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Numerical outcomes for the steady and unsteady flow situations are investigated for the mixed convection flow of Casson nanofluid caused by the motion of a nonlinear stretching sheet in porous media with chemical reaction and magnetic effects. In the present study, the impact of convective boundary conditions on the thermal and concentration profiles as well as in the presence of Brownian motion and thermophoresis effects on the flow field are also examined. Highly non-linear and coupled partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs) by using suitable similarity transformations and subsequently portray numerical and graphical results with the help of bvp4c tool using MATLAB. The validity of numerical results are compared and checked with previously published results in the literature. For deliberating the physical nature of the investigation, graphical and tabulated results are provided. The Casson parameter helps to reduce the intensity of the skin friction, while Casson fluid has a converse impact on velocity and temperature field, but parallel results are seen in the case of concentration and temperature profile. The impacts for the magnetic parameter on velocity and temperature is revealed more effective than nanoparticle concentration. The impact of thermal and concentration buoyancy parameter on velocity, temperature and concentration profiles are observed and found that velocity profile increases with slight increase in thermal buoyancy parameter but decreases the other two profiles.

The present research work scrutinizes numerical heat transfer in convective boundary layer flow having characteristics of magnetic ( Fe 3 O 4 ) and nonmagnetic ( Al 2 O 3 ) nanoparticles synthesized into two different kinds of Newtonian (water) and non-Newtonian (sodium alginate) convectional base fluids of casson nanofluid which integrates the captivating effects of nonlinear thermal radiation and magnetic field embedded in a porous medium. The characterization of electrically transmitted viscous incompressible fluid is taken into account within the Casson fluid model. The mathematical formulation of governing partial differential equations (PDEs) with highly nonlinearity is renovated into ordinary differential equations (ODEs) by utilizing the suitable similarity transform that constitutes nondimensional pertinent parameters. The transformed ODEs are tackled numerically by implementing b v p 4 c in MATLAB. A graphical illustration for the purpose of better numerical computations of flow regime is deliberated for the specified parameters corresponding to different profiles (velocity and temperature). To elaborate the behavior of Nusselt and skin friction factor, a tabular demonstration against the distinct specific parameters is analyzed. It is perceived that the velocity gradient of Newtonian fluids is much higher comparatively to non-newtonian fluids. On the contrary, the thermal gradient of non-Newtonian fluid becomes more condensed than that of Newtonian fluids. Graphical demonstration disclosed that the heat transfer analysis in non-Newtonian (sodium alginate)-based fluid is tremendously influenced comparatively to Newtonian (water)-based fluid, and radiation interacts with the highly denser temperature profile of non-Newtonian fluid in contrast to that of Newtonian fluid. Through such comparative analysis of magnetic or nonmagnetic nanoparticles synthesized into distinct base fluids, a considerable enhancement in thermal and heat transfer analysis is quite significant in many expanding engineering and industrial phenomenons.

Very recently, functions that map the open unit disc U onto a limaçon domain, which is symmetric with respect to the real axis in the right-half plane, were initiated in the literature. The analytic characterization, geometric properties, and Hankel determinants of these families of functions were also demonstrated. In this article, we present a q-analogue of these functions and use it to establish the classes of starlike and convex limaçon functions that are correlated with q-calculus. Furthermore, the coefficient bounds, as well as the third Hankel determinants, for these novel classes are established. Moreover, at some stages, the radius of the inclusion relationship for a particular case of these subclasses with the Janowski families of functions are obtained. It is worth noting that many of our results are sharp.

The purpose of the current work is to explore the outcome of suction/injection on Eyring–Powell’s non-linear radiation nanofluid. Non-Newtonian nanofluid flow has a variety of uses in the production of electrical devices, pharmaceuticals, medical equipment, glass fiber, polymer sheets, and more. We considered the Eyring–Powell fluid over an extending surface in the mechanism of a magnetic dipole with double diffusion, and activation energy, because of all these potential consequences. Nonlinear partial differential equation’s together with the supporting constraints are converted into nonlinear ordinary differential equation’s by a suitable similarity function. The obtained equations are solved numerically or analytically by using software MATLAB and MAPLE. This whole analysis is described by the effects of steady, laminar, and incompressible flow. By analyzing these combined effects, we can improve the thickness of the thermal boundary layer. The thermophoresis and Brownian properties that are specifically examined are elaborated by the Buongiorno model. The physical restraints, such as ohmic and viscous dissipation, as well as numerous other parametric factors, are depicted together with their final impacts on fluid flow. For both suction/injection skin friction coefficient decreases with the rise in [Formula: see text] ferromagnetic interaction parameter and Hartman number Ha. The thermal profile is inversely associated with the Prandtl number. The physical behavior of this flow problem in tabular and graphical form, agrees very well with the work already published. Some applications of this research are dosing pumps, vacuum suction machines, etc. To preserve this work, an absolute differentiation is considered that determines the validity of the current work.

An unsteady mixed convectional boundary layer flow of a Casson nanofluid having magnetic ( Fe3 O4) and non-magnetic ( Al2 O3) nanoparticles suspension within two different types of base fluids, water (Newtonian) and sodium alginate (non-Newtonian), which incorporates viscous dissipation effects over a nonlinear stretching sheet with magnetic field effects. Some suitable non-dimensional similarity transformations are applied to convert the governing coupled nonlinear partial differential equations into a set of ordinary differential equations and then solved by using differential transformation method in association with Pade-approximation. A comparison has been made with already published results to assure the validity and reliability of the computational results, good agreement is found between the current and previous studies. The impacts of different physical parameters active on flow, temperature, and nanoparticle concentration have been discussed both numerically and graphically. The impact of radiation, internal heat sink/source, viscous, and ohmic dissipation was discussed for magnetic and non-magnetic nanofluid categories. We have also presented the tabular results of various emerging parameters to discuss the nature of skin friction, Nusselt, and Sherwood numbers. It was observed that performance of non-Newtonian (sodium alginate) fluid in heat and mass transfer is slightly better than Newtonian (water) based fluid but no major difference was seen in heat and mass transfer when comparison was made with magnetic and non-magnetic nanoparticles.