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Computational analysis of magnetized Casson liquid stretching flow adjacent to a porous medium with Joule heating, stratification, multiple slip and chemical reaction aspects

Nasir, M; Kausar, MS; Waqas, M; Anwar Beg, O; Abdullaev, S S; Saadaoui, Salah; Khan, W A


M Nasir

MS Kausar

M Waqas

S S Abdullaev

Salah Saadaoui

W A Khan



This article aims to investigate the characteristics of thermo-solutal magnetohydrodynamic (MHD) non-Newtonian smart coating boundary layer flow of a stretching substrate adjacent to a porous medium, considering the influence of chemical reactions and thermal radiation subject to a transverse static magnetic field. A non-Darcy drag force model is deployed to capture both Darcy bulk drag and inertial Forchheimer (quadratic) drag effects. A diffusion flux model is deployed for radiative heat transfer. The Casson viscoplastic model has been utilized to simulate rheological characteristics. Due to polymeric slip effects, three slip phenomena are included at the wall (hydrodynamic, thermal and concentration) in the formulation. Furthermore, viscous dissipation and Ohmic heating (Joule dissipation) are also included. Robust scaling similarity variables are deployed to transform the governing partial differential equations into ordinary differential equations. Subsequently, the emerging dimensionless coupled nonlinear boundary value problem is solved utilizing the Bvp4c method in MATLAB version 2022. This numerical approach allows for a logical parametric examination of all key control parameters on the transport phenomena, enabling a comprehensive understanding of the system behavior. Validation with previous studies is included. Detailed graphical and tabular computations are included for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number, for the influence of Darcian parameter, Forchheimer inertial parameter, mixed convection, velocity (momentum) slip, magnetic number, Casson parameter, nonlinear thermal convection parameter, nonlinear concentration convection parameter, radiation parameter, thermal stratification parameter, Prandtl number, heat source/sink parameter, Eckert number, thermal slip parameter, Schmidt number, chemical reaction, solutal stratification parameter and solutal slip parameter. Detailed interpretation of the physics associated with these multiple effects is included. Flow deceleration is observed with increment in Darcy parameter, Forchheimer parameter, Hartmann number, Casson parameter and momentum slip whereas flow acceleration is computed with increasing mixed convection parameter. Temperatures are accentuated with elevation in Rosseland radiative parameter, magnetic parameter, thermal stratification parameter, heat source parameter and Eckert (dissipation) number, whereas it is depleted with thermal slip (jump) parameter, heat sink, Prandtl number and mixed convection parameter. An increment in Schmidt number, first order homogenous chemical reaction parameter, solutal stratification parameter and mass slip parameters induce a reduction in concentration magnitudes and species boundary layer thickness. Skin friction is elevated with Darcian parameter. Nusselt number is boosted with mixed convection parameter whereas it is suppressed with radiation parameter, magnetic number, Casson parameter, thermal stratification parameter and thermal slip parameter. Sherwood number is observed to decay with increment in solutal stratification parameter and solutal slip parameter whereas it is enhanced with Schmidt number and chemical reaction parameters. The simulations provide further insight into the transport characteristics of electromagnetic viscoplastic coating material manufacturing.


Nasir, M., Kausar, M., Waqas, M., Anwar Beg, O., Abdullaev, S. S., Saadaoui, S., & Khan, W. A. (in press). Computational analysis of magnetized Casson liquid stretching flow adjacent to a porous medium with Joule heating, stratification, multiple slip and chemical reaction aspects. Numerical Heat Transfer, Part A Applications,

Journal Article Type Article
Acceptance Date Feb 3, 2024
Deposit Date Feb 5, 2024
Journal Numerical Heat Transfer, Part A Applications
Print ISSN 1040-7782
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Keywords MHD, thermal radiation, chemical reaction, Casson viscoplastic fluid, heat generation and heat absorption, slips boundary conditions, Bvp4c method; MATLAB; smart magnetic polymers