Natural Convection Flow Of Nanofluid Research Articles

Numerical Study of Natural Convection Flow of Nanofluid Past a Circular Cone with Cattaneo–Christov Heat and Mass Flux Models

The objective of this study is to analyze the natural convection flow of nanofluid along a circular cone placed in a vertical direction. The generalized heat flux and mass flux models are commonly known as the Cattaneo–Christov heat flux model and mass flux models. In the present study, these models are used for both heat and mass transfers analysis in nanofluid flow. For the governing equations, the Buongiorno transport model is used in which two important slip mechanism, namely thermophoresis and Brownian motion parameters, are discussed. The resulting governing equations in the form of partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) due to similar flow along the surface of a circular cone. To solve these ODEs, a numerical algorithm based on implicit finite difference scheme is utilized. The effects of dimensionless parameters on heat and mass transfer in nanofluid flow are discussed graphically in the form of velocity profile, temperature profile, Sherwood number and Nusselt number. It is noted that in the presence of the Cattaneo–Christov heat flux model and mass flux model, the heat transfer rate decreases by increasing both thermal and concentration relaxation parameters; however, Sherwood number decreases by increasing the thermal relaxation parameter, and increases by increasing the concentration relaxation parameter.

Unsteady MHD Natural Convection Flow of Nanofluid in a Cavity Containing Adiabatic Obstacle with Heat Corners

Unsteady natural convection heat transfer of nanofluid within cavities with local heaters occurs in several engineering applications. Therefore, investigation of nanofluid flow and heat transfer processes in such systems has a considerable value for evolution of industry. In the current investigation, unsteady MHD natural convection flow of Cu-water nanofluid and heat transfer behavior in square cavity containing a centered adiabatic square block. The mathematical formulation part for present problem is presented in succeeding section. It has been found the size of the adiabatic obstacle influences the behavior of the nanofluid and conduction becomes dominant when size aspect ratio increases to 0.5. It is also noticed that angle of the applied magnetic field can maximize(minimum)the rate of heat transfer if applied in the stream-wise (normal) direction. The novelty of the present work is to consider cavity containing a centered adiabatic square block as well as unsteady effects in the natural convection of nanofluids.

Heat transfer in natural convection flow of nanofluid along a vertical wavy plate with variable heat flux

The present analysis is concerned to examine the enhancement of heat transfer in natural convection flow of nanofluid through a vertical wavy plate assumed at variable heat flux. The rate of heat transfer in nanofluid flow as compared to pure water can be increased due to increase the density of nanofluid which depends on the density and concentration of nanoparticles. For this analysis, Tiwari and Das model is used by considering two nanoparticles i. e. Al2O3 and Cu are suspended in a base fluid (water). A very efficient implicit finite difference technique converges quadratically is applied on the concerning PDE for numerical solution. The effects of pertinent parameters namely, volume fraction parameter of nanoparticle, wavy surface amplitude, Prandtl number and exponent of variable heat flux on streamlines, isothermal lines, local skin friction coefficient and local Nusselt number are shown through graphs. In this analysis, a maximum heat transfer rate is noted in Cu-water nanofluid through a vertical wavy surface as compared to Al2O3-water and pure water.

Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

Unsteady two-dimensional flows of a nanofluid over a vertical plate with time-exponential temperature

A two dimensional natural convective flow of nanofluid over a vertical plate in the presence of time-exponential temperature has been studied analytically. We have incorporated the effects of thermophoresis and Brownian motion in the considered nanofluid model. Moreover on the boundary of plate, it is assumed that the volumetric concentration of nanoparticles is passively controlled. The non-linear coupled governing equations have been solved with the help of the modified simple function equation method. Exact expressions for the concentration, temperature and velocity distribution profile have been established. Numerical computations are carried out in order to see the influence of different physical parameters like Lewis number, Pradtl number, buoyancy ratio parameter, thermophoresis parameter and Brownian motion parameter on the volumetric concentration of nanoparticles, temperature and velocity distribution profile and results are illustrated graphically and with tables. It is found that for decreasing values of the Brownian diffusion coefficient, therefore for increasing values of the Lewis number, the values of temperature and of particles concentration decrease. The temperature decreases with Prandtl number; while the nanoparticles concentration increases with Prandtl number (the thermal diffusivity has different influence on temperature and concentration).

