Browsing by Author "Abderrahim Wakif"

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A one-phase Stefan problem with size-dependent thermal conductivity and moving phase change material under the most generalized boundary condition
(Taylor and Francis Ltd., 2022) Vikas Chaurasiya; Rajneesh Kumar Chaudhary; Abderrahim Wakif; Jitendra Singh
In the current paper, we analyzed a one-phase moving boundary problem that includes a size-dependent thermal conductivity and a moving phase change material under the most generalized boundary condition. A numerical solution to the problem is obtained via heat balance integral method (HBIM) with an approximation of the quadratic temperature profile. In particular, numerical results are compared against the exact solution and previous work and found to be closed. The effect of dimensionless problem parameters on temperature profile and moving melting interface are shown in figures. The physical behavior of these parameters shows that the melting interface enhanced growing for a large value of either Stefan number, Péclet number or Kirpichev number while it deterred with increasing the Nusselt number. A comparative study between moving boundary problem with size-dependent thermal conductivity and moving PCM, moving boundary problem with constant thermal conductivity and moving PCM, and standard problem is presented in each kind of boundary conditions. We also found that the second kind flux boundary condition is physically more realistic for the melting process than the first and third kind temperature boundary condition for a moving boundary problem with size-no independent thermal conductivity and moving PCM. For limiting value of the Nusselt number ((Formula presented.)), we found a unique λ with the Stefan number and Péclet number. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
A study on cylindrical moving boundary problem with variable thermal conductivity and convection under the most realistic boundary conditions
(Elsevier Ltd, 2022) Vikas Chaurasiya; Abderrahim Wakif; Nehad Ali Shah; Jitendra Singh
The melting of a phase change material is the most applicable process in thermal energy storage system to capture heat transfer phenomena arising in a class of moving boundary problem. Demand of present technology motivates researchers to develop new theories and techniques for thermal management of a material. Experimental work on melting of a material may be difficult and development of robust theoretical formulation in cylindrical geometry with convection is critical. While there is already available study on cylindrical moving boundary problem, but still insufficient modeling of a size-dependent thermal conductivity and convection effect is not addressed properly, which is being considered in this paper and is expected to improve the previous understanding. In this work, a one-dimensional moving boundary problem with size-dependent heat conductivity and convection effect is analyzed in cylindrical geometry. In the mathematical model, we have considered a time-dependent temperature boundary condition which later assumed in periodic form, and a convective boundary condition at the outer surface of the body. The numerical result of the problem is obtained successfully via heat-balance integral method. Our numerical result is compared with a previous work and found in good acceptance. From mathematical framework, it is found that convection delayed melting process. With a size-no independent thermal conductivity, the rate of moving front decreases more in comparison to the fixed thermal conductivity. © 2022 Elsevier Ltd