# A uniform cylindrical bar is heated by a heating element along its entire length… 1 answer below »

Problem 3. A uniform cylindrical bar is heated by a heating element along its entire length, which generates q watts/m3 . The sides of the bar are insulated and both ends of the bar are open to the ambient air. The heat conductance varies linearly along the length of the bar as shown below. a. (10 pts) Set up the DE and the BC’s for the heat transfer problem BVP equation. b. (25 pts) Obtain an approximate solution for the steady state temperature distribution using Galerkin Finite Elements. Use 4 equal-sized linear elements. The physical properties of the system are: Length of the cylinder L = 2 m, Diameter of the cylinder D = 0.2 m, Thermal Conductivity k = 50 +50x W/m-K, Ambient air temperature = 20 deg C Heating Rate q=3000 W/m3 Convective heat transfer coefficient h =