Question

1. A fin with a diameter of 5 mm, a length of 100 mm, and a thermal conductivity of 133 w/m"C is attached to a base plate, which is at 200 oC. The fin is surrounded by a fluid at 20 ° C, and has a convection heat transfer coefficient of 30 W/(m2. c). 1.1 compute the temperature of the rod at 20 mm, 60 mm, and 100 mm points from the base 1.2 compute the total heat transfer rate from the fin

Answer 1

Considering the case of Convection Heat Transfer, we will use mentioned formula ;

Here m² = h.P/k.A_c

Given

Heat transfer cofficient (h) = 30 W/(m².^oC)

Thermal Conductivity (k) = 133 W/(m.^oC)

Perimeter (P) = 2.pi.r = 2*3.14*0.025 = 0.157 m

Crossection Area (A_c) = pi.r² =1.96*10^-3

thus, m² = h.P/k.A_c

m = 4.25

Using formula for the table we get

for x = 0.2

For x=0.6

For x=1

To calculate total heat transfer rate from fin we use given formula from table, we get

q = 221.61 W