An aluminium pot whose thermal conductivity is 237 W/m. K has a flat, circular bottom

with diameter 15 cm and thickness 0.4 cm. Heat is transferred steadily to boiling water in

the pot through its bottom at a rate of 1400 W. If the inner surface of the bottom of the pot

is at 105 °C, determine the temperature at the outer surface of the bottom of the pot

T₁ = 378.33 k = 105.33°C

Explanation:

From Fourier's Law of heat conduction, we know that:

Q = - KAΔT/t

where,

Q = Heat Transfer Rate = 1400 W

K = Thermal Conductivity of Material (Aluminum) = 237 W/m. k

A = Surface Area through which heat transfer is taking place=circular bottom

A = π (radius) ² = π (0.15 m) ² = 0.0707 m²

ΔT = Difference in Temperature of both sides of surface = T₂ - T₁

T₁ = Temperature of outer surface = ?

T₂ = Temperature of inner surface = 105°C + 273 = 378 k

ΔT = 388 k - T₁

t = thickness of the surface (Bottom of Pot) = 0.4 cm = 0.004 m

Therefore,

1400 W = - (237 W/m. k) (0.0707 m²) (378 k - T₁) / 0.004 m

(1400 W) / (4188.14 W/k) = - (378 k - T₁)

T₁ = 0.33 k + 378 k

T₁ = 378.33 k = 105.33°C