Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity,

Question:

Consider steady one-dimensional heat conduction in a plane wall with variable heat generation and constant thermal conductivity, as shown in Fig. P5–12 on the next page. The nodal network of the medium consists of nodes 0, 1, 2, 3, 4, and 5 with a uniform nodal spacing of Dx. Using the finite difference form of the first derivative (not the energy balance approach), obtain the finite difference formulation of the boundary nodes for the case of insulation at the left boundary (node 0) and radiation at the right boundary (node 5) with an emissivity of e and surrounding temperature of T_surr.