A modified Green-Naghdi fractional order model for analyzing thermoelectric MHD

Abstract

Purpose

Whereas, the classical Green-Naghdi Type II (GN-II) model struggles to accurately represent the thermo-mechanical behavior of thermoelectric MHD due to its inability to account for the memory effect. A new mathematical model of the GN-II theory incorporates a fractional order of heat transport to address this issue.

Design/methodology/approach

The employment of the matrix exponential method, which forms the basis of the state-space approach in contemporary theory, is central to this strategy. The resulting formulation, together with the Laplace transform techniques, is applied to a variety of problems. Solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also, a problem with the distribution of heat sources is considered. The numerical technique is used to achieve the Laplace transform inversion.

Findings

According to the numerical results and its graphs, the influences of the fractional order parameters, figure-of-merit factor, thermoelectric power and Peltier coefficient on the behavior of the field quantities are investigated in the new theory.

Originality/value

The new modeling of thermoelectric MHD has advanced significantly as a result of this work, providing a more thorough and precise tool for forecasting the behavior of these materials under a range of thermal and magnetic conditions.

Citation

Hendy, M.M. and Ezzat, M.A. (2024), "A modified Green-Naghdi fractional order model for analyzing thermoelectric MHD", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 6, pp. 2376-2398. https://doi.org/10.1108/HFF-02-2024-0133