Cooling fins are used to increase the area available for heat transfer between metal wals and poorly conducting fluids such as gases. consider a fin with a wall temperature of 4900 f with a heat transfer coefficient h-120 btu/thr ft f in air of temperature t,-3400 f. the fin length is l-0.2ft and the thickness b-0.13ft. given that the thermal conductivity is k-60 btuhr ft f) the differential equation govening the heat conduction is you want to calculate the temperature profile along the fin (direction z) given that at the base (z-0) the temperature should be equal to the wall temperature and at the tip (z-l) there is negligible heat loss l)-0. you decided to use central finite differences for your calculations . use a grid of 4 segments ( 5 points at z-0, 005,01.0.15, 02) to approximate the temperature profle, determine unknowns and write a system of linear equations to be solved solve the system of equations using software and plot the profile comparing to the analytical solution given in textbooks (le. transport phenomena, bird-stewart-lightfoot) as: θ cosh( n) sinh(nc) 昜 . ldimensionless temperature).c*t-dimensionless distance, n = where θ edimensionless heat transfer coefficient. provide a table of the temperatures from numerical and analytical solutions at the 5 points increase your segments to 49 (50 points) and generate a smooth plot of the temperature profile for your parameters