This paper presents the ideas on improvement of lumped-parameter model for unsteady state (transient) heat conduction in a slab with temperature-dependent thermal conductivity. The transient temperature depends on various model parameter, they are Biot number, heat source and time. Polynomial Approximation Method (PAM) has been possible to derive a unified relation for the transient thermal behavior of solid (slab and tube) with both internal heat generation and boundary heat flux. In all the cases, a closed form solution is obtained between temperature, Biot number, heat source parameter and time.
A lumped parameter model (steel slab) has been adopted through two point Hermite approximations for integrals. For linearly temperature-dependent thermal conductivity, it is shown by comparison with numerical solution of the original distributed parameter model that the higher order lumped model yields significant improvement of average temperature prediction over the lumped model. For both cooling and heating processes a unified Biot number limit depending on a single dimensionless parameter b is given. The result of the present analysis can be used for conduction slab in heat exchanger and can withstand up to given temperature range.
Key words: Hermite approximations, PAM, thermal conductivity, lumped model, nonlinear heat conduction, heat conduction, Biot number.