It is necessary to use more general models than the classical Fourier heat conduction law describe small-scale thermal processes. The effects of flow memory and capacity (internal energy) in solids are considered first-order integrodifferential evolutionary equations with difference-type kernels. main difficulties applying such nonlocal in-time mathematical associated need work a solution throu...

Abstract: Elliptic interface problems arise in various areas of science and engineering. The steady state heat conduction in layered bodies is one of the largest areas of application of elliptic interface problems. In this paper, a mathematical model and solution of a one dimensional elliptic interface problem which represents a steady state heat conduction problem in composite medium have been...

Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...