Investigation of Hall current and thermal diffusion effects on unsteady MHD mixed convective Jeffrey fluid flow over an inclined permeable surface with chemical reaction

Abstract

Jeffrey fluids, a subset of non-Newtonian fluids, have received substantial research attention owing to their versatile utility in industries, such as polymer processing, cosmetics, and glass manufacturing. This paper endeavors to introduce a pioneering outlook on the behavior of Jeffrey fluids by researching their intricate responses to an array of influencing factors, including slip conditions, thermal effects, magnetic fields, chemical influences, and pivotal roles in the enhancement of drug delivery systems. Jeffrey fluids hold particular significance in modeling physiological fluids found in biological systems, representing blood circulation with precision in terms of relaxation time and stress retardation. Interestingly, under specific conditions, when subjected to wall shear stress exceeding the yield strength, Jeffrey fluids transition to exhibit Newtonian fluid characteristics. Hence, we embark on a comprehensive exploration of the applicability of the Jeffrey fluid model across diverse industrial domains and its contribution to the realm of flow control. Our research focuses on the study of mixed convective Jeffrey fluid flow across an inclined vertical plate, considering the combined impacts of the Soret and Hall currents, along with slip conditions involving velocity, temperature, and concentration disparities. This intricate problem is analytically resolved through the careful use of the perturbation technique. Furthermore, the inclined angle parameter enhances the velocity profile, while the velocity slip parameter exhibits the opposite effect. Additionally, the thermal and concentration slip parameters attenuate the temperature and concentration profiles.

Appendix

$$\begin{gathered} m_{1} = \frac{{\Pr + \sqrt {\Pr^{2} + 4\Pr \xi } }}{2} \hfill \\ m_{2} = \frac{{\Pr + \sqrt {\Pr^{2} + 4\Pr \left( {\xi + \frac{n}{4}} \right)} }}{2} \hfill \\ m_{3} = \frac{{{\text{Sc}} + \sqrt {{\text{Sc}}^{2} + 4{\text{ScKr}}} }}{2} \hfill \\ m_{4} = \frac{{{\text{Sc}} + \sqrt {{\text{Sc}}^{2} + 4{\text{Sc}}\left( {{\text{Kr}} + \frac{n}{4}} \right)} }}{2} \hfill \\ m_{5} = \frac{{1 + \sqrt {1 + 4\lambda_{1} N} }}{2} \hfill \\ m_{6} = \frac{{1 + \sqrt {1 + 4\lambda_{1} \left( {N + \frac{n}{4}} \right)} }}{2} \hfill \\ \end{gathered}$$

$$\begin{aligned} & A_{1} = \frac{1}{{1 + m_{1} h_{2} }} \\ & A_{2} = \frac{{ - A_{3} \left( {1 + m_{1} h_{2} } \right)}}{{\left( {1 + m_{2} h_{2} } \right)}} \\ & A_{3} = \frac{{\Pr Am_{1} A_{1} }}{{m_{1}^{2} - \Pr m_{1} - \Pr \left( {\xi + \frac{n}{4}} \right)}} \\ & A_{4} = \frac{{1 - A_{5} \left( {1 + m_{1} h_{3} } \right)}}{{1 + m_{3} h_{3} }} \\ & A_{5} = \frac{{ - {\text{ScSr}}m_{1}^{2} A_{1} }}{{m_{1}^{2} - {\text{Sc}}m_{1} - {\text{ScKr}}}} \\ & A_{6} = \frac{{ - A_{7} \left( {1 + h_{3} m_{3} } \right) - A_{8} \left( {1 + h_{3} m_{2} } \right) - A_{9} \left( {1 + h_{3} m_{1} } \right)}}{{\left( {1 + h_{3} m_{4} } \right)}} \\ & A_{7} = \frac{{{\text{Sc}}Am_{3} A_{4} }}{{m_{3}^{2} - {\text{Sc}}m_{3} - {\text{Sc}}\left( {{\text{Kr}} + \frac{n}{4}} \right)}} \\ & A_{8} = \frac{{ - {\text{ScSr}}m_{2}^{2} A_{2} }}{{m_{2}^{2} - {\text{Sc}}m_{2} - {\text{Sc}}\left( {{\text{Kr}} + \frac{n}{4}} \right)}} \\ & A_{9} = \frac{{{\text{Sc}}m_{1} \left( {AA_{5} - {\text{Sr}}m_{1} A_{3} } \right)}}{{m_{1}^{2} - {\text{Sc}}m_{1} - {\text{Sc}}\left( {Kr + \frac{n}{4}} \right)}} \\ & A_{10} = \frac{{u_{w} - A_{11} \left( {1 + h_{1} m_{3} } \right) - A_{12} \left( {1 + h_{1} m_{1} } \right) - 1}}{{\left( {1 + h_{1} m_{5} } \right)}} \\ & A_{11} = \frac{{ - {\text{Gm}}A_{4} \cos \alpha }}{{\lambda_{1} m_{3}^{2} - m_{3} - N}} \\ & A_{12} = \frac{{ - \left( {{\text{Gr}}A_{1} \cos \alpha + {\text{Gm}}A_{5} \cos \alpha } \right)}}{{\lambda_{1} m_{1}^{2} - m_{1} - N}} \\ & A_{13} = \frac{{ - A_{14} \left( {1 + h_{1} m_{5} } \right) - A_{15} \left( {1 + h_{1} m_{4} } \right) - A_{16} \left( {1 + h_{1} m_{3} } \right) - A_{17} \left( {1 + h_{1} m_{2} } \right) - A_{18} \left( {1 + h_{1} m_{1} } \right) - 1}}{{\left( {1 + h_{1} m_{6} } \right)}} \\ & A_{14} = \frac{{Am_{5} A_{10} }}{{\lambda_{1} m_{5}^{2} - m_{5} - \left( {N + \frac{n}{4}} \right)}} \\ & A_{15} = \frac{{ - GmA_{6} \cos \alpha }}{{\lambda_{1} m_{4}^{2} - m_{4} - \left( {N + \frac{n}{4}} \right)}} \\ & A_{16} = \frac{{Am_{3} A_{11} - GmA_{7} \cos \alpha }}{{\lambda_{1} m_{3}^{2} - m_{3} - \left( {N + \frac{n}{4}} \right)}} \\ & A_{17} = \frac{{ - \left( {GmA_{8} \cos \alpha + GrA_{2} \cos \alpha } \right)}}{{\lambda_{1} m_{2}^{2} - m_{2} - \left( {N + \frac{n}{4}} \right)}} \\ & A_{18} = \frac{{\left( {Am_{1} A_{12} - GrA_{3} \cos \alpha - GmA_{9} \cos \alpha } \right)}}{{\lambda_{1} m_{1}^{2} - m_{1} - \left( {N + \frac{n}{4}} \right)}} \\ \end{aligned}$$