Question 4 25 points A long steel component, the cross section of which is schematically shown in Fig. HTQ1 below, is initially maintained at a uniform temperature T₁ = 500

°C. Suddenly surfaces are exposed to cooling by one airstream on the top and bottom of TT = TB = 18 °C with corresponding heat transfer coefficients h = h = 105 W.m-2. K-1, and an airstream on the left and right of TL = TR= 42°C with corresponding heat transfer coefficients h = h = 124 W.m-2 K-1. Thermal diffusivities a A and a B, and thermal conductivities kA and kB of the solid materials A and B are given as a A = aB 1E-5 m². -1, and kA=29 W.m-1.K-1 and kg = 54 W.m-1.K-1. The 1 S - component is shown schematically in Fig. HTQ1 having been spatially discretised on to a mesh where Ax = Ay = 0.01 m. The green dashed line in Fig. HTQ1 indicates a line of symmetry which should be considered in the current analysis to reduce workload. TL, hL 1 4 ljmu.mobius.cloud 7 TT, hT 2 KA Ax 5 8 3 KB Ay 6 9 TB, hB Ax = Ay = 0.01m Fig. HTQ1 TR, hR Submit Assignment Quit & Save Back Question Menu Next ljmu.mobius.cloud coefficients T hB = 105 W.m .K , and an airstream on the left and right of TL = TR=42°C with corresponding heat transfer coefficients h = h = 124 W.m-2. K-1. Thermal diffusivities a A and a B, and thermal conductivities kA and kB of the solid materials A and B are given as a = a = 1E-5 m². s-1, and kA = 29 W.m-¹.K-1 and kB = 54 W.m-1.K-1. The component is shown schematically in Fig. HTQ1 having been spatially discretised on to a mesh where Ax = Ay= 0.01 m. The green dashed line in Fig. HTQ1 indicates a line of symmetry which should be considered in the current analysis to reduce workload. TL, hL 1 4 7 TT, hT 2 KA Ax 5 8 KB Ay 3 6 For Node 1: Atm1 ≤ Number S Section Attempt 1 of 2 Verify 9 TB, hB Ax = Ay = 0.01m Fig. HTQ1 TR, hR TR₂ (a) Using the energy balance method for explicit time marching, and a mesh size Ax = Ay= A=0.01 m, find out the discretised equation for nodes 1 to 6 and determine the maximum allowable time step At for all the nodes. Please provide answers to 3d.p. Submit Assignment Quit & Save Back Question Menu Next