Magnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in Porous Medium

The 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 t.  Moreover, it is found that the fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction

Modeling of Au(NPs)-blood flow through a catheterized multiple stenosed artery under radial magnetic field

This paper introduces a theoretical study of Au(NPs)-blood flow through a catheterized artery with multiple stenosis under radial magnetic field effect. Blood is modeled as Newtonian fluid. Based on mild stenosis assumptions, the governing equations of gold nanoparticles blood flow model are simplified and solved analytically. Exact solution for axial velocity is obtained by using Cauchy Euler method. Solutions for temperature, wall shear stress, resistance impedance are introduced and plotted through graphs for pertinent flow and geometric parameters. The results show that Au(NPs) can enhance blood flow through stenosed artery while applying strong radial magnetic field can discourage blood flow through it

Numerical simulation of non-uniform heating due to magnetohydrodynamic natural convection in a nanofluid filled rhombic enclosure

Numerical simulation of magnetohydrodynamic natural convection heat transfer in a rhombic enclosure of inclination angle $${\mathrm {45}}^{\mathrm {^{\circ }}}$$ containing copper-water nanofluid has been presented in this paper. The top and bottom walls of the enclosure are subjected to non-uniform heating while left wall being subjected to lower temperature and right wall being maintained adiabatic. The finite element strategy (COMSOL Multiphysics) is used to solve the governing equations. The numerical simulations are done for the parametric values: 10$$^{4\, }\le$$ Rayleigh number $$\le$$ 10$$^{6}$$; 0 $$\le$$ Hartmann number $$\le$$ 100; 0 $$\le$$ volume fraction of nanofluid $$\le$$ 0.05. The phase deviation angle (top wall) is varied in the range from 0 to {\uppi } with amplitude of non linear heating being maintained constant. The motivation of this research goes with the fact that the associated transport phenomenon conveys the implication of designing an optimal thermal system analogous to the theme of non-uniform heating, with the phase angle being a crucial design parameter. The numerical results depict to the fact, that the rate of heat transfer follows non-monotonic trends and is considerably influenced by interplay of the phase shift angle, Rayleigh number and Hartmann number. The results showed that at Rayleigh number $$\ge 10^{5}$$, the heat transfer rate gets inhibited by enhancing the magnetic field intensity. The impact of different types of nano particles is illustrated by comparing the results with the results of three different nanofluids, silver– water, titanium dioxide–water and diamond–water nanofluids

Weber-Type Integral Transform Connected with Robin-Type Boundary Conditions

A new Weber-type integral transform and its inverse are defined for the representation of a function f(r,t), (r,t)∈[R,1]×[0,∞) that satisfies the Dirichlet and Robin-type boundary conditions f(R,t)=f1(t), f(1,t)−α∂f(r,t)∂r|r=1=f2(t), respectively. The orthogonality relations of the transform kernel are derived by using the properties of Bessel functions. The new Weber integral transform of some particular functions is determined. The integral transform defined in the present paper is a suitable tool for determining analytical solutions of transport problems with sliding phenomena that often occur in flows through micro channels, pipes or blood vessels. The heat conduction in an annular domain with Robin-type boundary conditions is studied. The subroutine “root(⋅)” of the Mathcad software is used to determine the positive roots of the transcendental equation involved in the definition of the new integral transform