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This paper is designed to analyze the entropy production in hybrid nanofluid ( MnZnF e 2 O 4 –NiZnF e 2 O 4 – H 2 O ) . Marangoni convection is the phenomena of mass transfer between two phases of fluids when gradient of surface tension take place. Darcy–Forchheimer flow is incorporated in momentum equation. In thermal equation we are studying additional effects of nonlinear heat source sink with thermal radiation. Heterogeneous–homogeneous reactions are also studied. Transformations are used to convert our system of equations in to ODE’s so we can easily solve them by using ND Solve MATHEMATICA. Characteristics of fluid (temperature, entropy generation, velocity, Bejan number, Nusselt number, concentration and skin friction) are calculated and studied in detail. Results are presented through graphs. Flow resists due to enhancement in Marangoni ratio parameter. Temperature boosts up for higher thermal and exponential heat source sink. Concentration field is rising for greater heterogeneous parameter. Entropy and Bejan have contrast behavior for Brinkman number.

Background Free convection and second law scrutiny of nano-encapsulated phase change material (NEPCM) suspension along with entropy production inside a circular cold cylinder involving a wavy hot baffle is a significant thermal management aspect subject to various industrial applications. Phase change material (PCM) undergoes a solid-liquid phase mutation at a particular fusion temperature, and absorbs/releases an appreciable amount of energy because of the latent heat of phase mutation. Hence, NEPCMs would be prospective owing to their capability to enhance the working liquids’ performance, keeping the system at a particular cooling temperature. Methods In order to simulatethe free convection along with entropy generation of NEPCMs inside a circular cold cylinder entails a wavy hot baffle under CattaneoChristov heat flux model(Altered Fourier theory) and magnetic field, the finite element method (FEM) could be utilized to solve the governing equations. In this study, the amplitude of baffle could be changeable while its undulation number is fixed at 2. Findings Amplifying Raylegh number intensifies streamlines, isotherms, horizontal and vertical velocities, total entropy generation whittles down local Bejan number. Higher magnetic field strength is responsible for slow movement of NEPCMs and augments local Bejan number. Growth of baffle size yields squeezes the streamlines, horizontal and vertical velocities and intensified tilted isotherms.

In the present communication, we have model peristaltic transport of γAl2O3/H2O and γAl2O3/C2H6O2 in an asymmetric channel by using small Reynolds number (Re) and long wavelength (δ ≪ 1) assumptions. Two dimensional equations of peristaltic nanofluid flow are modeled and then solved by using analytical regular perturbation technique. We have formulated the peristaltic motion equations of nanofluids by applied magnetic field effect on asymmetric channel and derive energy equation by using heat generation/absorption effect. By using numerical integration the solution of pressure behavior and solution of resulting governing equations are calculated by Mathematica software. By using Matlab software the graphical behavior of pressure rise, trapping phenomena, temperature profile and pressure gradient are illustrated. We found that the narrow region of channel requires large pressure gradient, also the pressure gradient decreases with increase of channel width d. The pressure gradient of nanofluids increases due to increase in nanoparticle volume fraction, amplitudes and Hartmann number. Moreover, in trap phenomena the bolus size decreases by increase of Hartmann number and bolus size increases by increase of volume flow rate.

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.

A numerical analysis on the thermo-natural convection as well as entropy generation of Al2O3-H2O nanofluid enclosed by two circular cylinders in the presence of magnetic fields was performed. The internal hot cylinder is fitted with rectangular fins of different lengths. Irreversibilities related to the thermal effects, friction effects, magnetic effects were considered. FEM was selected as solving method. Results described the impact of active parameters on the thermo-natural convective flow and heat transfer behaviour as well as entropy generation characteristics. In addition, a basic economic analysis has been proposed to consider the cost of nanofluids in comparison to their contribution in enhancing heat transfer rate. Results show that significant effects of pertinent parameters e.g. Rayleigh, Hartmann, and fins' size on flow, heat transfer, and irreversibilities within annulus. It is also found that for low Rayleigh, irreversibility related to thermo-effects is predominant within the annulus, and by augmenting Rayleigh values, the irreversibility due to the thermo-effects is no longer the key contributor to overall entropy production. The magnetic forces help to increase thermo-effects irreversibility contribution to overall irreversibilities. Finally, thermal transfer enhancement in case of the presence of magnetic forces is found to be more costly in terms of nanofluid utilization.

