Details

Snapshot 1: Without any heat being generated, the temperature profile is linear in each layer (with the slope dependent on the thermal conductivity). The heat flux across the wall is constant, and is driven by the temperature difference between the fluids. You can shift the origin of the plot using the buttons at the bottom of the controls. The directionality for the heat fluxes is consistent with the axis in the plot.

Snapshot 2: The location of the maximum temperature and fraction of the heat being transferred to each side depends on the resistances for convection and conduction on each side.

Snapshot 3: By significantly increasing the resistances on one side (left), the location of the maximum temperature also shifts toward the same side of the wall, approaching the limit of the adiabatic boundary condition. As a consequence, most of the heat generated in the volume must exit through the opposite surface.

In a steady state, the rate of energy generated within the wall (the product between and the volume of the central layer ) equals the sum of the heat transfer rates leaving each side of the wall. Because the vector for the heat flux follows the direction of the axis in the plot (positive from left to right), the heat transfer rate leaving the left surface is equal to . The heat fluxes are described as , where is the area on each side of the wall ( plane).

Reference

[1] T. L. Bergman, A. S. Levine, F. P. Incropera, and D. P. Dewitt, Fundamentals of Heat and Mass Transfer, 7th ed., New York: Wiley, 2011.