A hybrid computational approach for Jeffery–Hamel flow in non-parallel walls

Significance of Hall currents on hybrid nano-blood flow through an inclined artery having mild stenosis: Homotopy perturbation approach

The rheological perspective of blood flow with the suspension of metallic or non-metallic nanoparticles through arteries having cardiovascular diseases is getting more attention due to momentous applications in obstructed hemodynamics, nano-hemodynamics, nano-pharmacology, blood purification system, treatment of hemodynamic ailments, etc. Motivated by the novel significance and research in this direction, a mathematical hemodynamics model is developed to mimic the hemodynamic features of blood flow under the concentration of hybrid nanoparticles through an inclined artery with mild stenosis in the existence of dominating electromagnetic field force, Hall currents, heat source, and porous substance. Copper (Cu) and copper oxide (CuO) nanoparticles are submerged into the blood to form hybrid nano-blood suspension (Cu-CuO/blood). The attribute of the medium porosity on the blood flow is featured by Darcy's law. The mathematical equations describing the flow are formulated and simplified under mild stenosis and small Reynolds number assumptions. To determine the analytical solution of the resulting nonlinear momentum equation, the homotopy perturbation method (HPM) is employed. Several figures are graphed to assess the hemodynamical contributions of various intricate physical parameters on blood flow phenomena through the inclined stenosed artery. Significant outcomes from graphical elucidation envisage that the hemodynamic resistance to the blood flow is reduced due to the dispersion of more hybrid nanoparticles in the blood. The hemodynamic resistance (impedance) increases approximately two times by dispersing 0.11% hybrid nanoparticles in the blood flow. The temperature of Cu-CuO/blood is found to be lower in comparison to Cu-blood and pure blood. Intensification of Hall parameter attenuates the wall shear stress at the arterial wall. The trapping phenomena are also outlined via streamline plots which exemplify the blood flow pattern in the stenosed artery under the variation of the emerging parameters. As anticipated, the addition of a large number of hybrid nanoparticles significantly modulates the blood flow pattern in the stenotic region. The novel feature of this model is the impressive impact of Hall currents on hybrid nanoparticle doped blood flow through the stenosed artery. There is another piece of significance is that HPM is the most suitable method to handle the nonlinear momentum equation under the aforementioned flow constraints. Outcomes of this simulation may be valuable for advanced study and research in biomedical engineering, bio-nanofluid mechanics, nano-pharmacodynamics.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

This research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives. The offered technique is a fantastic blend of homotopy analysis method (HAM) and Laplace transform (LT) operator and has been used fruitfully in the numerical computation of various fractional differential equations (FDEs). This paper involves the fractional derivatives of Caputo style. The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions. It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only — a fact which authenticates the easiness and soundness of the suggested hybrid scheme. The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations. The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

Entropy Generation in MHD Conjugate Flow with Wall Shear Stress over an Infinite Plate: Exact Analysis

The current work will describe the entropy generation in an unsteady magnetohydrodynamic (MHD) flow with a combined influence of mass and heat transfer through a porous medium. It will consider the flow in the XY plane and the plate with isothermal and ramped wall temperature. The wall shear stress is also considered. The influences of different pertinent parameters on velocity, the Bejan number and on the total entropy generation number are reported graphically. Entropy generation in the fluid is controlled and reduced on the boundary by using wall shear stress. It is observed in this paper that by taking suitable values of pertinent parameters, the energy losses in the system can be minimized. These parameters are the Schmitt number, mass diffusion parameter, Prandtl number, Grashof number, magnetic parameter and modified Grashof number. These results will play an important role in the heat flow of uncertainty and must, therefore, be controlled and managed effectively.