM$.$

Compute the rate of heat loss from the air inside to the outside. Consider only conduction and convection. Make assumptions as necessary.

Compute the ratio of heat loss through the walls to that through the windows.

Determine the linear feet of baseboard heaters required to raise the inside air temperature to $70F$ in $30$ minutes

Determine the temperature on the outside of the copper pipe.

Determine the temperature of the water exiting the baseboard heater.

Conceptual Questions

Discuss ways in which the rate of heat loss to the outside air can be reduced.

Discuss the mechanisms of heat transfer occurring with the baseboard heating system

Discuss ways in which the heat transfer rate per linear foot could be increased if necessary.