Numerical study of the Stokes' first problem for thermoelectric micropolar fluid with fractional derivative heat transfer

M. A. Ezzat^{1, 2} , I. A. Abbas^{3, 4} , A. A. El-Bary⁵ , Sh. M. Ezzat²

¹ Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
² Department of Mathematics, Faculty of Science and Letter in Al Bukayriyyah, Al-Qassim University, Al-Qassim, Saudi Arabia
³ Department of Mathematics, Faculty of Science and Arts-Khulais, King Abdulaziz University, Jeddah, Saudi Arabia
⁴ Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt
⁵ Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt

Abstract
In this work, the flow of an electrically conducting thermoelectric micropolar fluid over a suddenly moved heated plate is considered using the methodology of fractional calculus. The governing system of coupled equations in the frame of the boundary layer equations is applied to the unsteady Stokes' first problem. Finite element technique is proposed to analyze the problem. Numerical solutions for temperature, velocity and microrotation distributions are obtained. Numerical results are computed and illustrated graphically. The effects of the flow parameters, such as fractional order α, thermoelectric figure-of-merit ZT₀, Seebeck coefficient k₀ and magnetic parameter M on all distributions are studied with the aid of figures. The theories of coupled thermoelectric micropolar fluid and of generalized thermoelectric micropolar fluid with one relaxation time follow as a limit case. Some comparisons have been shown in figures to estimate the effects of various parameters on all studied fields. Tables 1, Figs 13, Refs 37.