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The purpose of this study is to consider the dynamics of Casson–Walters-B alongside gyrotactic microorganisms through the investigation of antibacterial and antiviral mechanisms using silver nanoparticles (AgNPs). The Casson fluid and Walters-B flow from the penetrable plate to the boundary layer (BL) in this analysis. The antiviral and antibacterial mechanisms of AgNPs were separately examined in this study.

The physical phenomenon of this problem was analyzed with partial differential equations (PDEs). These PDEs were changed into ordinary differential equations (ODEs) to further explain the significance of pertinent control parameters. The set of equations is solved numerically by implementing the spectral relaxation method (SRM). SRM is a numerical technique that uses the basic techniques of Gauss-Seidel. The SRM first decouples and linearizes the coupled nonlinear set of ODEs.

In this finding, it is found that the thermal radiation parameter produces higher temperatures within the BL to cause blockage in viral replications. It is found in this study that the magnetic parameter assisted in disinfection by lowering the antiviral and antibacterial mechanisms within the momentum BL. This is evident from the reduction in the velocity and momentum BL as the Casson and Walters-B parameters increase.

This paper is unique because it examined the antiviral and antibacterial mechanisms by using AgNPs. Prior to the authors’ understanding, no study of this type was conducted in the past. To the best of the authors’ knowledge, no other study in the past has examined the mechanisms of antiviral and antibacterial separately within the BL. Also, the simultaneous flow of Casson (honey) and Walters-B fluids were considered flowing through the vertical porous plate to the BL.

This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper.

With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems.

The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer.

The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.

The purpose of this paper is to consider a two-dimensional unsteady Casson magneto-nanfluid flow over an inclined plate embedded in a porous medium. The novelty of the present study is to investigate the effects of Soret–Dufour on unsteady magneto-nanofluid flow.

Appropriate similarity transformations are used to convert the governing non-linear partial differential equations into coupled non-linear dimensionless partial differential equations. The transformed equations are then solved using spectral relaxation method.

The effects of controlling parameters on flow profiles is discussed and depicted with the aid of graphs. Results show that as the non-Newtonian Casson nanofluid parameter increases, the fluid velocity decreases. It is found that the Soret parameter enhance the temperature profile, while Dufour parameter decreases the concentration profile close to the wall.

The novelty of this paper is to consider the combined effects of both Soret and Dufour on unsteady Casson magneto-nanofluid flow. The present model is in an inclined plate embedded in a porous medium which to the best of our knowledge has not been considered in the past. The applied magnetic field gives rise to an opposing force which slows the motion of the fluid. A newly developed spectral method known as spectral relaxation method (SRM) is used in solving the modeled equations. SRM is an iterative method that employ the Gauss–Seidel approach in solving both linear and non-linear differential equations. SRM is found to be effective and accurate.