Please help! The fin model that has been standard since the beginning of time is
ID: 1862204 • Letter: P
Question
Please help!
The fin model that has been standard since the beginning of time is described in Essays 6 and 6A. The stripped-down model, shown in its most primitive form. is illustrated at the bottom of the preceding page. The heat flow in the model is confined to the x-direction. and the temperature of the fin is modeled as a function of x alone. That temperature variation is given by T(x)-Tair/Tbase-Tair=cosh mL(1-x/L)/cosh mL where m = and cosh is the hyperbolic cosine which can be found in most hand-held calculators. Otherwise, go to Google and if you need cosh(2.5), type that and get 6.13228. Suppose that the temperature of the fin tip (x = L) is measured to be 31.2 C. Also. Tbase is 65.3 C and Tair is 22.5 C. Find the value of the heat transfer coefficient h if the thermal conductivity k is 16 W/m-C, the fin length L is 15 mm and the thickness t is 0.5 mm.Explanation / Answer
(31.2-22.5)/(65.3-22.5) = cosh(m*0.015*0)/cosh(m*0.015) = 1/coh(m*0.015)
0.203 = 1/coh(m*0.015)
coh(m*0.015) = 4.926
e^(0.015m) + e^(-0.015m) = 9.85
e^(0.03m) - 9.85*e^(0.015m) + 1 = 0
Let e^(0.015m) = x
x^2 - 9.84x + 1 = 0
Solving this we get
x = 9.737 or 0.1027
0.015m = 2.276 or -2.27
Since negative value is not possible
m = 151.73
2*h/(16*0.0005) = 151.73^2
h = 92.088