1. Write the governing equation and boundary conditions for 1-D heat transfer in a concrete wall 25 cm thick and thermal conductivity k=0.9W/mK. Consider Convective boundary condition on one side h=100W/m²K and Tfluid=298K of the wall and heat flux 1250 W/m² on the other side. Consider heat flux to be leaving the wall (heat being removed from the wall at a certain rate). Consider heat generation 1x10⁴ W/m³ in the wall.
2. Derive discretized equations for the above problem
3. Rederive the discretized equations for a composite wall made up of two materials 20cm thick concrete slab and 5cm thick insulation layer with thermal conductivity 0.01W/mK.
4. In problem 1, consider heat generation to be a nonlinear function of temperature given by 1x10⁴ - T^1/2 W/m³. Derive discretized equations.