A cylindrical uranium fuel rod of radius 5 mm in a nuclear

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A cylindrical uranium fuel rod of radius 5 mm in a nuclear is generating heat at the rate of 4 × 107 W/m³. The rod is cooled by a liquid (convective heat transfer coefficient 1000 W/ m²K) at 25°C. At steady state, the surface temperature (in K) of the rod is

1. 308
2. 398
3. 418
4. 448

Correct Option: B

Given data: r = 0.005 m
d = 2r = 2 × 0.005 = 0.010 m

q₆ = 4 × 10⁷	W
	m³

h₀ = 1000	W
	m²K

T₀ = 25°c
For steady state,
Rate of heat generation in the rod} = Rate of convection H.T. from rod surface to fluid q_G × volume of rod = h₀ A(T_s – T₀)

q_G ×	π	d²l = h₀ × πdl (T_s - T₀)
	4

d.q_G (T_s - T₀)

= h₀

h₀	.010 × 4 × 10⁷	= 1000 (T_s - 25)
	m²4

T_s – 25 = 100
T_s = 125° c or 398 K