Natural Convection Flow of Nanofluids in Squeeze Film with an Exponential Curvature

A theoretical study of the laminar squeeze flow of copper water and alumina water nanofluids between a flat circular stationary disk and a curved circular moving disk is carried out using energy integral method. The squeeze film behaviour is examined analytically and the effects of inertia and curvature on the squeeze film pressure, load carrying capacity of the fluid and temperature are analysed. Further, the problem is solved numerically for a sinusoidal motion of the upper curved disk taking an exponential form of the gap width. It is found that the copper water nanofluid is better than alumina water nanofluid for better heat transfer rates. While high inertia forces strongly influence the squeeze film behaviour, low inertia forces are favourable for temperature distribution. Further, concave nature of the upper disk gives better squeeze film characteristics than convex disk. However, convex disk is better than concave disk as far as the temperature distribution is concerned.

Computational analysis of non-Newtonian boundary layer flow of nanofluid past a semi-infinite vertical plate with partial slip

Abstract An analysis of this paper is examined, two-dimensional, laminar with heat and mass transfer of natural convective nanofluid flow past a semi-infinite vertical plate surface with velocity and thermal slip effects are studied theoretically. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The influences of the emerging parameters i.e. Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Buoyancy ratio parameter (N), Lewis number (Le), Prandtl number (Pr), Velocity slip factor (Sf) and Thermal slip factor (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. The major sources of nanoparticle migration in Nanofluids are Thermophoresis and Brownian motion. A suitable agreement with existing published literature is made and an excellent agreement is observed for the limiting case and also validation of solutions with a Nakamura tridiagonal method has been included. It is observed that nanoparticle concentrations on surface decreases with an increase in slip parameter. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Natural Convection Flow of Nanofluids in a Composite System with Variable-Porosity Media

A numerical study is performed to examine the effects of nonuniform porosity of a porous medium and thermal dispersion on the natural convection flow and heat transfer of a nanofluid inside a rectangular enclosure containing a fluid and porous layers using a single-phase thermal dispersion model. Copper is considered as nanoparticles and is suspended in a base fluid (water) and the Brinkman–Forchheimer-extended Darcy model is assumed to represent the flow inside the porous layer. The finite volume method with the semi-implicit method for pressure-linked equations (SIMPLE) algorithm is used to solve the dimensionless governing equations, and validation tests of the obtained results are conducted. It is found that the increase in the fluid layer thickness enhances the heat transfer rate at the right wall. Also, an improvement with rate greater than 10% is obtained in the heat transfer rate when the nanoparticle volume fraction is increased to 4%.

Two-phase natural convection dusty nanofluid flow

An analysis is performed to study the two-phase natural convection flow of nanofluid along a vertical wavy surface. The model includes equations expressing conservation of total mass, momentum and thermal energy for two-phase nanofluid. Primitive variable formulations (PVF) are used to transform the dimensionless boundary layer equations into a convenient coordinate system and the resulting equations are integrated numerically via implicit finite difference iterative scheme. The effect of controlling parameters on the dimensionless quantities such as skin friction coefficient, rate of heat transfer and rate of mass transfer is explored. It is concluded from the present analysis, that the diffusivity ratio parameter, NA and particle-density increment number, NB have pronounced influence on the reduction of heat transfer rate.

Heat and mass transfer analysis in natural convection flow of nanofluid over a vertical cone with chemical reaction

PurposeIn recent years, nanofluids are being widely used in many thermal systems because of their higher thermal conductivity and heat transfer rate. The higher thermal conductivity depends on many parameters such as size, shape and volume and the Brownian motion and thermophoresis of added nanoparticles. The purpose of this paper is to analyze the influence of the Brownian motion and thermophoresis on natural convection heat and mass transfer boundary layer flow of nanofluids over a vertical cone with radiation.Design/methodology/approachUsing similarity variables, the non-linear partial differential equations, which represent momentum, energy and diffusion, are transformed into ordinary differential equations. The transformed conservation equations are solved numerically subject to the boundary conditions by using versatile, extensively validated, variational finite-element method.FindingsThe sway of significant parameters such as magnetic field (M), buoyancy ratio parameter (Nr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), thermal radiation (R), Lewis number (Le) and chemical reaction parameter (Cr) on velocity, temperature and concentration evaluation in the boundary layer region is examined in detail. The results are compared with previously published work and are found to be in agreement. The velocity distributions are reduced, while temperature and concentration profiles elevate with a higher (M). With the improving values of (R), the velocity and temperature sketches improve, while concentration distributions are lowered in the boundary layer region. The temperature and concentration profiles are elevated in the boundary layer region for higher values of (Nt). With the increasing values of (Nb), temperature profiles are enhanced, whereas concentration profiles get depreciated in the flow region.Social implicationsIn recent years, it has been found that magneto-nanofluids are significant in many areas of science and technology. It has applications in optical modulators, magnetooptical wavelength filters, tunable optical fiber filters and optical switches. Magnetic nanoparticles are especially useful in biomedicine, sink float separation, cancer therapy, etc. Specific biomedical applications involving nanofluids include hyperthermia, magnetic cell separation, drug delivery and contrast enhancement in magnetic resonance imaging.Originality/valueTo the best of the authors’ knowledge, no studies have assessed the impact of the two slip effects, namely, Brownian motion and thermophoresis, on the natural convection of electrically conducted heat and mass transfer to the nanofluid boundary layer flow over a vertical cone in the presence of radiation and chemical reaction; therefore, this problem has been addressed in this study. Comparison of the results of this study’s with those of previously published work was found to be in good agreement.

