Double-Diffusive Free Convection Flow Past an Inclined Plate Embedded in a Non-Darcy Porous Medium Saturated with a Nanofluid

In this investigation, we intend to present the influence of the prominent Soret effect on double-diffusive free convection heat and mass transfer in the boundary layer region of a semi-infinite inclined flat plate in a nanofluid saturated non-Darcy porous medium. The transformed boundary layer ordinary differential equations are solved numerically using the shooting and matching technique. Consideration of the nanofluid and the coupled convective process enhanced the number of non-dimensional parameters considerably thereby increasing the complexity of the present problem. A wide range of parameter values are chosen to bring out the effect of Soret parameter on the free convection process with varying angle of inclinations making the wall geometry from vertical to horizontal plate. The effects of angle of inclination and Soret parameter on the flow, heat and mass transfer coefficients are analyzed. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles, local wall temperature, local nanoparticle concentration, and local wall concentration reveal interesting phenomenon, and some of these qualitative results are presented through the plots.     

Non-axisymmetric Homann MHD stagnation point flow of Al_2O_3-Cu/water hybrid nanofluid with shape factor impact

The heat transfer of Homann flow in the stagnation region of the Al_2 O_3-Cu/water hybrid nanofluid is investigated by adopting the Tiwari-Das model over a cylindrical disk.The effects of the nanoparticle shape,the viscous dissipation,and the nonlinear radiation are considered.The governing equations are obtained by using similarity transformations,and the numerical outcomes for the flow and the temperature field are noted by bvp4 c on MATLAB.The numerical solutions of the flow field are compared with the asymptotic behaviors of large shear-to-strain-rate ratio.The effects of variations of parameters involved are inspected for both nanofluid and hybrid nanofluid flows,temperature profiles,local Nusselt numbers,and skin frictions.It is concluded that the velocity and temperature fields in the hybrid nanophase function more rapidly than those in the nanofluid phase.     

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.     

Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.

     

Slip effects on unsteady mixed convection of hybrid nanofluid flow near the stagnation point

The unsteady mixed convection of the Al2O3-Cu/H2O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed. The bvp4c technique is used to solve the resulting ordinary differential equations. The combined effects of the velocity and thermal slip are addressed. The effects of different relevant physical parameters are studied numerically. The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases, while the unsteadiness...     

Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid

This work is focused on the numerical modeling of steady laminar mixed convection flow in a lid-driven inclined square enclosure filled with water–Al₂O₃ nanofluid. The left and right walls of the enclosure are kept insulated while the bottom and top walls are maintained at constant temperatures with the top surface being the hot wall and moving at a constant speed. The developed equations are given in terms of the stream function–vorticity formulation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by a second-order accurate finite-volume method. Comparisons with previously published work are performed and found to be in good agreement. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and enclosure inclination angle on the flow and heat transfer characteristics. It is found that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.     

Effects of dimensional wall temperature on Reynolds stress budgets in a supersonic turbulent channel flow with thermally perfect gas

ABSTRACT

Direct numerical simulations of temporally evolving supersonic turbulent channel flow of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800, combined with constant dimensional wall temperatures from 149.075 to 1788.90?K to study the influence of dimensional wall temperature on the characteristics of Reynolds stress budgets. It is found that, as the dimensional wall temperature increases, the production, diffusion, pressure–velocity gradient correlation and dissipation terms increase, whereas the compressibility-related term decreases. This is mainly due to variations in mean flow properties. The mechanism of inter-component transfer (ICT) is insensitive to the dimensional wall temperature. The ICT relating to the pressure–velocity gradient correlation term can be divided into inner and outer regions, and the critical position separating these regions is at the semi-local scaling of approximately 16 irrespective of the different dimensional wall temperature.     

