Heat transfer characteristics in non-Newtonian fluid flow due to a naturally permeable curved surface and chemical reaction

In this research endeavor, Casson fluid flow and melting heat transfer due to a curved nonlinearly stretching sheet are investigated. The sheet is naturally permeable and the flow is considered in a porous medium. For flow in a porous medium, a modified Darcy's resistance term for Casson fluid is considered in the momentum equation. In the energy equation, heat transport characteristics, including viscous dissipation, are taken into account. Mass transport is also studied together with the impact of chemical reaction of higher order. The governing nonlinear partial differential equations of flow, heat, and mass transport are reduced to nondimensional ordinary differential equations using adequate similarity transformations and then solved numerically employing the bvp4c technique and Runge–Kutta fourth-order method on MATLAB. The impacts of numerous occurring parameters on relevant fields (velocity field, temperature field, and concentration field) are depicted and discussed by plotting graphs. We concluded the curvature parameter, $K$ reduces the pace of the flow. The impacts of the stretching index, $m$ and melting parameter, $Me$ are also found to reduce flow and temperature field. Furthermore, we noted that the reaction parameter, $K_n$ and its order, $n$ exhibit opposite impacts on the concentration field. Moreover, the numerical values of skin-friction coefficient and Nusselt number calculated employing bvp4c and Runge–Kutta fourth-order technique are expressed in tabular mode, and these are found in an excellent match. For validation of the results, skin-friction coefficient values were computed using the Runge–Kutta fourth-order technique and bvp4c solver, compared with the existing results, and a good agreement was found.