HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q21 Solution: A hollow tube has a length l, inner radius and outer radius .…

QPages 98-102: Q21: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q21 Solution: A hollow tube has a length l, inner radius and outer radius .…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently apply the linear conduction formula $Q/t = KA\Delta T/L$ directly to radial flow by substituting a single cross-sectional area, ignoring that the area $A = 2\pi r l$ varies with radius. To avoid this, one must integrate $dQ = -K(2\pi r l) dT/dr$ from $R_1$ to $R_2$, which yields the logarithmic term $\ln(R_2/R_1)$ in the denominator.

A hollow tube has a length l, inner radius

R_1

and outer radius

R_2

. The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if a) the flat ends are maintained at temperature

T_1

and

T_2

T_2 > T_1

) b) the inside of the tube is maintained at temperature

T_1

and the outside is maintained at

T_2

Step-by-Step Verified Solution

**Answer:** (a) Q/t = KA(T__T_)/l (b) Q/t = 2�Kl(T__T_)/ln(R_/R_). **Step-by-Step Explanation:** (a) For flat ends (heat flows along length): Q/t = KA(T__T_)/l. (b) For radial flow (inside to outside): Q/t = 2�Kl(T__T_)/ln(R_/R_).

QPages 98-102: Q21: HC Verma: Concepts of Physics - Volume 2 Heat Transfer Pages 98-102: Q21 Solution: A hollow tube has a length l, inner radius and outer radius .…

Step-by-Step Verified Solution

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