Analytical considerations of flow/thermal coupling of nanofluids in foam metals with local thermal non-equilibrium (LTNE) phenomena and inhomogeneous nanoparticle distribution

Foam metals with micro pores own excellent thermal performance, however, poor heat conductive ability of most heat-transfer fluids restricts further heat transfer improvement. Combination of foam metal and nanofluid with highly conductive nanoparticles is a promising solution. Convective thermal characteristics of nanofluids in porous foams are theoretically investigated in this work. Effects of Brownian motion and thermophoretic diffusion of nanoparticles in the base fluid on thermal performance are considered. The nanoparticle and the base-fluid are considered to be in thermal equilibrium and the temperature difference between the nanofluid and foam ligaments is especially considered. Compared with the base-fluid flow in a duct, the velocity distribution for the nanofluid flow in a porous foam is more uniform with a decreased dimensionless temperature. The pressure drop of the nanofluid increases with an increase in the concentration of the nanoparticles. By employing foam metals and nanofluid, the cross-sectional temperature becomes closer to the wall temperature. Simultaneously, notable difference between solid and fluid temperatures can be observed, revealing the LTNE effect of the nanofluid on the porous foam. It is found that the Nusselt number first increases and then decreases with an increase in nanoparticle concentration. Furthermore, the Nusselt number decreases with an increase in the foam porosity. It is found that the thermal performance of a nanofluid in a plain tube is different from that in the foam metals.     

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles: an analytical study

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H₂O, In-H₂O, and Au-H₂O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction.     

Stratified magnetohydrodynamic flow of tangent hyperbolic nanofluid induced by inclined sheet

This paper studies stratified magnetohydrodynamic(MHD) flow of tangent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations.The reduced systems are solved for convergent series solutions. The velocity, temperature,and concentration fields are discussed for different physical parameters. The results indicate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.     

Transient mixed convection flow instabilities in a vertical pipe

The present paper investigates a numerical study of flow instabilities in transient mixed convection in a vertical pipe. At the entrance of the pipe, the flow is suddenly submitted to a temperature step. The convection heat transfer on the outer surface of the pipe is taken into account. The governing equations are solved using a finite difference explicit scheme. The numerical results show that the time development of streamlines and isotherms is strongly dependent on the inlet temperature steps. For positive temperature steps, the unsteady vortex is significant in the vicinity of the wall and the reversal flow appears below the wave instability. In the case of negative temperature steps and especially for the low Reynolds number, the reversal flow appears on top of the wave instability. During the transient, the apparition of the vortical structures along the wall leads to the wall boundary layer instability. This phenomenon is due to the transient mixed convection flows. The temperature step effects on the heat transfer of the flow are presented in our paper.     

Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered.It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.     

TiO<Subscript>2</Subscript>-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO₂-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO₂ nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO₂ nanoparticles increases. This confirms the fact that the occurrence of the TiO₂ nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.     

Influence of lateral mass flux on mixed convection heat and mass transfer over inclined surfaces in porous media

 The effect of lateral mass flux on mixed convection heat and mass transfer in a saturated porous medium adjacent to an inclined permeable surface is analyzed. A similarity solution is obtained when surface temperature and concentration, free stream velocity and injection/suction velocity of fluid are prescribed as power functions of distance from the leading edge. The cases when the flow and buoyancy forces are in the same and opposite directions are discussed both for aiding and opposing buoyancy effects. The governing parameters are the mixed convection parameter Gr, the Lewis number Le, the buoyancy ratio N, the lateral mass flux parameter f _w, representing the effects of injection or withdrawal of fluid at the wall, and λ which specifies three cases of the inclined plate. The interactive effect of these parameters on heat and mass transfer rates are presented. It is observed that the diffusion ratio (Le) has a more pronounced effect on concentration field than on flow and temperature fields. It is found that the rates of heat and mass transfer increase with suction and decrease with injection of the fluid. Received on 31 August 2000 / Published online: 29 November 2001     

Conjugate natural convection of non-Newtonian hybrid nanofluid in wavy-shaped enclosure

The present study concerns the modelization and numerical simulation for the heat and flow exchange characteristics in a novel configuration saturated with a nonNewtonian Ag-MgO hybrid nanofluid. The wavy shaped enclosure is equipped with onequarter of a conducting solid cylinder. The system of equations resulting from the mathematical modeling of the physical problem in its dimensionless form is discretized via the higher-order Galerkin-based finite element method(GFEM). The dependency of vario...     

