The present research paper deals with the study of heat and mass transfer characteristics of steady viscous incompressible two-dimensional Maxwell fluid flow past a stretching sheet under the influence of magnetic field and the Soret effect. A well-known non-Newtonian Maxwell fluid flow model is used to differentiate it from the Newtonian fluids. The present physical problem gives the set of highly nonlinear-coupled partial differential equations that are not amenable to any of the direct techniques. The resultant nonlinear system of partial differential equations is reduced to a set of nonlinear ordinary differential equations by using suitable similarity transformations. Due to the inadequacy of analytical techniques, a bvp4c MATLAB function is used to solve the developed nonlinear system of equations. The simulated results are shown for various values of physical parameters in the flow regime. Additionally, the numerical values of skin-friction coefficient, heat, and mass transfer rates are calculated and tabularized. From the present investigation, it is observed that the normal and axial velocity profiles decreased for the enhancing values of the magnetic parameter. Increasing the Prandtl and Schmidt numbers reduces the temperature and concentration profiles in the flow region, respectively. Increasing the Maxwell fluid parameter decreases the velocity profile and magnifies the temperature field. Additionally, increasing the Soret number increases the concentration profile in the flow regime. Comparison of current similarity solutions with available results indicates the accuracy and guarantee of the present numerical results and the used method.

The main aim and novelty of this numerical analysis is to investigate the thermodynamic features of magnetized Cattaneo–Christov heat and mass flux models on the radiative Casson fluid flow past a stretching cylinder manifested with the thermal and mass flow mechanism within the boundary layer regime qualitatively under the influence of Soret and Dufour effects. Pertaining to this numerical investigation, the primitive forms of produced nonlinear coupled partial differential equations are reduced to ordinary differential equations via similarity transformations and are solved by employing numerically efficient and stable Runge–Kutta fourth-order scheme. The graphical results for velocity, thermal and concentration fields, wall shear stress, Nusselt and Sherwood numbers are presented for the various values of parameters such as, $0\le K\le 2.8$, $0.1\le M\le 2.3$, $1.2\le \text{β}\le 3.6$, $0.1\le Du\le 0.5$, $0.1\le Ra,Q\le 0.53$, $0.4\le Sr\le 0.8$, $0.1\le Ec\le 0.9$, $0.1\le \gamma \le 5$, $0.1\le \lambda \le 2.1$ and $0.3\le Sc\le 14$. In addition, the produced numerical solutions indicate that, the higher curvature number suppressed the velocity and thermal fields. Elevating thermal relaxation number diminished the thermal energy distribution over a cylinder. Magnifying Lorentz forces decayed the flow velocity and enhanced the thermal field. Finally, a reasonable agreement between the current analysis and previously published results is tabularized.

Contemporary investigation studies the silent features of the dissipative free convection couple stress fluid flow over a cylinder under the action of magnetic field, thermal radiation and porous medium with chemical reaction effect. Present two-dimensional viscous incompressible physical model is designed based on the considered flow geometry. Present physical problem gives the highly complicated nonlinear coupled partial differential equations (PDE's) which are not amenable to any of the known techniques. Thus, unconditionally stable, most accurate and speed converging with flexible finite difference implicit technique is utilized to simplify the dimensionless flow field equations. It is apparent from the current results that; the velocity profiles are diminished with enhancing values of magnetic field. Temperature profile increases with enhancing values of thermal radiation parameter. Velocity contours deviates away from the wall with enhancing magnetic parameter. Also, the effects of magnetic field, porous medium, thermal radiation, chemical reaction, buoyancy ratio parameter and Eckert number on couple stress flow velocity, temperature, and concentration profiles are studied. However, the present study has good number of applications in the various fields of engineering such as; polymer processing, solidification of liquid crystals, colloidal solutions, synovial joints, geophysics, chemical engineering, astrophysics and nuclear reactors etc. Finally, the current solutions are validated with the available results in the literature review and found to be in good agreement.