Question

Asked Feb 17, 2019

A rectangular fin 1.0 ft long, 1.0 ft wide, and 2in. thick loses heat to the atmosphere at70 F. The base of the fin is at 270 F.If h = 2Btu/h*ft2* F and the thermal conductivity of the fin is 24Btu/h*ft* F, find:

(a) The fin efficiency.

(b) The total rate of heat loss from the fin.

Ans. (a) 70.5%. (b) 712 Btu/h.

Step 1

Given that

Thermal conductivity=k=24 Btu/h.ft.^{0}F

Heat transfer coefficient=h= 2 Btu/h.ft^{2}.^{0}f

Atmospheric temperature = T_{∞}=70^{0}F

Base temperature = T=270^{0}F

Length=L= 1 ft, width=W= 1 ft and thickness=t= 2 in=(2/12 ft)

Part (a):

The fin efficiency is calculated as:

Step 2

L_{c} is called as correction length used when heat transfer takes place from the tip of the fin, t is thickness and P is the perimeter of the rectangular fin which is 2(W+t) and A is area of rectangular fin, is A=tW

Note that thickness is comparable of the width so in this question, in the calculation of the perimeter and area, thickness is considered.

Now the calculations are given below for the fin efficiency

Step 3

Put the values, fin ...

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