Shown in Figure Q.1 (page 4) is a cross-section of a long bar. This bar is...

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Shown in Figure Q.1 (page 4) is a cross-section of a long bar. This bar is made of two materials as shown by hatch-patterns in the figure. Thermal conductivities of the two materials are k and kB. The west boundary of this bar is insulated, the bottom boundary is subjected to a heat flux of 2000 W/m. The east boundary is exposed to a convective stream with h = 200 W/(m C) and temperature 10 C. The top boundary is at a constant temperature of 100 C. Internal heat generation in this bar is 400 kW/m. Thermal conductivities k = 50 W/(m C), kg = 100 W/(mC). An equally spaced grid in both directions is used to calculate temperatures in this cross-section. The grid and relevant dimensions are shown in Figure Q.1. a) Using the energy balance method write equations at nodes 1,2,3,4, 5 and 6 which could be used to calculate temperatures in this cross- section. b) Provide a summary of your equations. c) Re-arrange the above set of equations to use the Jacobi iterative technique. d) Using an initial temperature field of 50 C for all unknown temperatures, show calculations for two iterative steps of the Jacobi method to solve the set of equations obtained in (c). 2 cm Insulated 7 T = 100 C 21 8 5 AX KB 1111111111111 Flux 2000 W/m 2 cm Figure Q.1 Convective n = 200 W/(mC) Too = 10 C Convective Ax = Ay = 0.01 m Shown in Figure Q.1 (page 4) is a cross-section of a long bar. This bar is made of two materials as shown by hatch-patterns in the figure. Thermal conductivities of the two materials are k and kB. The west boundary of this bar is insulated, the bottom boundary is subjected to a heat flux of 2000 W/m. The east boundary is exposed to a convective stream with h = 200 W/(m C) and temperature 10 C. The top boundary is at a constant temperature of 100 C. Internal heat generation in this bar is 400 kW/m. Thermal conductivities k = 50 W/(m C), kg = 100 W/(mC). An equally spaced grid in both directions is used to calculate temperatures in this cross-section. The grid and relevant dimensions are shown in Figure Q.1. a) Using the energy balance method write equations at nodes 1,2,3,4, 5 and 6 which could be used to calculate temperatures in this cross- section. b) Provide a summary of your equations. c) Re-arrange the above set of equations to use the Jacobi iterative technique. d) Using an initial temperature field of 50 C for all unknown temperatures, show calculations for two iterative steps of the Jacobi method to solve the set of equations obtained in (c). 2 cm Insulated 7 T = 100 C 21 8 5 AX KB 1111111111111 Flux 2000 W/m 2 cm Figure Q.1 Convective n = 200 W/(mC) Too = 10 C Convective Ax = Ay = 0.01 m

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Based on the provided image were dealing with a twodimensional heat conduction problem on a crosssection of a long bar with a steady state assumption ... View the full answer