Effects of Joule heating and viscous dissipation on EMHD boundary layer rheology of viscoelastic fluid over an inclined plate

Aim: This paper presents a numerical simulation of the mixed convective boundary layer (BL) motion of a bio-rheological liquid over an inclined plate under viscous dissipation and Joule heating effects. This is significant because of the various applications of electro-osmotic force, inclined plates, and viscoelastic fluids in the biochemical engineering and industrial domains. Furthermore, the BL flow is controlled by electromagnetic force (EMF). In this study, a nonNewtonian liquid model, called the Jeffrey fluid model, was employed. Method: The rheological equations of the current study are nonlinear partial differential equations (PDEs). By applying a set of similarity transformations, these PDEs become coupled ordinary differential equations (ODEs), which are then solved numerically using the NDSolve method under realistic boundary constraints. Outcomes: Numerical solutions for the velocity profile ( f ' ( t )), temperature distribution ( Theta ( t )), skin friction (shearing stress), and Nusselt number (heat transfer rate) were obtained subject to convective boundary constraints. These numerical outcomes are dependent on 12 embedded parameters: Hartmann number ( Ha ), viscoelastic time relaxation parameter ( y ), inclination of the inclined plate with a horizontal line ( w ), mixed convection parameter ( Omega ), electro-osmotic parameter ( k ), electro-osmotic velocity parameter ( Uhs ), Prandtl number ( Pr ), Brinkman number ( Br ), suction/blowing parameter ( s ), velocity slip parameter ( g ), Joule heating parameter ( Gamma ), and thermal slip parameter ( S ). The authors discussed how these embedded variables affect rheological features through graphs and tables. The numerical solutions of viscous liquids are also discussed, and these outcomes are compared with the numerical solutions of a viscoelastic liquid. The enhancements of the Theta ( t ) and f ' ( t ) are largely dependent on the Joule heating parameter, Brinkman number, and Hartmann number. As the Prandtl number increases, diminishing behavior is observed in the Theta ( t ) and f ' ( t ). Increasing the magnetic and viscoelastic parameters increases the magnitudes of the skin friction coefficient and local Nusselt number. The validation of the numerical procedure is discussed by recovering the outcomes of research works from the available literature.