ENTROPY ANALYSIS OF UNSTEADY MAGNETOHYDRODYNAMIC NANOFLUID OVER STRETCHING SHEET WITH ELECTRIC FIELD

This paper reports the unsteady magnetohydrodynamic (MHD) natural convection flow of nanofluid over a permeable stretching sheet with buoyancy effects. Effects of Brownian motion and thermophoresis using a revised model are present. Entropy and heat transfer analysis is performed in the presence of viscous dissipation, Joule heating, and chemical reaction. Transformations techniques are applied to the constituted governing boundary layer equations to obtain a nonlinear couple of ordinary differential systems. Thereafter, the Keller-Box numerical method is applied to solve the problem and excellent agreement was found with those reported in the literature. The results corresponding to the velocity, temperature, concentration profiles, entropy generation and Bejan numbers profiles, tabular form for the skin friction, and the reduced Nusselt number for various pertinent parameters are examined. As the main outcome, our results show that on the flow field magnetic and electric fields exhibit opposite behavior; Hartmann number, Reynolds number, dimensionless Brinkman group, constant entropy parameter, and dimensionless group parameter intensify with entropy generation. Furthermore, thermal radiation, electric field, and Hartmann number gain the Bejan number.

Natural Convective Nanofluid Flow in an Annular Space Between Confocal Elliptic Cylinders

The natural convection fluid flow and heat transfer in an annulus of two differentially heated confocal elliptic cylinders filled with the Cu–water nanofluid are investigated numerically. The outer cylinder is maintained at a constant temperature Tc while the inner cylinder is kept at a differentially higher constant temperature Th. Equations of continuity, momentum, and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional steady, laminar, and incompressible flow, which is expressed in terms of stream function, vorticity, and temperature. The basic equations are discretized using the finite-volume method. Using a developed code, calculations were performed for Rayleigh number (103 ≤ Ra ≤ 3 × 105), volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.12), and eccentricity of the inner ellipse, ε1 = 0.7, 0.8, and 0.9. The eccentricity of outer ellipse and the angle of orientation are fixed at 0.6 deg and 0 deg, respectively. Results are presented in the form of stream lines, isotherm plots, and local and average Nusselt numbers. The results discussed in this present work show the existence of a very good agreement between the present results and those from the previous researches.

Heat transfer analysis in natural convection flow of nanofluid past a wavy cone

The problem of natural convective heat transfer of water-based nanofluid along wavy cone surface is investigated numerically. Analysis is performed to study the heat transfer augmentation due to five types of nanoparticles, namely, alumina (Al2O3), copper (Cu), silver (Ag), copper oxide (CuO) and titania (TiO2). The flow has been assumed to be steady and fluid properties have been supposed constant except for the density depending upon temperature giving rise to the buoyancy force. Famous Tiwari and Das model of nanofluid has been utilized in this study. The effects of cone half angle γ and amplitude of the waviness α on the Nusselt number (Nu) and skin friction (Cf) are studied. A comparison is made with the case of pure fluid flow past wavy cone at different values of α. It has been observed that the TiO2-nanoparticle shown to have the maximum cooling performance and Cu-nanoparticle appeared to have maximum heating performance for this study. The results shown in this research arrange for a significant source of reference for taming the natural convection heat transfer enactment along wavy cone. Present results for selected variables are matched with the already published work for pure fluid and are shown to be in good agreement.

