Question

Annular aluminum fins (K=240 W/m.K) of rectangular profile are attached to a circular tube having an outside diameter of 50 mm and an outer surface temperature of 200 C. The fins are 4 mm thick and 15 mm long. The system is in ambient air at a temperature of 20 C, and the surface convection coefficient is 40W/m².K.

a) What is the heat transfer from one fin? Use the fin efficiency chart.

Answer 1

The heat transfer from one fin is zero.

Step-by-step explanation:

To calculate the heat transfer from one fin, we can use the equation: Q = hA(θ₁-θ₂), where Q is the heat transfer, h is the surface convection coefficient, A is the surface area of the fin, θ₁ is the temperature difference between the fin surface and the surrounding air, and θ₂ is the temperature difference between the fin surface and the circular tube.

First, calculate the surface area of the fin: A = length x thickness = (0.015 m)(0.004 m) = 6 x 10^-5 m².

Next, calculate the temperature difference between the fin surface and the surrounding air: θ₁ = (200°C - 20°C) = 180°C.

Finally, calculate the temperature difference between the fin surface and the circular tube: θ₂ = (200°C - 20°C) = 180°C.

Plugging in these values, we get: Q = (40 W/m².K)(6 x 10^-5 m²)(180°C - 180°C) = 0 W.