question 6

QUESTION 6 [20 MARKS] X I . Is Firgue 2 When only convection is included in the analysis, the steady-state temperature distribution 7(x), along a pin fin as in Figure 2 can be calculated from the solution of the equation: d'T hP (1) dx2 KA. with boundary conditions: 7(0) = T, and T(Z) = T;. In equation (1), suppose he; the convectioneat transfer coefficient, P : the perimeter bounding the cross section of the fin material, A; the cross-sectional area of the fin, Is; the temperature of the surrounding air. |Determine the temperature distribution if given [ = 0.1m, T(0) =473 K, 7(0.1)=293K, T's=293 K, he= 40 W/m?/K, P=0.016 m-, k = 240 W/m/K, and A = 1.6 x105 m2. 1) Perform discretization process for the second order ordinary differential equation by dividing the interval, x into four equally spaced subintervals. [5 Marks] ii) By using your discretization output in i), write, I, at each interior nodes, x; . Hence, transform your system of linear equations into a tridiagonal system. [5 Marks] iii) Approximate the temperature distribution, 7(x,) a long a pin fin by using Thomas algorithm method. [10 Marks]