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Influence of magnetic field for metachoronical beating of cilia for nanofluid with Newtonian heating in an asymmetric channel is considered. The governing coupled equations are constructed under long wavelength and low Reynold's number approximation. The Newtonian heating is controlled by a dimensionless conjugate parameter, which varies between walls of channel. Numerical solutions are evaluated for nanoparticle fraction, heat transfer, stream function and pressure gradient. The important findings in this study are the variation of the conjugate parameter for Newtonian heating γ , Hartmann number M , thermophoresis parameter N t and Brownian motion parameter N b on pressure rise, nanoparticle fraction, heat transfer phenomena, pressure gradient and streamlines. The velocity field increases due to increase in M near the channel walls while velocity field decreases at the centre of the channel. [ABSTRACT FROM AUTHOR]

In this article, we investigate steady triple convective-diffusive boundary layer free convection flow past a vertical flat plate embedded in a porous medium filled by a water-based nanofluid and two salts. The plate is assumed to be convectively cooled by a surrounding fluid. It is assumed that there is no nanoparticle flux at the surface and the effect of thermophoresis is taken in to account in the boundary condition. The effects of Brownian motion and thermophoresis parameters are also introduced through a Buongiorno model in the governing equations. The self-similar solutions are obtained numerically using an implicit finite difference method. The effects of the buoyancy ratio, regular Lewis numbers and modified Dufour parameters of both salts and nanofluid parameters on the flow and heat transfer are investigated. It is found that the heat transfer rate increases as we include nanoparticles and salts. Furthermore, it is also shown that the Brownian motion has negligible effects on reduced Nusselt number. [ABSTRACT FROM AUTHOR]

Abstract: The steady triple diffusive boundary layer free convection flow past a horizontal flat plate embedded in a porous medium filled by a water-based nanofluid and two salts is investigated numerically. The plate is assumed to be convectively cooled by a surrounding fluid. It is assumed that there is no nanoparticle flux at the surface and the effect of thermophoresis is taken into account in the boundary condition. The effects of Brownian motion and thermophoresis parameters are also introduced through Buongiorno model in the governing equations. Using appropriate similarity variables, the partial differential equations are transformed to ordinary (similarity) equations, which are then solved numerically using an implicit finite difference method with quasi-linearization technique. The effects of the buoyancy ratio, regular Lewis numbers and modified Dufour parameters of both salts and nanofluid parameters on the flow and heat transfer are investigated. It is found that the heat transfer rate increases as we include nanoparticles and salts. [Copyright &y& Elsevier]

This framework is established for alumina and copper-water nanofluid over a shrinking sheet with thermal radiation effect. To determine the better thermal performance of base fluid, model is constructed in the form of effective thermal conductivity and viscosity for nanoparticles. Thermal radiation effects are also incorporated to determine the significant influence of temperature in the restricted domain of the model. Partial differential equations are acquired from momentum and energy equations along with the boundary constraint at the surface. The nonlinear ODEs are further acquired from governing PDEs by using the similarity transformation. Dual nature's results are accomplished in the form of closed form exact solutions. The consequences of various physical parameters on the velocity and temperature profile are investigated along with the assist of tables and graphs. Additionally, temperature undershoot is noticed in some cases. Consequently, the heat absorption on surface arises due to heat transfer from the surface in some situations. In addition, the alumina and copper nanoparticles based fluids tender astounding antimicrobial actions to various gram class microscopic organisms. Some major results affirm that local Nusselt number enhance by increasing the values of thermal radiation parameter for Cu- and Al 2 O 3 -water. In addition, rate of heat transfer is higher for the first solution of both of Al 2 O 3 - and Cu-water. [ABSTRACT FROM AUTHOR]

In this article, combine effects of the inclined magnetic field and velocity slip conditions are analyzed for nanofluid flow over a moving over a flat surface. Two different kind of Carbon nanotubes are also incorporated within the base fluid, namely: Single wall carbon nanotubes (SWCNTs) and multiple wall carbon nanotubes (MWCNTs). Rheological characteristics of CNTs-Water and CNTs-Kerosene are studied under the influence of inclined applied magnetic field between 0 ≤ γ ≤ π /2. Close form solutions are obtained for both momentum and energy equation in the form of hypergeometric function. The core objective of aligned angle magnetic field is to use the governing magnetic intensity on the nanofluid and to extend the appraisals of aligned angle of the magnetic field produce to upgrade the local skin friction and decline the local Nusselt number. Significant consequences of inclined magnetic field with rest of the physical parameters including Hartmann number, velocity slip and solid volume fraction nanoparticles are presented and analyzed via numerical and graphical illustrations. It is found that SWCNTs-kerosene depicts the high friction and heat transfer rate at the surface as compare to the rest of the mixtures. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of oblique hydromagnetic stagnation point flow of a variable viscosity electrically conducting optically dense viscous incompressible nanofluid over a convectively heated stretching sheet in the presence of thermal radiation. The nanofluid model employed in this study incorporates the effects of Brownian motion and thermophoresis. The governing nonlinear partial differential equations for momentum, energy and nanoparticles concentration are reduced into a set of non-linear ordinary differential equations with the aid of suitable similarity transformations. The transformed equations are numerically integrated using fourth–fifth order Runge–Kutta–Fehlberg method. The effects of various controlling parameters on the dimensionless velocity, temperature, nanoparticles concentration, skin friction, Nusselt and Sherwood numbers are analysed and presented graphically. Obtained numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. It is found that non-alignment of the re-attachment point on the sheet surface decreases with an increase in magnetic field intensity. [ABSTRACT FROM AUTHOR]

