Ilyas Khan

Dual thermal analysis of magnetohydrodynamic flow of nanofluids via modern approaches of Caputo–Fabrizio and Atangana–Baleanu fractional derivatives embedded in porous medium

This manuscript investigates the temperature difference versus temperature or time and the effects of newly introduced fractional operators, namely Caputo–Fabrizio and Atangana–Baleanu fractional derivatives, on the magnetohydrodynamic flow of nanofluid in a porous medium. Three different types of nanoparticles are suspended in ethylene glycol, namely titanium oxide, copper and aluminum oxide. The mathematical modeling of the governing equations is developed by the modern fractional derivatives. The general solutions for velocity field and temperature distribution have been established by invoking Laplace transforms, and obtained solutions are expressed in terms of special functions, namely Fox-H function

A new Caputo time fractional model for heat transfer enhancement of water based graphene nanofluid: An application to solar energy

{\mathbf{H}}_{\upalpha ,\upbeta + 1}^{1,\alpha } \left( F \right)

Entropy Generation in MHD Mixed Convection Stagnation-Point Flow in the Presence of Joule and Frictional Heating

Hα,β+11,αF and

Energy transfer of Jeffery–Hamel nanofluid flow between non-parallel walls using Maxwell–Garnetts (MG) and Brinkman models

{\mathbf{M}}_{\upbeta ,\upgamma }^{\alpha } \left( F \right)

Double Convection of Unsteady MHD Non-coaxial Rotation Viscous Fluid in a Porous Medium

Mβ,γαF Mittag-Leffler functions. Dual solutions have been analyzed by graphical illustrations for the influence of pertinent parameters on the motion of a fluid. The base fluid and three different types of nanoparticles have intersecting similarities and differences in the heat transfer and fluid flows. The results show the reciprocal behavior of different types of nanoparticles which are suspended in ethylene glycol via Caputo–Fabrizio and Atangana–Baleanu fractional operators.

Application of time-fractional derivatives with non-singular kernel to the generalized convective flow of Casson fluid in a microchannel with constant walls temperature

This paper provides a comparative analysis of two different types of nanofluids for Stokes second problem. Additional effects of MHD, porosity and viscous dissipation are also considered. Two types of Newtonian liquids (water and ethylene glycol) are considered as base fluids with suspended nanosized Cu particles. A homogenous model of Newtonian nanofluids over a flat plate is used to describe this phenomenon with Stokes boundary conditions such that the ambient fluid is static and with uniform temperature. The problem is first written in terms of nonlinear partial differential equations with physical conditions; then after non-dimensional analysis, the Laplace transform method is used for its closed-form solution. Exact expressions are determined for the dimensionless temperature, velocity field, Nusselt number and skin friction coefficient and arranged in terms of exponential and complementary error functions satisfying the governing equations and boundary conditions. They are also reduced to the known solutions of Stokes second problem for Cu-water nanofluids. Results are computed using Maple software. The results showed that both skin friction and rate of heat transfer increase with increasing solid volume fraction of nanoparticles. MHD and porosity had an opposite effect on velocity for both types of nanofluids. The dimensionless temperature increases by increasing the Eckert and Hartmann numbers.