A non‐Newtonian fluid's Poiseuille flow in a porous medium with variable inclination and permeability is investigated. Let us assume for the sake of simplification that permeability varies as a quadratic parabolic function form. The porous medium is used by the Brinkman methodology to control the flow. The equations for velocity distribution and mass flow that result from this are evaluated using different input values. This problem describes the effect of inclination, Jeffrey parameter, and variable permeability on the classical Poiseuille flow between parallel plates. This problem can also be treated as an extension of the work of Hamdan and Kamel for non‐Newtonian fluid flow in an inclined channel. Also, the effects of these variables on the variation of mass flux with Jeffrey parameter λ1 is analyzed through graphs, and the skin friction coefficient is analyzed through table values. It is observed that the maximum permeability of the porous medium affects both the mass flow rate and the velocity, which increase with rising λ1 and decrease with rising Ha, respectively.
Physiological applications of the study of heat transfer and peristaltic pumping of magnetohydrodynamic thermal diffusion include heart–lung machines during surgery, dialysis, vitamin injections, and cancer treatment. In addition, it has numerous industrial applications, including pharmaceutical fluid production, filtration, and contamination‐free cosmetic and glue emulsion dispensing. Studying the influence of diffusion‐thermo and thermal diffusion on peristaltic flow with slip boundaries propelled by internal Joule energy is the key motivation for this study. By utilizing a long‐wavelength approximation, ignoring the wave number, and performing under conditions of low Reynolds number, closed‐form solutions for the velocity, temperature, and concentration fields are achieved. Fluid flow along the axial pressure gradient tends to decrease as slip parameters increase. It is shown that when the amount of the second‐order slipping parameter increases, the pressure rate decreases in the back and peristaltic pumping zones but increases in the copump zone. The fluid's temperature and concentration tend to decrease as the slip parameters increase. Changes in thermal diffusion and thermo‐diffusion factors cause changes in the fluid's temperature and concentration. The Nusselt number improves as a result of increasing the Prandtl number, thermo‐diffusion constraint, Dufour number, and Schmidt number, whereas the Sherwood number exhibits the reverse trend.
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