Consider two-dimensional transient heat transfer in an L-shaped solid bar that is initially at a uniform temperature of 140°C and whose cross section is given in the figure. The thermal conductivity and diffusivity of the body are k = 15 W/m · K and α = 3.2 × 10^-6 m²/s, respectively, and heat is generated in the body at a rate of ė = 2 × 10⁷ W/m³. The right surface of the body is insulated, and the bottom surface is maintained at a uniform temperature of 140°C at all times. At time t = 0, the entire top surface is subjected to convection with ambient air at T_∞ = 25°C with a heat transfer coefficient of h = 80 W/m² · K, and the left surface is subjected to uniform heat flux at a rate of q̇_L = 8000 W/m². The nodal network of the problem consists of 13 equally spaced nodes with Δx = Δy = 1.5 cm. Using the explicit method, determine the temperature at the top corner (node 3) of the body after 2, 5, and 30 min.

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AL 4 2 1.5 cm 1.5 cm 5 Convection 3 6 140°C h, T 7 00 Insulation