Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 1.8 W/m·K, and surface area A = 30 m². The left side of the wall is maintained at a constant temperature of T₁ = 90°C while the right side loses heat by convection to the surrounding air at T_∞ = 25°C with a heat transfer coefficient of h = 24 W/m²·K. Assuming constant thermal conductivity and no heat generation in the wall,

(a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall,

(b) Obtain a relation for the variation of temperature in the wall by solving the differential equation,

(c) Evaluate the rate of heat transfer through the wall.