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The homogeneous and heterogeneous reactions in the boundary-layer of a flat surface are considered. The autocatalysts are assumed to be of regular sizes, while the solution is a dilute nanofluid. The heat release due to the chemical reactions is taken into account. The Buongiorno's model is used to describe the behaviors of this reaction system. This configuration makes the current model be different from all previous publications. Multiple solutions are given numerically to the rescaled nonlinear system, whose stability is verified. The results show that the strength coefficients of the homogeneous and heterogeneous reactions are key factors to cause the appearance of the multiple solutions in the distribution of the chemical reactions. Nanofluids enhance the diffusion of heat and help maintain the stability of chemical reactions. [ABSTRACT FROM AUTHOR]

A fully developed steady immiscible flow of nanofluid in a two-layer microchannel is studied in the presence of electro-kinetic effects. Buongiorno's model is employed for describing the behavior of nanofluids. Different from the previous studies on two-layer channel flow of a nanofluid, the present paper introduces the flux conservation conditions for the nanoparticle volume fraction field, which makes this work new and unique, and it is in coincidence with practical observations. The governing equations are reduced into a group of ordinary differential equations via appropriate similarity transformations. The highly accurate analytical approximations are obtained. Important physical quantities and total entropy generation are analyzed and discussed. A comparison is made to determine the significance of electrical double layer (EDL) effects in the presence of an external electric field. It is found that the Brownian diffusion, the thermophoresis diffusion, and the viscosity have significant effect on altering the flow behaviors. [ABSTRACT FROM AUTHOR]

Highlights • The Buongiorno’s nanofluid model is introduced for cavity nanofluid flow. • The buoyancy term is given more concisely. • Non-uniform heating types of practical importance overlooked in literature are presented. • A novel wavelet-homotopy technique is proposed. • Physical mechanisms on cavity flows with various types of heated and lid-driven walls are conducted. Abstract The laminar mixed convection flow in an inclined lid-driven cavity filled with a nanofluid is investigated in the presence of internal heat generation. The two sidewalls of the enclosure are sinusoidally heated while the top and bottom walls are insulted. The Buongiorno’s model that incorporates the effects of Brownian motion and thermophoresis is applied to describe the nanofluid behaviours. Parametrical studies are given on the regimes of the complex flow, temperature and concentration fields. The developed equations are nondimensionalized and then solved numerically by the newly developed wavelet-homotopy technique. Comparisons with previously studies in literature are presented and found to be in excellent agreement. The results of this work indicate that the Grashof number, the slipping parameters, the nanoparticles related parameters, the inclination, the boundary coefficients including amplitude ratios of temperature and concentration, as well as the phase deviation have significant effects on characteristics of the cavity flow. [ABSTRACT FROM AUTHOR]

The behaviour of microchannel flow of a nanofluid between two parallel flat plates in the presence of the electrical double layer (EDL) is investigated in this paper. The problem is formulated based on the Buongiorno nanofluid model with the electrical body force due to the EDL being considered in the momentum equation. As one of the highlights of the present investigation, the unphysical assumption introduced in previous studies often leading to the discontinuities of flow field that the electrostatic potential in the middle of the channel has to be equal to zero is eliminated. In addition, the inappropriate assumption that the pressure constant is treated as a known condition is also rectified. The new model is developed with the governing equations being reduced by a set of dimensionless quantities to a set of coupled ordinary differential equations. Based on the analytical approximations, the influences of various physical parameters on the flow field and temperature field, and the important physical quantities of practical interests are analysed and discussed in detail. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the two-dimensional pulsating nanofluid flow through a parallel-plate channel in the presence of a magnetic field. The pulsating flow is produced by an applied pressure gradient that fluctuates with a small amplitude. A kind of proper transformation is used so that the governing equations describing the momentum and thermal energy are reduced to a set of non-dimensional equations. The analytical expressions of the pulsating velocity, temperature, and Nusselt number of nanofluids are obtained by the perturbation technique. In the present study, the effects of the Cu-H2O and Al2O3-H2O nanofluids on the flow and heat transfer in pulsating flow are compared and analyzed. The results show that the convective heat transfer effect of Cu-H2O nanofluids is better than that of Al2O3-H2O nanofluids. Also, the effects of the Hartmann number and pulsation amplitude on the velocity, temperature, and Nusselt number are examined and discussed in detail. The present work indicates that increasing the Hartmann number and pulsation amplitude can enhance the heat transfer of the pulsating flow. In addition, selecting an optimal pulsation frequency can maximize the convective heat transfer of the pulsating flow. Therefore, improved understanding of these fundamental mechanisms is conducive to the optimal design of thermal systems. [ABSTRACT FROM AUTHOR]

