Physics
Physics
Problem
A section of an exterior wall is constructed from two uniform layers perfectly bonded together: 150 mm of common brick on the outside and 80 mm of fiberglass insulation on the inside. The wall area is 12 m². On a winter day, the indoor surface of the fiberglass is at 20 °C while the outdoor surface of the brick is at −5 °C. Relevant material properties are given below. • Common brick: thermal conductivity 0.72 W/(m · K) • Fiberglass: thermal conductivity 0.040 W/(m · K) Assume one-dimensional steady conduction perpendicular to the wall surfaces and disregard any additional surface resistances. a. Determine the total thermal resistance per unit area of the composite wall section. b. Calculate the steady-state rate at which energy leaves the house through this 12 m² portion of wall. c. Estimate the total energy lost through this wall section during a 24 h period under the same conditions.Intuitive explanation
This is a steady-state heat conduction through composite layers problem. The key insight is that in steady state, the same heat flow rate must pass through both materials—they're in series thermally. Use Fourier's law () for each layer to find their individual temperature drops, then apply the constraint that the heat flow is identical across both layers to solve for unknowns like the interface temperature or total heat loss.
Intuitive explanation
This is a steady-state heat conduction through composite layers problem. The key insight is that in steady state, the same heat flow rate must pass through both materials—they're in series thermally. Use Fourier's law () for each layer to find their individual temperature drops, then apply the constraint that the heat flow is identical across both layers to solve for unknowns like the interface temperature or total heat loss.