Consider a cylindrical bar connecting two pieces of machinery. The temperature a

Question

Consider a cylindrical bar connecting two pieces of machinery. The temperature at one end of the bar is held at a reference temperature T(ref), while the other end of the bar is completely insulated. Heat flux through the bar is given by:

Heat also comes into the bar along its length, according to the source term f(x) = 1

The insulated end is at x = 0.

Derive and implement a second-order infinite difference scheme to solve for the temperature distribution in the bar. Produce plots for k = 0.2 and 0.5. Discretize your domain into 4, 8, and 16 cells, for a total of 6 plots.

Explanation / Answer

A long square bar with cross-sectional dimensions of 30 mm x 30 mm has a specied temperature on each side, The temperatures are:

Assuming isothermal surfaces, write a software program to solve the heat equation to determine the two-dimensional steady-state spatial temperature distribution within the bar. Your analysis should use a finite difference discretization of the heat equation in the bar to establish a system of equations:

2. Relevant equations

Must use Gauss-Seidel Method to solve the system of equations

3. The attempt at a solution

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