Conduction Through a Composite Wall
This Demonstration calculates temperature profiles and the heat flux for steady-state conduction through four walls in series; the total wall thickness is 10 cm. The temperature of the left wall can be changed with a slider; the temperature of the right wall is fixed at 45°C. The thicknesses of the first three walls are changed with sliders, and the composition of the end wall (fiberglass, brick, or lead) is selected with buttons. The heat flux is the same through each wall. 

Download the CDF file to view the simulation using the free Wolfram CDF player.

Details

The steady-state heat flux for four walls in series was calculated from the total heat-transfer resistance. The flux is the same for each wall (since there is no heat generation), and thus the flux equation can be applied to each wall. The heat flux, conductivities, wall thicknesses, and the wall temperatures were used to determine the temperatures at the interfaces between walls.

,

,

,

where  is the total thermal resistance (),  is the wall thickness (cm),  is thermal conductivity (W/[cm K]),  is heat flux (),  is temperature (°C), and  is the thermal resistance for conduction ().