Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45365120190101Magnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in Porous Medium1501611366610.22055/jacm.2018.25682.1285ENNehadAli ShahDepartment of Mathematics, Lahore Leads University, Lahore PakistanAbdus Salam School of Mathematical Sciences, GC University Lahore, PakistanNajmaAhmedAbdus Salam School of Mathematical Sciences, GC University Lahore, PakistanThanaaElnaqeebDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt0000-0003-1492-9518Mohammad MehdiRashidiDepartment of Civil Engineering, School of Engineering, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK0000-0002-6309-8688Journal Article20180428The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. The exact solutions for the fractional governing differential equations for fluid temperature, Nusselt number, velocity field, and skin friction are obtained by using the Laplace transform method. The numerical calculations are carried out and the results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with the thermal memory and the ordinary fluid is made. It was observed that due to evolution in the time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time <em>t</em>. Moreover, it is found that the fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction.https://jacm.scu.ac.ir/article_13666_df7a81762c59dac1769c5d47f3158d07.pdf