Motivated from numerous practical applications, the present theoretical and numerical work investigates the nonlinear magnetohydrodynamic (MHD) laminar boundary layer flow of an incompressible, viscous fluid over a porous stretching sheet in the presence of suction/injection (mass transpiration). The flow characteristics are obtained by solving the underlying highly nonlinear ordinary differential equation using homotopy analysis method. The effect of parameters corresponding to suction/injection (mass transpiration), applied magnetic field, and porous stretching sheet parameters on the nonlinear flow is investigated. The asymptotic limits of the parameters regarding the flow characteristics are obtained mathematically, which compare very well with those obtained using the homotopy analysis technique. A detailed numerical study of the laminar boundary layer flow in the vicinity of the porous stretching sheet in MHD and offers a particular choice of the parametric values to be taken in order to practically model a particular type of the event among suction and injection at the sheet surface.

Numerical analysis is performed for magnetohydrodynamics (MHD) couple stress nanofluid flow over a stretching sheet with melting and nonlinear radiation. The second law of thermodynamics is also incorporated with first-order slip. Nanofluid characteristics for thermophoresis and Brownian moments are encountered. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge–Kutta–Fehlberg fourth-fifth (RKF-45) order technique. The physical parameters, which emerges from the derived system are discussed in graphical format. The significant outcomes of the current investigation are that the velocity field decays for a higher magnetic parameter. Another, important outcome of the study is both temperature and concentration are increasing functions of the first-order slip. Nusselt and Sherwood numbers are decreasing with an increase in magnetic strength. Further, Bejan number augment due to enhancement in the first-order slip and couple stress fluid parameters whereas a differing tendency is shown for magnetic and radiation parameters.

The viscous fluid flow past a semi-infinite porous solid, which is proportionally sheared at one boundary with the possibility of the fluid slipping according to Navier’s slip or second order slip, is considered here. Such an assumption takes into consideration several of the boundary conditions used in the literature, and is a generalization of them. Upon introducing a similarity transformation, the governing equations for the problem under consideration reduces to a system of nonlinear partial differential equations. Interestingly, we were able to obtain an exact analytical solution for the velocity, though the equation is nonlinear. The flow through the porous solid is assumed to obey the Brinkman equation, and is considered relevant to several applications.

Silicone fluids belong to the group of pseudoplastic non-Newtonian fluids with complex rheological characteristics. They are considered in basic and applied researches and in a wide range of industrial applications due to their favorable physical and thermal properties. One of their specific field of applications in the automotive industry is the working fluid of viscous torsional vibration dampers. For numerical studies in the design and development phase of this damping product, it is essential to have thorough rheological knowledge and mathematical description about the silicone oil viscosity. In the present work, adopted rheological measurement results conducted on polydimethylsiloxane manufactured by Wacker Chemie with initial viscosity of 1000 Pas (AK 1 000 000 STAB silicone oil) are processed. As a result of the parameter identification by nonlinear regression, the temperature-dependent parameter curves of the Carreau–Yasuda non-Newtonian viscosity model are generated. By implementing these parameter sets into a Computational Fluid Dynamics (CFD) software, a temperature- and shear-rate-dependent viscosity model of silicone fluid was tested, using transient flow and thermal simulations on elementary tube geometries in the size range of a real viscous torsional vibration damper’s flow channels and filling chambers. The numerical results of the finite volume method provide information about the developed flow processes, with especial care for the resulted flow pattern, shear rate, viscosity and timing.

In this paper, we have investigated thermally stratified MHD flow of an Oldroyd-B fluid over an inclined stretching surface in the presence of heat generation/absorption. Similarity solutions for the transformed governing equations are obtained. The reduced equations are solved numerically using the Runge–Kutta Fehlberg method with shooting technique. The influences of various involved parameters on velocity profiles, temperature profiles, local skin friction, and local Nusselt number are discussed. Numerical values of local skin friction and local Nusselt number are computed. The significant outcomes of the study are that the velocity decreases when the radiation parameter $$R_{d}$$R d is increased while the temperature profile is increased for higher values of radiation parameter $$R_{d}$$R d in case of opposing flow, moreover, growth in Deborah number $$\beta_{2}$$β 2 enhance the velocity and momentum boundary layer. The heat transfer rate is decrease due to magnetic strength but increase with the increased values of Prandtl and Deborah numbers. The results of this model are closely matched with the outputs available in the literature.