The flux of heat in a metal bar of length L is given by the expression q(x) = −κ(x + 0.1)dT/dx

If heat is added to the bar along its length with a flux equal everywhere to 0.5, the temperature at the left (x = 0) is held at some reference temperature, and the right end (x = 2) is insulated,

Required:
a. Write a differential equation for the steady-state temperature profile in the bar with respect to the reference temperature, including boundary conditions.
b. Derive a finite difference approximation for the differential equation, and write the associated stencils Honors students.