A straight fin of uniform cross section is fabricated from a material of thermal conductivity k = 5 W/m*K, thickness w = 20 mm and lenghth L = 200 mm. The fin is very long in the direction normal to the page. The base of the fin is maintained at Tb = 200 degrees C, and the tip conditions allow for convection (case A of Table 3.4), with h = 500 W/m2*K and T∞ = 25 degrees C.
(a) Assuming one-dimensional heat transfer in the fin, calculatethe fin heat rate, qf` (W/m), and the tip temperature TL. Calculate the Boit number for the fin to determine Whether the one-dimensional assumption is valid.
(b) Using the finite-element method of FEHT, perform a two-dimensional analysis on the fin to determine the fin heat rate and tip temperature. Compare your results with those from the one-dimensional, analytical solution of part (a). Use the View/Temperaure Contours option to display isotherms, and discuss key features of the corresponding temperature field and heat flow pattern. Hint: In drawing the outline of the fin, take advantage of symmetry. Use a fine mesh near the base and a coarser mesh near the tip. Why?
(c) Validate your FEHT model by comparing predictions with the analytical solution for a fin with thermal conductivities of k = 50 W/m*K and 500 W/m*K. Is the one-dimensional heat transfer assumption valid for these conditions?