An insulated frame wall of a house has an average thermal conductivity of 0.0318 Btu/h-ft^2-R degrees. The wall is 6 in thick and it has an area of 160 ft^2. The inside air temperature is 70 degrees F and the heat transfer coefficient for convection between the inside air and the wall is 1.5 Btu/h-ft^2-R degrees. On the outside of the wall, the convection heat transfer coefficient is 6 Btu/h-ft^2-R degrees and the air temperature is -10 degrees F. Ignoring radiation, determine the rate of heat transfer through the wall at steady-state in Btu/h© BrainMass Inc. brainmass.com March 5, 2021, 12:38 am ad1c9bdddf
** Please see the attached document for the formatted calculations **
At steady state, the convection heat transfer rate into the wall must be equal to the rate at which heat is conducted through the wall and that must be equal to the rate at which heat is removed from the wall by convection on the outside. We can write 3 eqns in 3 unknowns: Newton's Law of Cooling for the inside and outside surfaces and Fourier's Law of Conduction for heat transfer through the wall. The three unknowns are the inside and outside wall surface temperatures and the heat transfer rate.
This solution explains a thermodynamics question on heat transfer and includes calculations.