Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

Multiple integral-balance method: Basic idea and an example with Mullin’s model of thermal grooving

A multiple integration technique of the integral-balance method allowing solving high-order diffusion equations is conceived in this note. The new method termed multiple-integral balance method is based on multiple integration procedures with respect to the space co-ordinate and is generalization of the widely applied heat-balance integral method of Goodman and the double integration method of Volkov. The method is demonstrated by a solution of the linear diffusion models of Mullins for thermal grooving.

An alternative integral-balance solutions to transient diffusion of heat (mass) by time-fractional semi-derivatives and semi-integrals: Fixed boundary conditions

A new approach to integral-balance solutions of the diffusion equation of heat (mass) with constant transport properties by applying time-fractional semi-derivatives and semi-integrals of Riemann-Liouville sense has been developed. The time-fractional semiderivatives and semiintegrals replace the surface gradient (temperature) which in the classical Heat-balance integral method (HBIM) of Goodman and the Double-integration method (DIM) should be expressed through the assumed profile. The application of semiderivatives and semiintegrals reduces the approximation errors to levels less than the ones exhibited by the classical HBIM and DIM. The method is exemplified by solutions of Dirichlet and Neumann boundary condition problems.

Application of Heat Balance Integral Method in Freezing Process of Overheated Melt on Cold Structure

Relocation process of molten materiel in core assembled with plate-type fuel is a significant process during severe accident which determines sequences of core degradation. Recently, HBI methods used in system codes for severe accident are generally applied in freezing problems with two plates structure. Actually, there are three plates existing during freezing process and the former methods are not quite available. Different temperature profiles will be compared in this paper for choosing the best suitable profile which has the least errors compared with exact solution of freezing process. A new HBI method combining quasi-steady method and numerical method is developed in this paper which can solve freezing problems with three plates structure, and comparing results between my HBI method and numerical method, equilibrium method and experimental results indicate the applicability of my method.