Question $3$: A $5050cm$ square plate is heated by a constant uniform heat flux of $1500\frac{W}{m^2}$ at

the top face and cooled uniformly by convection from its sides. At the left face of the plate, the

temperature of the fluid is $25C$ and the convection heat transfer coefficient is $35\frac{W}{m^2}.K,$

whereas at right face, the temperature of the fluid is $15C$ and the convection heat transfer

coefficient is $20\frac{W}{m^2}.K.$ The square is perfectly insulated at the bottom face. Disregarding the

singularity effect at the corners of the square, obtain the differential equation and the boundary

conditions for the steady$-$state heat conduction across the plate, assuming temperature

dependence of the thermal conductivity and no internal heat generation in the plate. No need to

solve the differential equation.