Answer Happy

XO 8 Consider a long solid cylinder with an outer radius, R, length, L, and thermal conductivity, k, subject to a uniform volumetric thermal energy generation as shown. The outer surface is at a constant temperature as shown. Assuming steady state conditions and 1-D heat transfer, determine the following. Tr=R Tr=R = 85 °C r = R R = 0.7 m w L = 10 m k q= 2.0E+05 W/m³ k= 30 W/mK a) Write the general form of the heat diffusion equation, and cancel out all terms that are able to be ignored in the analysis of this plane wall. (worth 5 of 45 total points) b) Obtain the general solution to the differential equation (i.e. you should have an equation in terms of unknown constants) (worth 10 of 45 total points) c) How many boundary conditions are needed to solve this differential equation? (worth 2 of 45 total points) d) Write the boundary condition(s) needed to solve this differential equation. (worth 13 of 45 total points) e) Using your boundary condition(s) from part c and general solution from part a, determine the values of your unknown constant(s). You should arrive at final number for the constantle and induidel bereits of those VIZIO

XO R= 0.7 m L = q= k = 10 m 2.0E+05 W/m³ 30 W/mK TL a) Write the general form of the heat diffusion equation, and cancel out all terms that are able to be ignored in the analysis of this plane wall. (worth 5 of 45 total points) b) Obtain the general solution to the differential equation (i.e. you should have an equation in terms of unknown constants) (worth 10 of 45 total points) c) How many boundary conditions are needed to solve this differential equation? (worth 2 of 45 total points) d) Write the boundary condition(s) needed to solve this differential equation. (worth 13 of 45 total points) e) Using your boundary condition(s) from part c and general solution from part a, determine the values of your unknown constant(s). You should arrive at a final number for the constant(s), and include the units of those constants in your answer. (worth 10 of 45 total points) f) Determine the heat transfer rate at the surface of the cylinder. q k