Consider a steady two-dimensional heat transfer in an L-shaped solid body whose cross section is given...

 

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Consider a steady two-dimensional heat transfer in an L-shaped solid body whose cross section is given in Figure Q3B. The thermal conductivity of the body is k= 38 W/m-K, and heat is generated in the body at a rate of g' = 4 x 10° W/m³. The right surface of the body is insulated, while the bottom surface is maintained at a uniform temperature of 120°C. The entire top surface is subjected to convection with ambient air at T-= 28°C with a heat transfer coefficient of h = 50 W/m²-K, and the left surface is subjected to heat flux at a uniform rate of q' = 6000 W/m². The nodal network of the problem consists of 13 equally spaced nodes with Ax = Ay = 1.5 cm. Five of the nodes are at the bottom surface and thus their temperatures are known. Write the finite difference equations required to calculate the temperature of the following nodes: i) Temperature at node 3/ ii) Temperature at node 4 iii) Temperature at node 6 iv) Temperature at node 8 9₁ |||||||||||| 10 11 120°C h = 50 W/m²-K T..=28°C 12 13 INSULATION Consider a steady two-dimensional heat transfer in an L-shaped solid body whose cross section is given in Figure Q3B. The thermal conductivity of the body is k= 38 W/m-K, and heat is generated in the body at a rate of g' = 4 x 10° W/m³. The right surface of the body is insulated, while the bottom surface is maintained at a uniform temperature of 120°C. The entire top surface is subjected to convection with ambient air at T-= 28°C with a heat transfer coefficient of h = 50 W/m²-K, and the left surface is subjected to heat flux at a uniform rate of q' = 6000 W/m². The nodal network of the problem consists of 13 equally spaced nodes with Ax = Ay = 1.5 cm. Five of the nodes are at the bottom surface and thus their temperatures are known. Write the finite difference equations required to calculate the temperature of the following nodes: i) Temperature at node 3/ ii) Temperature at node 4 iii) Temperature at node 6 iv) Temperature at node 8 9₁ |||||||||||| 10 11 120°C h = 50 W/m²-K T..=28°C 12 13 INSULATION