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The central goal of the current research work is to develop a mathematical model by which we evaluate the influence of mixed convection on the flow rate, temperature profile and concentration rate in the occurrence of radiation and concentration impact respectively, through asymmetric divergent channel. The obtained resultant mathematical equations are transformed into system of first order differential equation by applying suitable transformation. Next we apply shooting method to calculated the numerical solutions with the help of MATLAB. Furthermore we graphically analysis the impact of geometry parameter a, Grashof number Gr and modified Grashof number Br on velocity profile. Also, we discuss the impact of heat generation parameter M and Prandtl number Pr on thermal profile. Moreover, we interpreter the consequence of activation energy E and temperature difference parameter Ω on concentration profile. Velocity profile u(y) reduces by enlarging geometry parameter a, velocity profile u(y) gives opposite performance for high value of Grashof Gr and modified Grashof numbers Br, temperature profile grows for large values of Prandtl numbers Pr and heat generation parameter M and concentration profile shows prominent impact more large values of activation energy and decreases for high values of difference parameter.

The transfer mechanism in fluid over a convectively and heated boundary with the consideration of Buoyancy and porous medium forces, Joule heating, viscous dissipation, temperature and concentration gradient and dispersion of nanoparticles is modeled. The related models are solved using finite element method (FEM). The convergent and mesh-free solutions are obtained. The dynamics of parameters on the flow fields are noted and displayed in the form of graphical and numerical data. Heat transfer rate can be increased by establishing temperature gradient whereas heat transfer can be increased by the compositional gradient. Flow over vertical boundaries experiences significant Buoyant force. Therefore, Buoyant force must be considered for vertical flows. The finite element solutions converge more faster than the solution obtained by the shooting method. Flow experience retardation due to Lorentz and porous medium forces. Thus flow can be controlled by applying an external magnetic field. The heat and mass transfer can be enhanced by the dispersion of nanoparticles in the fluid. Mass flux can be increased by establishing temperature gradient whereas heat transfer can be accelerated by the compositional gradient.

Natural convection (NC) of nanoliquids specifically in enclosures is of use in diverse fields such as solar collectors, HVAC, and medical treatment. Recent research shows that suspension of nano-materials within the base fluid enhanced the heat transfer performance. NC heat transfer of Al2O3–H2O nanoliquid within a crown cavity with a circular cylinder inside it is studied in this paper. The flow is considered buoyancy-driven which is under thermal radiation (Rd) and constant magnetic field within the porous media. Dimensionless modes of Navier-Stokes equations are considered as governing equations, and FEM is used to discrete the equations. Two scenarios are considered in the present paper. In the first scenario, the effect of parameters namely; Rayleigh number (103-105), Darcy number (0.001–0.1), Hartmann number (0–20), Radiation parameter (0.1–0.3), angle of magnetic field ( 0 ∘ − 90 ∘ ), and nanoparticle concentration (0.01–0.04) on heat transfer performance and entropy generation (Sgen) is studied. In the second scenario, the effect of geometry on Nusselt number (Nu) and Sgen is investigated. Da, Rd, and nanoparticle concentration have a positive impact on Nuavg and enhance heat transfer. Besides, the geometry with the best heat transfer performance is the one with the base wavy wall and the cylinder at the left side.

In this paper, numerical study of nanoparticles immersed in a viscoelastic fluid is discussed. The condition of zero normal flux is assumed which means that no mass flux exists near the variable thick surface. To control the arbitrary motion of nanoparticles, magnetic field is applied at the surface of sheet. After boundary layer, the governing partial differential equations are converted into ordinary differential equations by means of similarity transformations. The following system is calculated numerically by employing shooting method in conjunction with RK-five method. The velocity profile shows an increasing behavior for large values of α and λ. The base flow temperature profile reduces for increasing values of Pr number and N b parameter. Also, the results for skin frictions coefficient, mass and heat transport rate are explored with the help of tables. A comparative study has been made with prior published work.

The present article reveals the study of heat transfer via buoyancy-driven flow and entropy generation of magnetic Fe3O4–H2O nanoliquid inside a porous enclosure using two square cylinders. The shape factor of diverse particle shapes may well be also considered. Numerical technique called FEM is implemented for the transformed governing equations. Results of Nusselt number, entropy generation, Bejan number along with the streamlines and the isotherms are obtained for disparate contributing parameters. Validation with earlier studies exhibits an excellent agreement in particular case and findings portray that entropy generation rises with growing Hartmann number and mounting Rayleigh number could overshoot the velocity gradient within the enclosure.

The present article has been groomed to explore the boundary-driven magnetized flow of cross nanoliquid over thin needle subject to auto catalysis chemical reactions. In addition to it, the effect of entropy optimization model is incorporated and transportation of heat under non-uniform heat source/sink, Cattaneo-Christov heat flux (rectified Fourier) viewpoint (CCHF), and non-linear thermal radiation is also taken into account. Furthermore, the Brownian and thermophoresis aspects of nanoliquid are invoked. The dimensionless governing equations are solved by apposite shooting scheme. The outcomes of the present study via demonstrated graphs and numerical benchmarks seem to indicate that controlled Sakiadis and Blausius flow pattern of cross nanofluids is attained due to incremented magnetic field strength. Temperature ratio parameter contributes the upgradation of thermal boundary layer thickness and homogenous reaction rate leads to the diminution of nanoparticles concentration. The relative values of needle velocity and the velocity of cross nanofluid are most important factor for the regulation of viscous drag force and rate of heat transportation. Augmented Weissenberg parameter and Reynolds number are the prime factor for the uplift of the flow field and the related layer thickness. Furthermore, the existence of CCHF could result in augmentation in Nusselt.