Natural-Convection Flow of Nanofluids Over Vertical Cone Embedded in Non-Darcy Porous Media

In this paper, non-Darcy flow and natural convection over a vertical cone embedded in a porous medium saturated with a nanofluid is studied using the Forchheimer-extended Darcy law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. An analytical technique, similarity solution method, is used to convert the governing equations into a set of ordinary differential equations, and then numerically solved using the finite difference method. The effect of non-Darcy parameter and nanofluid parameters on the velocity, temperature, and nanoparticles volume fraction profiles, as well as on the two important parameters of heat and mass transfer, i.e., reduced Nusselt and Sherwood numbers, are discussed. The results show that an increase in the non-Darcy parameter decreases the velocity profiles, whereas it would increase the temperature and concentration profiles. Simulation results also show that an increase in the non-Darcy parameter would decrease the reduced Nusselt and Sherwood numbers, whereas an increase of Lewis number would increase the reduced Nusselt and Sherwood numbers.

Numerical study of influence of nanoparticle shape on the natural convection in Cu-water nanofluid

The natural convection flow of the Cu-water nanofluid inside a square cavity is simulated by using the radial basis integral equation (RBIE) method. The RBIE is a meshless method and it has the benefit of solving at each node for the velocity and its spatial gradients via integral equations. The effects of the spherical and spheroidal nanoparticles (NPs) on the natural convection flow of the nanofluids are examined. The different NPs shapes and sizes were found to affect differently the thermal conductivity and the viscosity of the nanofluids. Numerical results showed that the oblate spheroid with aspect ratio of 10 produced the largest enhancement of the overall heat transfer characteristic.

Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition

Heat transfer characteristics of a two-dimensional steady hydromagnetic natural convection flow of nanofluids over a non-linear stretching sheet taking into account the effects of radiation and convective boundary condition has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The local similarity solutions are obtained by using very robust computer algebra software Maple 13. The results corresponding to the dimensionless temperature profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. The results show that temperature within the boundary layer is enhanced with the increase of the Biot number, buoyancy due to nanoparticle concentration, strength of the applied magnetic field, Brownian motion parameter, and thermophoresis parameter. An opposite trend is observed for the increase of the buoyancy due to temperature, stretching index, and the radiation parameter. The results also show that the local rate of heat transfer strongly depends on the nonlinear stretching index, radiation parameter, Biot number, Brownian motion parameter, and thermophoresis parameter.

Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill-based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.

Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the Lattice Boltzmann model

This work applied the Lattice Boltzmann Method (LBM) to investigate the effect of CuO nanoparticles on natural convection with magnetohydrodynamic (MHD) flow in a square cavity. The left and right vertical walls of the cavity were kept at constant temperatures, Th and Tc, respectively, with two insulated walls at the top and bottom. A uniform magnetic field was used in a horizontal direction. Results were carried out for different Hartmann numbers ranging from 0–100, Rayleigh numbers from 103–105 and the solid volume fraction from 0 to 0.05. Effects of the solid volume fraction and magnetic field on hydrodynamic and thermal characteristics were investigated and discussed. The averaged Nusselt numbers, on hot wall, streamlines, temperature contours, and the vertical component of velocity for different values of a solid volume fraction, Hartmann and Rayleigh numbers were illustrated. The results indicate that the averaged Nusselt number increases for nanofluids when increasing the solid volume fraction, while, in the presence of a high magnetic field, this effect decreases.

DRBEM solution of natural convection flow of nanofluids with a heat source

This paper presents the dual reciprocity boundary element method (DRBEM) solution of the unsteady natural convective flow of nanofluids in enclosures with a heat source. The implicit Euler scheme is used for time integration. All the convective terms are evaluated in terms of DRBEM coordinate matrix. The vorticity boundary conditions are obtained from the Taylor series expansion of stream function equation. The results report that the average Nusselt number increases with the increase in both volume fraction and Rayleigh number. It is also observed that an increase in heater length reduces the heat transfer. The average Nusselt number of aluminum oxide-water based nanofluid is found to be smaller than that of copper-water based nanofluid. Results are given in terms of streamlines, isotherms, vorticity contours, velocity profiles and tables containing average Nusselt number for several values of Rayleigh number, heater length, volume fraction, and number of iterations together with CPU times.

Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary Conditions

Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary Conditions