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

Question

Consider a large plane wall of thickness L = 0.3m, thermal conductivity k = 2.5 w/m.K, and surface area A = 12 m². The left side of the wall at x = 0 is subjected to a net hear flux of q = 700 w/m², while the temperature at that surface is maintained at T₁ =  80⁰C. Assuming constant thermal conductivity And no heat generation in the wall.

1. Express the differential equation and boundary conditions for steady, one-dimensional heat conduction through the wall.
2. Obtain a relation for the variation of temperature in the wall by solving the differential equation.
3. Evaluate the temperature of the right surface of the wall.