MHD Blasius flow of radiative Williamson nanofluid over a vertical plate

An analysis of a laminar mixed convection boundary-layer flow of an optically dense viscous fluid along a highly heated permeable vertical flat plate in the presence of thermal radiation is performed. The radiative heat flux term is expressed using the Rosseland diffusion approximation. Here, the fluid density is assumed to vary exponentially with temperature. The dimensionless boundary layer equations are reduced to a convenient form by primitive variable transformation and then integrated numerically employing the implicit finite difference method along with the Gaussian elimination technique. Furthermore, the boundary-layer equations are also reduced to a set of nonsimilar equations with the help of the stream function formulation and are simulated by the implicit finite-difference Keller box method. The influence of different physical parameters on the velocity and temperature profiles, as well as on the shear stress and heat transfer rate, is shown and analyzed.

The effect of double stratification on boundary-layer flow and heat transfer of nanofluid over a vertical plate

This paper investigates non-similar solution of free convective boundary layer flow of a viscous incompressible fluid along a vertical cone and plate embedded in a Darcian porous medium filled with power law non-Newtonian nanofluids. The effects of the thermal and mass convective boundary conditions are taken into account, which makes the present analysis practically applicable. The governing boundary layer equations are converted into a system of non-similar differential equations by using suitable transformations before being solved numerically. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, and the local Nusselt and Sherwood numbers are reported. It is found that the velocity, temperature, and concentration increase with mass transfer velocity for both the vertical plate and cone. Further, the velocity reduces whilst the temperature and concentration increase with increasing buoyancy ratio parameter for all three types of nanofluids in the case of both geometries. The local Nusselt and the local Sherwood numbers are found to be higher for dilatant nanofluids than pseudoplastic nanofluids and Newtonian fluids in each case. The numerical results for special cases are compared with the published data and an excellent agreement has been found.

MHD stagnation point flow heat and mass transfer of nanofluids in porous medium with radiation, viscous dissipation and chemical reaction

In this study, an investigation has been carried out to examine the effects of thermal radiation, heat generation/absorption, viscous dissipation and suction parameter on MHD flow of water-base nanofluid (Ag, Cu, Al2O3, CuO and TiO2). This study also focused on the mixed convective flow of water-base nanofluid due to a vertical permeable plate in the presence of convective boundary condition. Further, heat transfer has been inspected for water-base fluid influenced by heat generation/absorption and viscous dissipation. Moreover, the governing equations are reduced to nonlinear ordinary differential equations via Sparrow–Quack–Boerner local non-similarity method. These nonlinear ODEs are simulated numerically by means of Runge–Kutta–Fehlberg method (RKF-45). The impact of pertinent parameters on the dimensionless velocity, nanofluid temperature, skin friction and local Nusselt number are discussed and displayed. The results match with a special case of formerly available work. The present exploration exhibits that nanoparticle volume fraction increases the velocity and temperature of Cu-water nanofluid. It is also shown that magnetic parameter reduces the heat transfer rate.

The present study scrutinizes slip effects and stagnation point flows of upper-convected Maxwell fluid past a stretching sheet. The non-linear ordinary differential equations are obtained from the governing partial differential equations and solved using implicit finite difference method. The impacts of non-dimensional governing parameters such as Brownian motion parameter, velocity ratio, velocity slip parameter, suction/injection parameter, Lewis numbers, upper-convected Maxwell parameter, magnetic field, thermophoresis parameter, chemical reactions parameter, thermal slip parameter, solutal slip parameter, and heat source parameter on the velocity field, heat and mass transfer characteristics are discussed and presented through graphs. The values of local Sherwood number, local Nusselt number, and skin friction coefficient are discussed and presented through tables. The results indicate that when the magnetic field is intensified, it reduces velocity profiles and raises temperature and concentration profiles. Moreover, with an upsurge in velocity slip parameter, the local Nusselt number and local Sherwood number diminish.

This paper is devoted to investigate the influences of thermal radiation, Dufour and Soret effects on doubly diffusive convective heat transfer of nanoliquid over a wedge in the presence of wall suction. The governing equations are transformed to nonlinear ordinary differential equations using similarity transformation. The resulting system is solved numerically using fourth-order Runge-Kutta-Gill method with shooting technique and Newton-Raphson method. The solutions are expressed in terms of velocity, temperature, solutal concentration and volume fraction profiles. The effects of pertinent parameters entering into the problem such as wedge angle, thermal radiation, Brownian motion, thermophoresis, Soret and Dufour numbers on the skin friction coefficient, local Nusselt number and local Sherwood number are discussed in detail.

The mixed convection boundary layer flow over a heated horizontal plate is studied using high accuracy numerical method. Present analysis is valid when the buoyancy force effects are small compared to forced convection effects. The mixed convection boundary layer equations are given with the buoyancy term represented by Boussinesq approximation. The non-similar mixed convection boundary layer equations are solved directly using direct integration method without any approximation for non-similar terms. Numerical results are reported for assisting and opposing mixed convection flows for air. Reported results show that both the local Nusselt number and local friction factor values are increasing with increase in buoyancy parameter for assisting mixed convection flows and decreases with increasing buoyancy parameter for opposing mixed convection flows. Reported results reveal that both the local Nusselt number and the local friction factor values are high compared to local similarity and local non-similarity methods for assisting mixed convection flows and less compared to local similarity and local non-similarity methods for opposing mixed convection flows. Reported results show that velocity and temperature profiles in the boundary layer are exactly matches compared to local similarity method for low value of buoyancy parameter (I¾). For assisting mixed convection flows, the significant buoyancy effects are encountered for I¾ ≥ 0.05 and the velocity exhibit an overshoot beyond the free stream velocity for high values of I¾. For opposing mixed convection flows, the effect of buoyancy is to reduce the velocity compared to pure forced convection. The thickness of thermal boundary layer decreases with increasing buoyancy parameter for assisting mixed convection flows and increases with increasing buoyancy parameter for opposing mixed convection flows. Present study provides an accurate numerical approach to solve non-similar mixed convection boundary flows. © 2010 by Begell House, Inc.

