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Two identical rods AB and CD, each of le...

Two identical rods AB and CD, each of length L are connected as shown in figure-4.22. Their cross-sectional area is A and their thermal conductivity is k. Ends A, C and D are maintained at temperatures `T_(1),T_(2) and T_(3)` respectively. Neglecting heat loss to the surroundings, find the temperature at B.

Text Solution

Verified by Experts

In steady state we use
`|(dQ)/(dt)|_(AB)=|(dQ)/(dt)|_(BC)+|(dQ)/(dt)|_(BD)`
`implies (kA(T_(1)-T_(B)))/(L)=(kA(T_(B)-T_(2)))/(L//2)+(kA(T_(B)-T_(3)))/(L//2)`
`implies T_(1)-T_(B)=2T_(B)-2T_(2)+2T_(B)-2T_(3)`
`implies T_(B)=(T_(1)+2T_(2)+2T_(3))/(5)`
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