Two phase mixed convection Al2O3–water nanofluid flow in an annulus

Heat transfer enhancement of a mixed convection laminar Al₂O₃–water nanofluid flow in an annulus with constant heat flux boundary condition has been studied employing two phase mixture model and effective expressions of nanofluid properties. The fluid flow properties are assumed constant except for the density in the body force, which varies linearly with the temperature (Boussinesq’s hypothesis), thus the fluid flow characteristics are affected by the buoyancy force. The Brownian motions of nanoparticles have been considered to determine the effective thermal conductivity and the effective dynamic viscosity of Al₂O₃–water nanofluid, which depend on temperature. Three-dimensional Navier–Stokes, energy and volume fraction equations have been discretized using the finite volume method while the SIMPELC algorithm has been introduced to couple the velocity–pressure. Numerical simulations have been presented for the nanoparticles volume fraction (?) between 0 and 0.05 and different values of the Grashof and Reynolds numbers. The calculated results show that at a given Re and Gr, increasing nanoparticles volume fraction increases the Nusselt number at the inner and outer walls while it does not have any significant effect on the friction factor. Both the Nusselt number and the friction coefficient at the inner wall are more than their corresponding values at the outer wall.     

On the Reynolds-number independence of mixed convection in a vertical channel subjected to asymmetric wall temperatures with and without flow reversal

The problem of mixed convection in a vertical channel with asymmetric wall temperatures including situations of flow reversal is studied numerically. The SIMPLER algorithm with a staggered grid system is employed to solve the corresponding numerical equations formulated by the finite-volume method. A second-order upwind scheme is used to model the convective term, and a suitable grid distribution is introduced. The ranges of the parameters studied are 0 r_t 1, 1 Re 1000, and 0 Gr/Re 500.

The numerical results, with the streamwise coordinate scaled by the Reynolds number (Re), show that solutions for the velocity and temperature fields are independent of the Reynolds number when Re 50, even in the presence of flow reversal. These solutions, however, are dependent on r_t and Gr/Re. Subsequently, correlations are proposed for the bulk temperature distribution and the local Nusselt numbers along the hot wall and the cold wall.     

Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere

A numerical analysis is provided to scrutinize time-dependent magnetohydrodynamics(MHD) free and forced convection of an electrically conducting non-Newtonian Casson nanofluid flow in the forward stagnation point region of an impulsively rotating sphere with variable wall temperature. A single-phase flow of nanofluid model is reflected with a number of experimental formulae for both effective viscosity and thermal conductivity of nanofluid. Exceedingly nonlinear governing partial differential equations(PDEs)subject to their compatible boundary conditions are mutated into a system of nonlinear ordinary differential equations(ODEs). The derived nonlinear system is solved numerically with implementation of an implicit finite difference procedure merging with a technique of quasi-linearization. The controlled parameter impacts are clarified by a parametric study of the entire flow regime. It is depicted that from all the exhibited nanoparticles,Cu possesses the best convection. The surface heat transfer and surface shear stresses in the x-and z-directions are boosted with maximizing the values of nanoparticle solid volume fraction ? and rotation λ. Besides, as both the surface temperature exponent n and the Casson parameter γ upgrade, an enhancement of the Nusselt number is given.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration

In this article we derive semi-analytical/numerical solutions for transport phenomena (momentum, heat and mass transfer) in a nanofluid regime adjacent to a nonlinearly porous stretching sheet by means of the Homotopy analysis method (HAM). The governing equations are reduced to a nonlinear, coupled, non-similar, ordinary differential equation system via appropriate similarity transformations. This system is solved under physically realistic boundary conditions to compute stream function, velocity, temperature and concentration function distributions. The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation. Furthermore the current HAM solutions demonstrate very good correlation with the non-transpiring finite element solutions of Rana and Bhargava (Commun. Nonlinear Sci. Numer. Simul. 17:212–226, 2012). The influence of stretching parameter, transpiration (wall suction/injection) Prandtl number, Brownian motion parameter, thermophoresis parameter and Lewis number on velocity, temperature and concentration functions is illustrated graphically. Transpiration is shown to exert a substantial influence on flow characteristics. Applications of the study include industrial nanotechnological fabrication processes.