- #1

knc

- 20

- 0

## Homework Statement

## Homework Equations

[tex] P = k A \frac{dT}{dx}[/tex]

## The Attempt at a Solution

*a)*

Assuming steady state transfer, energy transfers through rods at the same rate everywhere.

Letting

**T**be the temperature at the point of welding.

[tex] P_1 = k_1 A \frac{T_h-T}{L} \\ P_2 = k_2 A \frac{T - T_c}{L} [/tex]

Setting rates equal to represent steady-state system:

[tex] k_1 A \frac{T_h-T}{L} = k_2 A \frac{T - T_c}{L} [/tex]

Solving for T:

[tex] T = \frac{k_1 T_h + k_2 T_c}{k_1 + k_2} [/tex]

Plugging this into either equation for individual rod:

[tex] P = \frac{T_h - T_c}{L} \frac{k_1k_2}{k_1 + k_2} A [/tex]

*a)*

I don't know where to begin with part B. I would imagine I would try to find a ratio between the conductors in series and parallel.

Thanks in advance