Heat transfer mechanisms problem; Conduction

AI Thread Summary
The discussion revolves around a heat transfer problem involving two identical metal rods. In the first scenario, the rods are welded end to end, resulting in a heat transfer of 10J over 2 minutes. When the rods are positioned side by side, the time required to conduct the same amount of heat is calculated to be 30 seconds. This is due to the difference in the area-to-length ratio, which is four times greater in the side-by-side configuration compared to the end-to-end setup. The solution involves understanding conduction in series versus parallel pathways to derive the time required for heat transfer.
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Homework Statement



Diagram is attached showing part (a) and part (b)
Two identical rectangular rods of metal are welded end to end (a), with temperature of T1=0 0C on the left side and a temperature of T2=100 0C on the right hand side. In 2.0 minutes, 10J is conducted at a constant rate from the right side to left side. How much time would be required to conduct 10 J if the rods were welded side to side (b).

Homework Equations



P=kA(T1-T2) / L


The Attempt at a Solution



Now I know that the answer is 30 seconds or 1/4 of a minute. This means that the ratio of A/L for the first diagram is 4 times greater than the ratio of A/L for the second diagram, as the thermal conductivity and temperature difference is the same. However I have no idea how that result was achieved. Can anyone please provide me with help to find the solution.
 

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please answer
 
when the two metal rods are placed side to side , area of cross section together as -
new A = twice of previous A

and length is only the length of one length (length wise)

initially it was ..end to end ..so it was 2L
so..effective is the factor four
 
In part "a" the rods are in series and in part "b" the rods are in parallel so you will need to review conduction in series and parallel pathways. q in part "a" is 10J/120 sec in part "b" q is 10J/ X sec. You have two equations set L/(K*A) = L/(K*A) and solve for T.
 
OOPS! Sorry, solve for X in Seconds not T
 

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