1. Consider two-dimensional steady-state heat conduction in a composite solid region consisting of two materials A...

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1. Consider two-dimensional steady-state heat conduction in a composite solid region consisting of two materials A and B and subjected to boundary conditions as shown in Fig. 1. Materials A and B have thermal conductivities KA=40 W/m K and KB=20 W/m K. There is a volumetric heat generation q =3.0 MW/m³ in the component with thermal conductivity KB. The side CE falls on the symmetry line. (i) Using a square grid of side 0.02 m, derive the steady-state, discretised heat conduction equations for the internal and surface nodes. (14 marks) (ii) Use the Gauss-Seidel procedure to show how you would determine the two-dimensional temperature distribution in the column. Carry out just two iterations using 20°C as the initial guess. (6 marks) (iii) Comment on the appropriateness of the assumption that the solution based on this grid is the actual temperature distribution in this domain. (5 marks) Symmetry h=100 W/m²K To=20°C E 4 8 A D q" 1 5 9 A Ax Insulated B T=220°C 2 G 6 10 Ay 7 B 3 H h=150 W/m²K Too=20°C 1. Consider two-dimensional steady-state heat conduction in a composite solid region consisting of two materials A and B and subjected to boundary conditions as shown in Fig. 1. Materials A and B have thermal conductivities KA=40 W/m K and KB=20 W/m K. There is a volumetric heat generation q =3.0 MW/m³ in the component with thermal conductivity KB. The side CE falls on the symmetry line. (i) Using a square grid of side 0.02 m, derive the steady-state, discretised heat conduction equations for the internal and surface nodes. (14 marks) (ii) Use the Gauss-Seidel procedure to show how you would determine the two-dimensional temperature distribution in the column. Carry out just two iterations using 20°C as the initial guess. (6 marks) (iii) Comment on the appropriateness of the assumption that the solution based on this grid is the actual temperature distribution in this domain. (5 marks) Symmetry h=100 W/m²K To=20°C E 4 8 A D q" 1 5 9 A Ax Insulated B T=220°C 2 G 6 10 Ay 7 B 3 H h=150 W/m²K Too=20°C

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