A rectangular plate of length and width $W$ with its boundary conditions

is shown in the above figure. Write the governing equation, along with its

boundary conditions. Apply separation of variables method, obtain two

ordinary differential equations. Obtain the characteristics function, and

characteristic value. Apply orthogonality. No need to solve for the

constant. Finally, express the steady state two$-$dimensional temperature

distribution in terms of summation of series $(5$ Marks$)$