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Two metal cubes with 3cm edges of copper and aluminum are arranged as shown if figure (k cu =385W/m-K,K Al =209W/m-K) then find the total thermal current from one reservoir to the other

Two metal cubes with 3cm edges of copper and aluminum are arranged as shown if figure (kcu=385W/m-K,KAl=209W/m-K) then find the total thermal current from one reservoir to the other
 

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2 Answers

Gaurav Gupta
askIITians Faculty 686 Points
3 years ago
564-1588_Capture.JPG
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

Let the thermal resistance of Al cube be R1.
Let the thermal resistance of Cu cube be R2.
Applying the formula of thermal resistance,
R = l/KA
Thermal resistance of Al will be
R1 = l/KA
R1 = 3 × (10^-2)/209 × (3 × 10^-2)^2
R1 = 0.159 K/W
Calculation of thermal resistance of Cu
R2 = l/KA
R2 = 3 × (10^-2)/385 × (3 × 10^-2)^2
R2 = 0.086 K/W
From the figure we can clearly see that the given two resistances are connected in parallel way, so their equivalent resistance will be -
R = (R1R2/R1 + R2)
R = 0.159 × 0.086/(0.159 + 0.086)
R = 0.055 K/W
the total thermal current from one reservior to the other = Thermal Difference/Thermal Resistance
= (100 – 20)/0.055
= 1.45 × 10^3 W
Hence, the required answer is 1.45 × 10^3

Thanks and Regards

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