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Question: 80 100 120 140 120 100 80 60 60 40...

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80 100 120 140 120 100 80 60 60 40 F-- T-1-40 10mm 20 20 40 60 80 100 8060 40 Figure A rectangular plate with temperature defined on the boundaries 4 Figure shows a rectangular plate made of a homogeneous isotropic mateial. The temperature distribution in this plate satisfies the indicated boundary conditions (given in degrees centigrade) and has reached a steady-state condition so that it is described by Laplaces equation (i) Draw a sketch of the solution domain showing clearly the line of symme- try for the temperature distributio and indicating which of the unknown temperatures are equal to each other i) Use the finite difference formulae on the formulae sheet to formulate the finite difference equations required to find estimates of the nodal temper atures, TA, TB. Tc and TD (ii) Express these finite difference equations in the form AT B where A is a 4x4 matrix, T (TA. TB T, To)and B (-160,-160,-200,-240) is a 4 x 1 column vector. Find matrix A, hence, given that -0.27-0.07-0.02-0.01 -0.07-0.29 -0.08-0.02 0.02-0.08-0.31 -0.08 -0.0 -0.04 -0.15-0.29 estimate A, TB, Tc and TD correct to one degree

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