Question

Considering the analogy between electrical circuit and thermal circuit, show your approach to derive an expression for the thermal resistance for a wall

Answer 1

Thermal resistance for a wall depends on the material, the thickness of the wall and the cross-section area.

Step-by-step explanation:

Current flow and heat flow are very similar when we are talking about 1-dimensional energy transfer. Attached you can see a picture we can use to describe the heat flow between the ends of the wall. First of all, a temperature difference is required to flow heat from one side to the other, just like voltage is required for current flow. You can also see that
`R_(th)` represents the thermal resistance. The next image explains more about the parameters which define the value of the thermal resistances which are the following:

1. Wall Thickness. More thickness, more thermal resistance.
2. Material thermal conductivity (unique value for each material). More conductivity, less thermal resistance.
3. Cross-section Area. More cross-section area, less thermal resistance.

A expression to define the thermal resistance for the wall is as follows:
`R_(th) =(l)/(Ak)`, where l is the distance between the tow sides of the wall, that is to say the wall thickness; A is the cross-section area and k is the material conducitivity.