Consider a trapezoidal computational domain of length L and expansion angle 0, with unity thickness normal to the page, as shown in Figure Q4. The left-hand side dimension is So. The domain consists of a stationery solid of known and uniform p, k, and c, with no internal heat generation. The domain is discretised into N equally-spaced control volumes (CVS). Boundary conditions are: known and fixed temperatures on the left (To) and right (TL), respectively; and known and fixed heat flux rates (units W m²) on the top (9) and bottom (90), respectively. You may assume a steady state for your analysis. (a) Prove that the heat transfer rate (in W) from the top boundary into each CV is given by the following. [5] q+L NCos (b) Prove that the heat transfer rate due to conduction (in W) with the boundary at L for the right- most CV, N, is given by the following. [5] Q₁ 2kN L (S,+2LTano)(T,-T₁) (c) Starting with the general energy conservation equation given below and using the central differencing scheme (CDS) where necessary, derive the discretised form of the equation for an internal CV in the domain, P, in terms of the known variables given above, temperatures of P and neighbouring CVs, and position of P, xp. მ [(pcT) dV +√(pcT) v.ndS = [k(gradT) .ndS + ſq;dV q@B.C.=q [15] T@B.C.-To WPE x Adiabatic boundary Figure Q4 T@B.C.-TL