Conductivity Thermal And Electrical

The given problem involves three rods with different thermal conductivities, forming a series connection. To find the ratio , we must set up thermal equilibrium equations. Consider each rod:

• The first rod has conductivity , length , cross-sectional area , and its ends at temperatures and .
• The second rod has conductivity , length , cross-sectional area , and its ends at temperatures and .
• The third rod has conductivity , length , cross-sectional area , and its ends at temperatures and .

In a steady state, the heat current (Q/t) through each rod must be the same because they are in series:

1. For the first rod:
2. For the second rod:
3. For the third rod:

Equating the heat currents:

1.  (i)
2.  (ii)

From equation (i):

Therefore:

 (iii)

From equation (ii):

Let

Substitute in equation (ii):

Simplifying:

Substituting into equation(iii):

Therefore, the ratio , but is not viable. We can check other calculations.

Revelation leads to correction via symmetrics:Ratio using integral:
.