GATE & PSUs - Mechanical Engineering (ME)

Fins & Extended Surfaces question bank (Heat & Mass Transfer)

Practice 7 free GATE & PSUs - Mechanical Engineering (ME) Heat & Mass Transfer - Fins & Extended Surfaces questions with answers and step-by-step solutions.

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Q1.
[Fins & Extended Surfaces Concept 2] A solid metal sphere of radius $R_1$ with uniform internal heat generation $q_g\text{ (W/m}^3\text{)}$ has thermal conductivity $k$. What is the temperature distribution $T(r)$ within the sphere if the surface temperature is maintained at $T_s$?

(A)
$T(r) = T_s + \frac{q_g}{6k} (R_1^2 - r^2)$
(B)
$T(r) = T_s + \frac{q_g}{4k} (R_1^2 - r^2)$
(C)
$T(r) = T_s + \frac{q_g}{2k} (R_1^2 - r^2)$
(D)
$T(r) = T_s + \frac{q_g}{3k} (R_1 - r)$
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Q2.
[Fins & Extended Surfaces Concept 7] A solid metal sphere of radius $R_1$ with uniform internal heat generation $q_g\text{ (W/m}^3\text{)}$ has thermal conductivity $k$. What is the temperature distribution $T(r)$ within the sphere if the surface temperature is maintained at $T_s$?

(A)
$T(r) = T_s + \frac{q_g}{6k} (R_1^2 - r^2)$
(B)
$T(r) = T_s + \frac{q_g}{4k} (R_1^2 - r^2)$
(C)
$T(r) = T_s + \frac{q_g}{2k} (R_1^2 - r^2)$
(D)
$T(r) = T_s + \frac{q_g}{3k} (R_1 - r)$
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