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The viscoelastic fluid flow model across a porous medium has captivated the interest of many contemporary researchers due to its industrial and technical uses, such as food processing, paper and textile coating, packed bed reactors, the cooling effect of transpiration and the dispersion of pollutants through aquifers. This article focuses on the influence of variable viscosity and viscoelasticity on the magnetohydrodynamic oscillatory flow of second-order fluid through thermally radiating wavy walls. A mathematical model for this fluid flow, including governing equations and boundary conditions, is developed using the usual Boussinesq approximation. The governing equations are transformed into a system of nonlinear ordinary differential equations using non-similarity transformations. The numerical results obtained by applying finite-difference code based on the Lobatto IIIa formula generated by bvp4c solver are compared to the semi-analytical solutions for the velocity, temperature and concentration profiles obtained using the homotopy perturbation method (HPM). The effect of flow parameters on velocity, temperature, concentration profiles, skin friction coefficient, heat and mass transfer rate, and skin friction coefficient is examined and illustrated graphically. The physical parameters governing the fluid flow profoundly affected the resultant flow profiles except in a few cases. By using the slope linear regression method, the importance of considering the viscosity variation parameter and its interaction with the Lorentz force in determining the velocity behavior of the viscoelastic fluid model is highlighted. The percentage increase in the velocity profile of the viscoelastic model has been calculated for different ranges of viscosity variation parameters. Finally, the results are validated numerically for the skin friction coefficient and Nusselt number profiles.

The viscoelastic fluid flow model across a porous medium has captivated the interest of many contemporary researchers due to its industrial and technical uses, such as food processing, paper and textile coating, packed bed reactors, the cooling effect of transpiration and the dispersion of pollutants through aquifers. This article focuses on the influence of variable viscosity and viscoelasticity on the magnetohydrodynamic oscillatory flow of second-order fluid through thermally radiating wavy walls. A mathematical model for this fluid flow, including governing equations and boundary conditions, is developed using the usual Boussinesq approximation. The governing equations are transformed into a system of nonlinear ordinary differential equations using non-similarity transformations. The numerical results obtained by applying finite-difference code based on the Lobatto IIIa formula generated by bvp4c solver are compared to the semi-analytical solutions for the velocity, temperature and concentration profiles obtained using the homotopy perturbation method (HPM). The effect of flow parameters on velocity, temperature, concentration profiles, skin friction coefficient, heat and mass transfer rate, and skin friction coefficient is examined and illustrated graphically. The physical parameters governing the fluid flow profoundly affected the resultant flow profiles except in a few cases. By using the slope linear regression method, the importance of considering the viscosity variation parameter and its interaction with the Lorentz force in determining the velocity behavior of the viscoelastic fluid model is highlighted. The percentage increase in the velocity profile of the viscoelastic model has been calculated for different ranges of viscosity variation parameters. Finally, the results are validated numerically for the skin friction coefficient and Nusselt number profiles.

In this paper, a non-linear mathematical model is formulated to examine the impact of rhinoceros beetles on coconut plantations through the interactions among healthy coconut trees, infected trees, and the beetle population. The model consists of three coupled non-linear ordinary differential equations (ODEs) with a Holling type II functional response to describe beetle-induced infection. Positivity and boundedness analyses ensure the biological feasibility of the system. The basic reproduction number (R₀) is derived using the next-generation matrix method to determine the threshold for beetle persistence. Local and global stability analyses of the equilibrium points are performed to investigate the long-term behavior of the system. The biological interpretation of equilibrium points explains the conditions for pest eradication and persistence. Optimal control strategies are incorporated to identify effective measures for reducing beetle infestation. The homotopy perturbation method (HPM) is employed to obtain approximate analytical solutions of the non-linear system. Sensitivity analysis identifies the parameters that strongly influence pest dynamics. Numerical simulations validate the analytical findings and show that reducing the contact rate between beetles and healthy trees can effectively control infestation and protect coconut plantations.

In this paper, a non-linear mathematical model is formulated to examine the impact of rhinoceros beetles on coconut plantations through the interactions among healthy coconut trees, infected trees, and the beetle population. The model consists of three coupled non-linear ordinary differential equations (ODEs) with a Holling type II functional response to describe beetle-induced infection. Positivity and boundedness analyses ensure the biological feasibility of the system. The basic reproduction number (R₀) is derived using the next-generation matrix method to determine the threshold for beetle persistence. Local and global stability analyses of the equilibrium points are performed to investigate the long-term behavior of the system. The biological interpretation of equilibrium points explains the conditions for pest eradication and persistence. Optimal control strategies are incorporated to identify effective measures for reducing beetle infestation. The homotopy perturbation method (HPM) is employed to obtain approximate analytical solutions of the non-linear system. Sensitivity analysis identifies the parameters that strongly influence pest dynamics. Numerical simulations validate the analytical findings and show that reducing the contact rate between beetles and healthy trees can effectively control infestation and protect coconut plantations.