Write the steady-state form of the heat diffusion equation for the layer of coal. verify, by direct substitution, that this equation is satisfied by a temperature distribution of the form t x t ql k x l ( ) 2 s 1 2 2 2 = + − from this distribution, what can you say about conditions at the bottom surface (x = 0)? sketch the temperature distribution and label key features. (b) obtain an expression for the rate of heat transfer by conduction per unit area at x = l. applying an energy balance to a control surface about the top surface of the layer, obtain an expression for ts. evaluate ts and t(0) for the prescribed conditions. (c) daily average values of gs and h depend on a number of factors, such as time of year, cloud cover, and wind conditions. for h = 8 w/m2 ⋅ k, compute and plot ts and t(0) as a function of gs for 50 ≤ gs ≤ 500 w/m2. for gs = 500 w/m2, compute and plot ts and t(0) as a function of h for 5 ≤ h ≤ 50 w/m2 ⋅ k.