In this paper, the three-dimensional nanofluid bio-convection near a stagnation attachment is studied. With a set of similarity variables, the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticles and microorganisms are reduced to a set of fully coupled nonlinear differential equations. The homotopy analysis method (HAM)-finite difference method (FDM) technique is used to obtain exact solutions. The effect of various physical parameters on distribution of the motile microorganisms and the important physical quantities of practical interests are presented and discussed. [ABSTRACT FROM AUTHOR]

An investigation is made for a three-dimensional unsteady mixed nano-bioconvection flow between two contracting or expanding rotating discs. The passively controlled nanofluid model in which Brownian diffusion and thermophoresis are considered as the two dominant factors for nanoparticle/base-fluid slip mechanisms is introduced for description of this flow problem. A novel similarity transformation is introduced so that the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticle volume fraction, and microorganisms are reduced to a set of five fully coupled ordinary differential equations. Exact solutions are then obtained analytically for this complex nonlinear system. Besides, the influences of various physical parameters on distributions of velocity, temperature, nanoparticle volume fraction, and the density of motile microorganisms, along with the local Nusselt number and the local wall motile microorganisms flux, are presented and discussed. It is expected that this study can provide a theoretical base for understanding the transport mechanisms of unsteady bioconvection in nanofluids. [ABSTRACT FROM AUTHOR]

This article describes the unsteady flow of liquid containing nanoparticles and motile gyrotactic microorganisms between two parallel plates while keeping one moving and other fixed. The passively controlled nanofluid model is used to describe the nanoparticles concentration. Some instances of direct application of this nanofluid bioconvection study can be found in pharmaceutical industry, microfluidic devices, microbial enhanced oil recovery, modeling oil and gas-bearing sedimentary basins and many more. The governing partial differential equations are transformed to ordinary differential equations using the similarity transformations. The mathematica package based on homotopy analysis method is used to solve this problem. The physical phenomenon is explained by drawing the graphs for the temperature, nanoparticles concentration and density of motile microorganisms profiles. Also the tables are given which completely depicts the convergence of gained results. [ABSTRACT FROM AUTHOR]

The influence of stress jump conditions on a steady, fully developed two-layer magnetohydrodynamic electro-osmotic nanofluid in the microchannel, is investigated numerically. A nanofluid is partially filled into the microchannel, while a porous medium, saturated with nanofluid, is immersed into the other half of the microchannel. The Brinkmann-extended Darcy equation is used to effectively explain the nanofluid flow in the porous region. In both regions, electric double layers are examined, whereas at the interface, Ochoa-Tapia and Whitaker's stress jump condition is considered. The non-dimensional velocity, temperature, and volume fraction of the nanoparticle profiles are examined, by varying physical parameters. Additionally, the Darcy number, as well as the coefficient in the stress jump condition, are investigated for their profound effect on skin friction and Nusselt number. It is concluded that, taking into account the change in shear stress at the interface has a significant impact on fluid flow problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an analysis is made for the fully developed mixed bioconvection flow in a horizontal channel filled with a nanofluid that contains both nanoparticles and gyrotactic microorganisms. The passively controlled nanofluid model proposed by Kuznetsov and Nield (2013) is then introduced for modeling this flow problem, which is found to be more physically realistic than previous nanofluid models. Analytical approximations with high precision are obtained by the improved homotopy analysis technique for complicated boundary conditions. Besides, the influences of various physical parameters on the distributions of temperature, the nanoparticle volume fraction, as well as the density of motile microorganisms are investigated in detail. [Copyright &y& Elsevier]

Abstract: The laminar, fully developed mixed convection flow between two paralleled vertical flat plates filled by a nanofluid is investigated. By means of a new set of similarity variables, the governing equations are reduced to a set of three coupled equations with an unknown constant. The exact solutions are obtained by means of the homotopy analysis method for both the buoyancy-assisted and the buoyancy-opposing cases and their accuracies are checked in detail. The effects of the Grashof number Gr and the Prandtl number Pr on the nanofluid flows are then investigated successively. We further consider the effects of the buoyancy ratio Nr, the Brownian motion parameter Nb, the thermophoresis parameter Nt on the pressure parameter σ and the Nusselt number Nu. It is found that the heat transfer characteristic can be improved significantly as the proper nanofluids are applied. [Copyright &y& Elsevier]