A straight fin of uniform cross section is fabricated from a material of thermal conductivity 50 W/m*K, thickness w=6mm, and length L=48mm, and is very long in the direction normal to the page. The convection heat transfer coefficient is 500 W/m2 *K with the ambient air temperature of T∞=30C. The base of the fin is maintained at Tb = 100C, while the fin tip is will insulated.
A). Using a finite-difference method with a space increment of 4mm, estimate the temperature distribution within the fin. Is the assumption of one-dimensional heat transfer reasonable for this fin?
B). Estimate the fin heat transfer rate per unit length normal to the page.
C). Using the finite-difference mesh of part (A), compute and plot the fin temperature distribution for values of h = 10, 100, 500, and 1000 W/m2 *K. Determine and plot the fin heat transfer rate as a function of h.