Radius of a metallic rod varies with x (distance from end A) as r = ( x + 1 ) 3/2 m . End A and B of rod are maintain at 100°C and 0°C respectively. Thermal conductivity and length of rod are π 3 W

Question

Radius of a metallic rod varies with x (distance from end A) as $r = (x + 1)^{3/2} m$ . End A and B of rod are maintain at 100°C and 0°C respectively. Thermal conductivity and length of rod are $\frac{3}{π} W / m - K$ and 2 m respectively. Assume steady state flow of heat in rod and rod is covered with adiabatic coating :-

TestHub · Accepted Answer

A ( x ) = π ( x + 1 ) 3 , k = π 3 ​ R ( 0 , x ) = ∫ 0 x ​ k A ( x ) d x ​ = 6 1 ​ ( 1 − ( x + 1 ) 2 1 ​ ) R ( 0 , 2 ) = 27 4 ​ K/W Q ˙ ​ = 4/27 100 ​ = 675 W  = 600 W R ( 0 , 1 ) = 8 1 ​ ⇒ T ( 1 ) = 100 − 675 ( 8 1 ​ ) ≈ 15. 6 ∘ C R ( 1 , 2 ) R ( 0 , 1 ) ​ = 4/27 − 1/8 1/8 ​ = 5 27 ​ Thus C and D are correct.

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