The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed in terms of nonlinear and coupled partial differential equations, with the symmetry of the conditions normal to the surface. To solve the mathematical model of the proposed phenomenon, the partial differential equations are first reduced to ordinary differential equations; then, MATLAB built-in Numerical Solver bvp4c is used to obtain the numerical results of these equations. The influence of all the pertinent parameters that appeared in the flow model on the unknown material properties of interest is depicted in the forms of tables and graphs. The physical attitude of the unknown variables is discussed with physical reasoning. From the numerical solutions, it is inferred that, as Lorentz force parameter $M$ is increased, the velocity of the fluid decreases, but fluid temperature and mass concentration increase. This is due to the fact that Lorentz force retards the motion of fluid, and the increasing resistive force causes the rise in the temperature of the fluid. It is also noted that, owing to an increase in the magnitude of chemical reaction parameter $R$, the velocity profile and the mass concentration decline as well, but the fluid temperature increases in a reasonable manner. It is noted that, by augmenting the values of the local inertial coefficient $Fr$ and the permeability parameter $K^{*}$, the velocity field decreases, the temperature field increases, and mass concentration also increases with reasonable difference. Increasing values of Prandtl number $Pr$ results in a decrease in the profiles of velocity and temperature. All the numerical results are computed at the angle of inclination $\alpha =\pi /6$. The current results are compared with the available results in the existing literature for this special case, and there is good agreement between them that shows the validation of the present study. All the numerical results show asymptotic behavior by satisfying the given boundary conditions.

The major aim of the current investigations is to study the magnetohydrodynamic effects on heat and mass transfer phenomena in third-grade fluid past an inclined exponentially stretching sheet fixed in a porous medium with Darcy–Forchheimer law influence. The constitutive equations compatible for heat and mass transportation in third-grade fluid in terms of partial differential equations are modeled. These partial differential equations are then converted to ordinary differential equations by using suitable similarity variables formulation. The transformed flow model is solved by using MATLAB built-in numerical solver bvp4c. Effects of pertinent parameters on physical properties that are velocity field, temperature field and mass concentration along with skin friction coefficient, Nusselt number and Sherwood number are demonstrated in graphs and tables. The impact of dimensionless numbers on the physical properties is analyzed and discussed with a physical view point at angle $\alpha =\pi /6$ (inclined sheet). It is seen that as the third-grade fluid parameter $\left(0.1\le \beta \le 11\right)$ is increased, the velocity profile increases, but the temperature field and mass concentration are decreased. It is observed that as the permeability parameter $(1\le K^{*}\le 11)$ is raised, the velocity distribution decreases and mass concentration increases. It is concluded from the results that owing to an increase in the local inertial coefficient $\left(0.1\le Fr\le 5\right)$, the velocity profile reduces but an increment in mass concentration is noted. It is concluded that by increasing values of magnetic field parameter $\left(0.1\le M\le 10\right)$ the velocity field is delineated and temperature field is elevated exactly according to the physics of magnetic field parameters. The present results are compared with already published results and it is observed that there is good agreement between them. This good agreement ensures the validation of accuracy of the results.