# Identify Temperature Profiles for Heat Generation or Conduction through Composite Walls

Heat is generated at a constant rate in either wall or (whichever wall is slowly changing color intensity). The object of this Demonstration is to identify the correct steady-state temperature profile in each wall. The thermal conductivity for each wall is indicated on the figure, and the contact resistance between the walls is given. The left side of wall is insulated and heat is transferred from the right side of wall to flowing air at 20 °C. Use buttons to select the correct temperature profile for each wall in sequence; check the "hint" box for help. Once you select a temperature profile for a wall, you must check "solution" before clicking the "next" button; you cannot move backward. Click the "new problem" button to start over with a new set of conditions.

### DETAILS

Heat is conducted through a composite wall with heat generation in either wall or wall . Differential equations determine the temperature profile of each wall. View Figure 1 to see a labeled diagram of surface temperatures. When heat is generated in wall :
,
,
,
where is temperature (°C), is wall thickness (m), is the volumetric heat generation rate (), is the thermal conductivity in wall (), is the thickness of wall (m), and is the surface temperature of the right side of wall (°C).
A thermal circuit is considered starting from the right side of the wall with heat transfer to the air by forced convection. If wall generates heat, then the heat flux is
.
The heat flux when wall generates heat is:
,
where is heat flux ().
For generation in either wall, the surface temperatures are:
,
,
,
where is the heat transfer coefficient (), and is the contact resistance ().
Figure 1:
For heat generation in wall , the rest of the surface temperatures are:
,
,
the solution to the differential equations.
The heat flux when wall generates heat is:
.
and
,
,
.
For heat generation in wall , the remaining surface temperatures are:
the solution to the differential equations,
.
Figure 2:

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