The unsteady laminar boundary layer flow of a nanofluid and heat transfer over a permeable shrinking cylinder using the Buongiorno’s nanofluid model is investigated. Using a similarity transformation, the governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically using a shooting method. The numerical results are obtained for velocity, temperature and concentration profiles as well as the skin friction coefficient, the local Nusselt number and the local Sherwood number. Dual solutions are found to exist in a certain range of the suction and unsteadiness parameters. It is observed that suction parameter increase both the skin friction coefficient and the heat transfer rate at the surface, whereas the opposite trend is obtained for the Sherwood number. It is also observed that suction widens the range of the unsteadiness parameter for which the solution exists.

The present perusal is to scrutinize the consequences of free-forced convective heat-mass transportation and n th order chemical reaction on MHD, non-Darcian, incompressible nanofluid fluid flow through an extended lamina, immersed in a permeable medium along with an external constant magnetic field. The fluid flow governing equations (PDEs) has been transformed into a system of nonlinear ODEs with the help of appropriate similarity transformation, and then solved numerically by using SQLM (Spectral quasilinearization method) method. Solution error for temperature and concentration profile against radiation parameter, Brownian motion parameter, and Hartman number also has been depicted diagrammatically. The graphical representation shows that the Hartman number, Brownian motion parameter, and chemical reaction parameter decline in velocity. While, the thermal boundary layer enhances with an enhancement of the Hartman number, Brownian motion parameter, radiation parameter, and chemical reaction parameter. Generation of entropy increases with the Brinkman number, Reynolds number, and Hartman number in the vicinity of the stretching lamina. Brinkman number and Reynolds number reduce the Bejan number. For the engineering interest Skin-friction, the local Nusselt number, and local Sherwood number also have been calculated. Impacts of pertinent parameters on the skin friction, Nusselt number, and Sherwood number are examined graphically and also numerically.

Purpose The purpose of this paper is to study the steady mixed convection hybrid nanofluid flow and heat transfer past a vertical thin needle with prescribed surface heat flux. Design/methodology/approach The governing partial differential equations are transformed into a set of ordinary differential equations by using a similarity transformation. The transformed equations are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The features of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for different values of the governing parameters are analyzed and discussed. Findings It is found that dual solutions exist for a certain range of the mixed convection parameter where its critical values decrease with the increasing of the copper (Cu) nanoparticle volume fractions and for the smaller needle size. It is also observed that the increasing of the copper (Cu) nanoparticle volume fractions and the decreasing of the needle size tend to enhance the skin friction coefficient and the local Nusselt number on the needle surface. A temporal stability analysis is performed to determine the stability of the dual solutions in the long run, and it is revealed that only one of them is stable, while the other is unstable. Originality/value The problem of hybrid nanofluid flow and heat transfer past a vertical thin needle with prescribed surface heat flux is the important originality of the present study where the dual solutions for the opposing flow are obtained.

This study investigates the effects of slip parameters and velocity power index parameter along with wall thickness on the magnetohydrodynamic (MHD) boundary layer flow of a Williamson nanofluid through a stretching sheet in porous medium. The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) using the relevant similarity variables. These nonlinear ODEs are solved numerically using the Runge-Kutta Fehlberg in MAPLE software. The effects of the pertinent parameters on the velocity, temperature and nanoparticle volume fraction profiles are presented graphically. The impact of the physical parameters on the skin friction coefficient, the local Nusselt number and the local Sherwood number are computed and analyzed. The velocity profile increases when the velocity slip parameter increases. The temperature slip and nanoparticle fraction slip parameters reduce the temperature and the nanoparticle volume fraction profiles respectively. The temperature and the nanoparticle volume fraction profiles significantly increase due to the increase in the velocity power index. An opposite behaviour is observed on different values of the wall thickness parameter when the power index is less than one compared to greater than one.

Gyrotactic microorganisms mixed convection flow of nanofluid over a vertically surfaced saturated porous media

The two-dimensional magnetohydrodynamic boundary layer flow of non-Newtonian power-law nanofluids past a porous stretching sheet with linear hydrodynamic slip boundary condition in the presence of chemical reaction and temperature dependent slip boundary condition. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, bvp4c MATLAB solver has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and Concentration profiles for different values of the governing parameters, namely, the power-law index parameter, Lewis number, Prandtl number, thermophoresis parameter, Brownian motion parameter, magnetic field parameter, linear momentum slip parameter, permeability parameter, temperature dependent slip parameter and chemical reaction parameter.

The effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical flat plate have been investigated. The results are obtained numerically by transforming the governing system of boundary layer equations into a system of non‐dimensional equations. Numerical results for different values of pressure stress work parameter, viscous dissipation parameter, and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction coefficient, and the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters. Results are compared with previous investigation.