Consider transient heat conduction in a plane wall with variable heat generation and constant thermal conductivity The nodal network of the medium consists of nodes 0, 1, 2, 3, and 4 with a uniform nodal spacing of Δx. The wall is initially at a specified temperature. The temperature at the right boundary (node 4) is specified. Using the energy balance approach, obtain the explicit finite difference formulation of the boundary node 0 for the case of combined convection, radiation, and heat flux at the left boundary with an emissivity of e, convection coefficient of h, ambient temperature of T_∞, surrounding temperature of T_surr, and uniform heat flux of q̇₀ toward the wall. Also, obtain the finite difference formulation for the total amount of heat transfer at the right boundary for the first 20 time steps.

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Tsurr Radiation do h, T Convection Ax ė(x, t) N انرا 3 4 TL L X