Consider one-dimensional steady state conduction in a wall of thickness L. One side is at while the opposite side exchanges heat by convection. The heat transfer coefficient is h and the ambient temperature is T∞ = 0°C. The thermal conductivity varies with temperature according to
Where ki is the conductivity at the reference temperature Ti and ß is constant. Formulate the dimensionless governing equations and identify an appropriate perturbation parameter based on 1.