Consider steady one-dimensional 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, 4, and 5 with a uniform nodal spacing of Δx. The temperature at the right boundary (node 5) is specified. Using the energy balance approach, obtain the finite difference formulation of the boundary node 0 on the left boundary 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. Also, obtain the finite difference formulation for the rate of heat transfer at the right boundary.

Transcribed Image Text:

Tsurr Radiation E Convection h, T Δ.χ ė(x) 0 1 2 3 45 T5