This article develops a system of partial differential equations (PDEs) for thermal enhancement in Oldroyd-B rheological fluid (OBF) using Cattaneo-Christov heat flux theory for simultaneous transport of heat energy and species in the presence of nanostructures (Cu, Al2O3). System of PDE characterizing thermal heat, momentum, and conservations relaxation times are modeled via conservation of momentum, energy, and species. This system of nonlinear PDEs is solved by the finite element method (FEM). Convergence and grid-independent solutions are derived which are further used for numerical simulations against parametric analysis. An increase in momentum relaxation time causes a significant declination in wall shear stress. However, the opposite trend for wall heat transfer rate and mass flux versus momentum relaxation time is noted. The impact of Prandtl number on wall heat transfer rate is similar to the impact of Schmidt number on wall mass flux.

Background Current paper elaborate the impact of MHD flow of Newtonian liquid over a extendable Riga sheet. Cattaneo-Christov (CC) heat and mass flux models in formulation are taken here. Fluid filling porous medium is considered. Influences of activation energy is also considered. Boundary layer approximation is used in obtaining partial differential equations (PDEs). Applying suitable transformation to reduce the given PDEs into ordinary differential (ODEs) system. Method Homotopy method is utilized to solve non-linear differential system. Results The impacts of influencing parameters like modified Hartman number, mixed convection parameter, inverse Darcy parameter, non-dimensional parameter, Biot number, non-dimensional activation energy, Eckert number, thermal relaxation and solutal concentration variables are examined through graphs. Conclusions Velocity profile enhances for larger estimation of ratio parameter and modified Hartman number. Temperature distribution is higher for Eckert and Biot number. Concentration profile is enhancing for more values of nondimensional activation energy.

Power law rheological model is used for mathematical modeling of simultaneous transport of heat and energy via hybrid nanoparticles distributed in heat generating fluid exposed to magnetic field. Governing conservation laws, correlation between thermos-physical properties fluid, solid particles, suitable no-slip momentum and temperature boundary conditions are provided system of boundary value problems which are solved numerically using finite element method (FEM). The FEM simulations are used in capturing the dynamics of physical parameters on the momentum transport and heat energy transfer under the influence of non-uniformly moving surface which is being heated in non-uniform manner. Power law fluid flow experiences retardation as intensity of magnetic field is increased. Hybrid nanofluid is more heat generative than mono nanofluid and power law index causes a decrease in flow. Consequently, convective transport of heat is compromised. Generative and destructive chemical reactions have opposite trend on transport of species in power law fluid.

A mathematical study is analyzed to explore the impact of zero normal flux condition on boundary layer flow of Carreau-Yasuda nanofluid flow over a heated surface. In this case the mean flow does not give the analytical solution of the Navier-Stocks, temperature, and concentration equations, hence for high Reynold's number the flow of boundary-layer can be determined by non-similarity transformations. The converted boundary-layer equations along with appropriate boundary conditions are then solved numerically. The solution of the modelled differential equations is calculated by utilizing moderate and well-known numerical technique namely BVP4C method. Carreau-Yasuda fluid model is employed to explore the characteristics of shear thinning and thickening fluids. It is generalized form of Carreau-Yasuda fluid which is applicable for having small and infinite shear rates.

Simultaneous influence of thermal memory, micro-rotation, nanoparticles and dust particles are modeled using two-phase-conservation laws. The governing set of models is made dimensionless and expressions for skin friction, couple stress and heat flux are derived. Finite element method (FEM) is implemented for simulations purpose. Particles rotation has significantly impacted translational motion. Vortex effects are responsible in enhancing micro-rotations. However, this enhancement in micro-rotation field associated with mono-nano dusty fluid has received more impact rather than hybrid nanofluid. Thermal relaxation parameter characterizes memory effects in fluid due to which fluid restores its thermal equilibrium state. The fluid having viscoelastic rheology has this characteristics and such fluid offers resistance to momentum and thermal changes and tries to continue momentum and thermal equilibrium state.