Electro-thermoelasticity theory with memory-dependent derivative heat transfer

2016 ◽  
Vol 99 ◽  
pp. 22-38 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Ahmed S. El Karamany ◽  
A.A. El-Bary
Keyword(s):  
Heat Transfer ◽  
Thermoelasticity Theory ◽  
With Memory

A novel magneto-thermoelasticity theory with memory-dependent derivative

2015 ◽  
Vol 29 (8) ◽  
pp. 1018-1031 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Ahmed S. El-Karamany ◽  
Alaa A. El-Bary
Keyword(s):  
Thermoelasticity Theory ◽  
With Memory

Analysis of wave propagation in the presence of a continuous line heat source under heat transfer with memory dependent derivatives

2017 ◽  
Vol 23 (5) ◽  
pp. 820-834 ◽  
Author(s):  
Rakhi Tiwari ◽  
Santwana Mukhopadhyay
Keyword(s):  
Heat Transfer ◽  
Wave Propagation ◽  
Time Delay ◽  
Heat Source ◽  
Hankel Transform ◽  
Heat Transfer Process ◽  
Numerical Results ◽  
Continuous Line ◽  
Line Heat Source ◽  
With Memory

In the present work, the recently proposed new concept of “memory dependent derivative” in heat transfer process in a solid body has been employed to investigate the problem of wave propagation in a homogeneous, isotropic and unbounded solid due to a continuous line heat source. Both Laplace and Hankel transform techniques are employed for the solution of the problem. Analytical results for the distributions of different fields like temperature, displacement and stresses inside the medium have been derived. The problem is illustrated by computing the numerical values of the field variables for a particular material. We have attempted to exhibit the significance of a kernel function and a time-delay parameter that are characteristic of memory dependent derivative heat transfer in the behavior of field variables such as temperature, displacement and stresses with the help of numerical results. Detailed comparative analysis is represented through the numerical results to estimate the effects of the kernels and time-delay parameter on the behavior of all of the field variables such as temperature, displacement and stresses in the presence of a heat source in the medium.

On dual-phase-lag thermoelasticity theory with memory-dependent derivative

2016 ◽  
Vol 24 (11) ◽  
pp. 908-916 ◽  
Author(s):  
Magdy A. Ezzat ◽  
Ahmed S. El-Karamany ◽  
Alaa A. El-Bary
Keyword(s):  
Phase Lag ◽  
Dual Phase ◽  
Thermoelasticity Theory ◽  
With Memory

Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Biswajit Singh ◽  
Indranil Sarkar ◽  
Smita Pal (Sarkar)
Keyword(s):  
Variational Principle ◽  
Relaxation Times ◽  
Thermoelastic Medium ◽  
Rate Dependent ◽  
Thermoelasticity Theory ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature Rate ◽  
With Memory ◽  
Coupled Theory

Abstract This article is focused on developing a new mathematical model on the temperature-rate-dependent thermoelasticity theory (Green–Lindsay), using the methodology of memory-dependent derivative (MDD). First, the energy theorem of this model associated with two relaxation times in the context of MDD is derived for homogeneous, isotropic thermoelastic medium. Second, a uniqueness theorem for this model is proved using the Laplace transform technique. A variational principle for this model is also established. Finally, the results for Green–Lindsay model without MDD and coupled theory are obtained from the considered model.

scholarly journals Heat Transfer Analysis For Oscillating Flow of Magnetized Fluid By Using The Modified Prabhakar-Like Fractional Derivatives

2021 ◽  
Author(s):  
Ali Raza ◽  
Sami Ullah Khan ◽  
M. Ijaz Khan ◽  
Essam Roshdy El-Zahar
Keyword(s):  
Heat Transfer ◽  
Fractional Derivatives ◽  
Velocity Fields ◽  
Heat Transfer Analysis ◽  
Solution Approach ◽  
Flow Parameters ◽  
And Behavior ◽  
Temperature And Velocity Fields ◽  
Oscillating Plate ◽  
With Memory

Abstract In this analysis, an unsteady and incompressible flow of magnetized fluid in presence of heat transfer has been presented with fractional simulations. The oscillating plate with periodically variation has induced the flow. The model is formulated in terms of partial differential equations (PDE’s). The traditional PDEs cannot analyze and examine the physical behavior of flow parameters with memory effects. On this end, the solution approach is followed with the efficient mathematical fractional technique namely Prabhakar fractional derivative. The non-dimensional leading equations are transformed into the fractional model and then solved with the help of the Laplace transformation scheme. The effects and behavior of significant physical and fractional parameters are analyzed graphically and numerically. As a result, we have concluded that the temperature and velocity profiles decrease with the enhancement of fractional parameters. Furthermore, with time both (temperature and velocity fields)decreasing away from the plate and asymptotically increases along y-direction, which also satisfies the corresponding conditions.

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