solve all, show all steps assumptions and conclusion comments

heat transfer problem

2. Aplane wall is initially at temperature 7. At time t =0, the heater on the left side is turned on and provides a heat flux of g," at x = 0. At the same time, the surface at x = L is exposed to a fluid at 7, (higher than T} ) with convection coefficient /. Note that the location x = 0 is at the interface of the heater and the wall (the heater is not part of the wall). T. 1 h Heater Insulation = (a) Write the simplified governing differential equation (after making appropriate assumptions) and the boundary and initial conditions that could be used to solve for the temperature distribution as a function of time and space. Do not attempt to solve this equation. (b) On T x coordinates, sketch the temperature distributions for the initial condition, the steady-state condition ( o), and two intermediate times. (c) Solve for the steady-state temperature at the left side of the wall T(0, ) in terms of q,", T, k, h, and L