You solve a 2D steady state state conduction problem using a

You solve a 2D steady state state conduction problem using a finite difference program. You check the solution and find a difference between the total generated in the part and the net heat flow rate out of the part. You expect this difference to be zero. Your response should be: Run for the hills. The world as we know it is ending. The difference doesn\'t matter. The computer solved the problem so it must be correct. Since the difference should be zero, you search to find the causes so they can be corrected. Small errors are to be expected because a numerical solution is not an exact solution. You check to ensure the error is small.

Solution

solution:

1) for two dimensional steady state heat conduction, it is govern by laplace equation as

d^2T/dx^2+d^2T/dy^2=0

2)above equation can be soved by finite difference approach numerically by various method as

gauss seidal or liebmann\'s method.

3)as computer works on programms and as per processing speed of computer,it will take care of rounding numbers to higher level of significant numbers and try to minimize truncation error but still it is inducting some error in answer,so each time we get approximate solution and we need to find causes responsible for it and neccesary remedy or correction to minimize that error.

4)from our options first one has nothing to do with solution so it is incorrect ,for second one we must accept that computer follows command of human,so if there is error in commanding,computer will gives us wrong answer too so second one is incorrect as we must imply check on solution.

5)for third option we are just narrowing our view to find causes and correction imply must have check so third option is incorrect too and fourth one we are accepting earlier that solution will error prone and we are applying correction and also checking for error to be kept as small a possible so it is correct option.

6)hence correct answer is option 4.

7)as in case gauss seidal method we are using convergence formula but still to find accuracy level we are checking relative error whle computing solution and hence fourth one will be correct response to above case.