An electrical cable, experiencing a uniform volumetric generation q, is half buried in an insulating material while the upper surface is exposed to a convection processes (T∞, h).

(a) Derive the explicit, finite-difference equations for an interior node (m, n), the center node (m = 0), and the outer surface nodes (M, n) for the convection and insulated boundaries.

(b) Obtain the stability criterion for each of the finite difference equations. Identify the most restrictive criterion.

Transcribed Image Text:

n, n+1 T h Ar Δφ m-1. n m, n Cable I, n-1