Question

A 10 cm long fin with a square cross section and width of w= 1 cm is attached to a base with a constant temperature of �" = 127 ℃. The fin is made out of copper with the thermal conductivity of � = 400 ��#$�#$ and is insulated at the tip. An air flow is blowing over the fin is with the temperature of �! = 27℃, Reynolds number of 20000 and the Pr number of 0.7. What is the heat dissipation through the fin?

Answer 1

2.1145 watts.

Step-by-step explanation:

Ok, we are given the following data or parameters or infomation which is going to help us in solving this particular Question efficiently, they are;

(1). "A 10 cm long fin with a square cross section and width of w= 1 cm is attached to a base with a constant temperature, Tb of 127°C."

(2). "The fin is made out of copper with the thermal conductivity, k of = 400 "

(3). "Reynolds number of 20000 and the Pr number of 0.7." And the temperature at infinity = 27°C.

So, in order to solve this question, we are going to make use of Hilpert equation.

Step one: determine the transfer coefficient. This can be done by following the equation below;

hLc/k = c × Re^0.675 × p^1/3.

(Lc = w = 0.01).

h × 0.01/ 0.0298 = 0.102 × 20,000^ 0.675× 0.7^1/3.

h = 215.96 w/m^2.k.

Step two: Calculate the heat dissipation from the equation below;

The heat dissipation = √(h × p × kw × A) × j × tanh (m × l).

The heat dissipation = √( 215.96 × 0.04 × 400 × 0.0001) × 100 × tanh (14.965 × 0.1).

=> The heat dissipation = 2.1145 watts.