In the first problem, an attempt has been made to determine the unknown temperature, displacement and stress functions on the edge x = a of a thin rectangular plate occupying the space D : 0 £ x £ a, 0 £ y £ b by applying finite Fourier sine transform technique.
The temperature T(x, y) = f(y) for a fixed value of x, 0 < x < a is a known function of y and the temperature is maintained at zero on the edges y = 0, b of a thin rectangular plate and on the edge x = 0, the temperature is maintained at h(y), which is a known function of y.
In the second problem, an attempt has been made to determine the unknown temperature, displacement and stress functions on the edge x = a of a thin rectangular plate occupying the space D : 0 £ x £ a, – b £ y £ b by applying finite Marchi-Fasulo transform and Laplace transform techniques.
The temperature T(x, y, t) = f(y, t), t > 0 for a fixed value of x, 0 < x < a is a known function of y and t and homogeneous boundary condition of third kind is maintained on the edges y = – b, b and on the edge x = 0, the temperature is maintained at zero of a thin rectangular plate.
