Answer to Question #283102 in Mechanical Engineering for tricky

Question

Answer needs to be in matlab coding

Problem-2: This problem consist of analyzing the accuracy of the finite element method in modeling the plane wall thermal problem. The plane wall is 1 m thick. The left surface of the wall (x=0) is maintained at a constant temperature of 200˚C, and the right surface (x=L=1m) is insulated. The thermal conductivity is Kxx=25 W/(m˚C) and there is a uniform generation of heat inside the wall of Q=400 W/m3 .

1. Use the Matlab code provided to you in class to model the problem. Also, use 5 elements for Hand Solution.  

2. Compare your results to the analytical solution, given by: T(x)=QxL/K_xx(1-x/2L)+T(0)

3. Prepare a table that reports the nodal temperature results of Matlab, and the analytical solution evaluated at the nodal points.

Answer 1

Thermal conductivity can be defined as the rate at which heat is transferred by conduction through a unit cross-section area of a material when a temperature gradient exists perpendicular to the area.

$T(x)=\frac{QxL} {K_xx(1-x/2L)}+T(0)$

$T(x) = \frac{400\times 1}{25\times (1-\frac{1}{2})} = 32+200 =230 ^0 C$