Calculating Effective Thermal Conductivity

[LoopQG]

Homework Statement

Quick question about Thermal Conductivity,

I have 2 plates each with thickness x, with respective thermal conductivities A and B. what is the effective thermal conductivity?

Homework Equations

Q/(delta t) = -k(Area)dT/dx where k= thermal conductivity A or B T=temperature Q= heat t=time

The Attempt at a Solution

Can I just add the thermal conductivities? solve the equation for k in both A and B cases taking into account that when solving for B T initial is different.

 

[mark726]

Hello, thank you for your question. The effective thermal conductivity in this case would not simply be the sum of the individual thermal conductivities. It would be more accurate to use the weighted average of the two conductivities, taking into account the relative thickness of each plate. This can be calculated using the following equation:

k_eff = (A * k_A + B * k_B) / (A + B)

Where k_eff is the effective thermal conductivity, k_A and k_B are the thermal conductivities of the two plates, and A and B represent their respective thicknesses.

Additionally, when solving for the temperatures, it is important to consider the boundary conditions at the interface between the two plates. This may require using a different equation or taking into account the temperature difference between the two plates.

I hope this helps. Let me know if you have any further questions.