Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

This note considers the problem of estimating unknown time-varying strength of the temporal-dependent heat source, from measurements of the temperature inside the square domain, when the prior knowledge of the source functions is not available. This problem is an inverse heat conduction problem. In this process, the direct problem will be solved by using the heat fundamental solution. Then a se...

The main goal of our paper is to study the regularization problems which occur in predictive control of systems with severely ill-posed inverse model. We propose a new formulation of predictive control where the future controls are obtained as a solution of certain ill-posed inverse problem. This formulation leads to a possibility of closed loop on-line control of complex systems with ill-posed...

Abstract: During solidification and casting in metallic molds, the heat flow is controlled by the thermal resistance at the casting-mold interface. Thus heat transfer coefficient at the metal- mold interface has a predominant effect on the rate of heat transfer. In some processes such as low pressure and die-casting, the effect of pressure on molten metal will affect the rate of heat transfer a...

In an inverse heat conduction problem (IHCP), the boundary conditions, initial conditions, or thermo-physical properties of material are not fully specified, and they are determined from measured internal temperature profiles. The challenge is that the effect of changes in boundary conditions are normally damped or lagged, i.e. the varying magnitude of the interior temperature profile lags behi...

This paper considers a linear one dimensional inverse heat conduction problem with non constant thermal diffusivity and two unknown terms in a heated bar with unit length. By using the WKB method, the heat flux at the end of boundary and initial temperature will be approximated, numerically. By choosing a suitable parameter in WKB method the ill-posedness of solution will be improved. Finally, ...