Consider the annular fin shown. Suppose that k =30 W/m/K, h = 1000 W/m2/K, r =3

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Consider the annular fin shown. Suppose that k =30 W/m/K, h = 1000 W/m2/K, r =3 cm, t = 3 mm and ro =4.5 cm. The temperature at the base of the fin is Tb = 350 degree and the fluid temperature is Tinfinity = 25 degree . Using the finite difference method, write an equation for the steady state temperature of each of the 10 nodes shown in the figure. Write a program (or use excel) to solve your system of equations, and present a table of the node temperatures. Determine the thermal resistance of the fin from your numerical results. As was determined in Homework 2, the conduction equation for the annular fin is: d2theta/deta2 + 1/eta d theta/deta 2Bi/a2 theta = 0, where theta = T-Tinfinity/Tb-Tinfinity, Bi = ht/k, a = t/ri and eta = r/ri, What are the necessary boundary conditions to solve this equation for theta? Solve the fin equation using the ODE solver in Matlab (Octave). Plot the temperature profile theta(eta). Using your numerical solution for theta(eta), determine the thermal resistance of the fin. Rfin = 1/2pikt(-d theta | delta|eta=1) How do the results of part A) and B) compare?

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This might help you:-

http://www.digikey.co.uk/suppliers/uk/advanced-thermal-solutions.page?lang=en

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