The pressure driven peristaltic flow of nanofluid in a curved channel is investigated. The flow exploration demeanors the induced magnetic field. Long wavelength and low Reynolds number approach is followed. Numerical solutions are obtained by employing shooting method. The effects of substantial parameters have been portrayed and discussed on the temperature and mass distributions, stream function, magnetic force function, induced magnetic field and pressure rise per wavelength. [ABSTRACT FROM AUTHOR]

In the present study, thermal conductivity and viscosity of both single-wall and multiple-wall Carbon Nanotubes (CNT) within the base fluids (water, engine oil and ethylene glycol) of similar volume have been investigated when the fluid is flowing over a stretching surface. The magnetohydrodynamic (MHD) and viscous dissipation effects are also incorporated in the present phenomena. Experimental data consists of thermo-physical properties of each base fluid and CNT have been considered. The mathematical model has been constructed and by employing similarity transformation, system of partial differential equations is rehabilitated into the system of non-linear ordinary differential equations. The results of local skin friction and local Nusselt number are plotted for each base fluid by considering both Single Wall Carbon Nanotube (SWCNT) and Multiple-Wall Carbon Nanotubes (MWCNT). The behavior of fluid flow for water based-SWCNT and MWCNT are analyzed through streamlines. Concluding remarks have been developed on behalf of the whole analysis and it is found that engine oil-based CNT have higher skin friction and heat transfer rate as compared to water and ethylene glycol-based CNT. [ABSTRACT FROM AUTHOR]

Abstract: The combined effects of Navier slip and magnetic field on boundary layer flow with heat and mass transfer of a water-based nanofluid containing gyrotactic microorganisms over a vertical plate are investigated. Using Oberbeck–Boussinesq approximation and similarity transformation, the nonlinear model equations are obtained and tackled numerically to obtain the dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms together with the reduced Nusselt, Sherwood and motile microorganism numbers. The present numerical results are compared with available data and are found in an excellent agreement. Pertinent results are presented graphically and discussed quantitatively with respect to variation in the controlling parameters. It is observed that the magnetic field suppresses the dimensionless velocity and increases the dimensionless temperature inside the boundary layers. The bioconvection parameters tend to reduce the concentration of the rescaled density of motile microorganisms. It is also found that the reduced Nusselt, Sherwood and density numbers of microorganisms depend strongly upon the magnetic, buoyancy, nanofluid and bioconvection parameters. [Copyright &y& Elsevier]

Abstract: This paper analyzes the combined effects of buoyancy force, convective heating, Brownian motion, thermophoresis and magnetic field on stagnation point flow and heat transfer due to nanofluid flow towards a stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and Sherwood numbers. The results indicate that dual solutions exist for shrinking case. The effects of various controlling parameters on these quantities are investigated. It is found that both the skin friction coefficient and the local Sherwood number decrease while the local Nusselt number increases with increasing intensity of buoyancy force. [Copyright &y& Elsevier]

This paper deals with a problem where the effect of variable magnetic field and chemical reaction on free convective flow of an electrically conducting incompressible water based nanofluid over an exponentially stretching sheet has been investigated. In the present study, Buongiorno model associated with Brownian motion and thermophoretic diffusion is employed to describe the heat transfer enhancement of nanofluids. Some suitable similarity transformations reduced the governing boundary layer non-linear partial differential equations into a set of ordinary non-linear differential equations. The transformed equations are then solved numerically using fourth order Runga-Kutta method along with Shooting technique. The major outcomes of the present study is that the magnetic field impedes the fluid motion while thermal as well as mass buoyancy forces accelerate it, the thermophoretic diffusion enhances dimensionless fluid temperature as well as concentration leading to thicker thermal and concentration boundary layers. On the other hand, concentration exponent, Brownian motion parameter and chemical reaction parameter exhibit reverse trend on temperature and concentration. In addition, the presence of magnetic field under the influence of thermal as well as mass buoyancies supports to reduce the rate of heat transfer as well as wall shear stress while the first order chemical reaction develops a thinner concentration boundary layer. [ABSTRACT FROM AUTHOR]