Numerical study on heat/mass transfer by shear/thermal/solutal-convection in a cavity under counteracting buoyancies

This study provides physical insights into a lid-driven square cavity filled with a mixture of a solvent vapor and non-condensable gas, subjected to the vertically parallel thermal and solutal gradients. The top lid is maintained at constant speed while bottom lid and the other two walls are kept fixed. Zero heat and mass fluxes are imposed on the vertical side walls. The transport equations are solved numerically through a pressure-correction-based iterative algorithm (SIMPLE) with the QUICK scheme for convective terms. The diffusivities of heat and salt are assumed to be equal throughout this investigation. The essential details of flow, temperature and concentration fields are presented for the opposing buoyancy forces ratio (B < 0) with special attention being given for the values of parameters for which either the flow inside the cavity is operated by the mechanically induced convection; or the flow structure inside the cavity is akin to a single-diffusive thermal or solutal convection. The variations of average rates of heat and mass transfer are uniform with the Reynolds number, while the variations of these quantities against the solutal Richardson number (Ri _C ) and thermal Richardson number (Ri _T ) point to the existence of the local minimum/maximum. Finally, two linear relations between Ri _C and Ri _T at a constant sliding speed are proposed to identify the above points of high and low transport phenomena and justified with the exhibition of the flow structures inside the cavity.     

Fluid flow due to combined convection in lid-driven enclosure having a circular body

The present work is aimed to study mixed convection heat transfer characteristics for a lid-driven air flow within a square enclosure having a circular body. Flows are driven by the left lid, which slides in its own plane constant velocity. This wall is isothermal and it moves up or down in y direction while the other walls remain stationary. The horizontal walls are adiabatic. The cavity is differentially heated and the left wall is maintained at a higher temperature than the right wall. Three different temperature boundary conditions were applied for the inner cylinder as adiabatic, isothermal or conductive. The computation is carried out for wide ranges of Richardson numbers, diameter of inner cylinder and center and location of the inner cylinder. It was found that the most effective parameter on flow field and temperature distribution is the orientation of the moving lid. The circular body can be a control parameter for heat and fluid flow. An interesting obtained result that the thermal conductivity becomes insignificant for small values of diameter of the circular body.     

Non-isobaric Marangoni boundary layer flow for Cu,Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and TiO<Subscript>2</Subscript> nanoparticles in a water based fluid

In this paper, a non-isobaric Marangoni boundary layer flow that can be formed along the interface of immiscible nanofluids in surface driven flows due to an imposed temperature gradient, is considered. The solution is determined using a similarity solution for both the momentum and energy equations and assuming developing boundary layer flow along the interface of the immiscible nanofluids. The resulting system of nonlinear ordinary differential equations is solved numerically using the shooting method along with the Runge-Kutta-Fehlberg method. Numerical results are obtained for the interface velocity, the surface temperature gradient as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ (0≤φ≤0.2) and the constant exponent β. Three different types of nanoparticles, namely Cu, Al₂O₃ and TiO₂ are considered by using water-based fluid with Prandtl number Pr =6.2. It was found that nanoparticles with low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to Al₂O₃ and Cu. The results also indicate that dual solutions exist when β<0.5. The paper complements also the work by Golia and Viviani (Meccanica 21:200–204, 1986) concerning the dual solutions in the case of adverse pressure gradient.     

Numerical study of Prandtl effect on MHD flow at a lid‐driven porous cavity

In this paper, the lattice Boltzmann method is used to study the Prandtl number effect on flow structure and heat transfer rates in a magnetohydrodynamic flow mixed convection in a lid‐driven cavity filled with a porous medium. The right and left walls are at constant but different temperatures (θ_h and θ_c), while the other walls are adiabatic. Gallium and salt water (0.02 < Pr < 13.4) are used as samples of the electroconducting fluids in the cavity. Typical sets of streamlines and isotherms are presented to analyze the flow patterns set up by the competition among the forced flow created by the lid‐driven wall, the buoyancy force of the fluid and the magnetic force of the applied magnetic field. Mathematical formulations in the porous media were constructed based on the Brinkman–Forchheimer model, while the multidistribution‐function model was used for the magnetic field effect. Numerical results were obtained and the effects of the Prandtl number and the other effective parameters such as Richardson, Hartman, and Darcy numbers were investigated. It was found that the fluid fluctuations within the cavity were reduced by increasing the Hartman number. A similar pattern was observed for the Darcy number reduction. Heat transfer was essentially dominated by the conduction for the low Prandtl number and forced convection dominated as the Prandtl number increased. Also, the average Nusselt number was raised by increasing the Prandtl number. It was discovered that a remarkable heat transfer enhancement of up to 28% could be reached by increasing the Prandtl number (from 0.02 to 13.4) at constant Richardson and Darcy numbers. Copyright © 2011 John Wiley & Sons, Ltd.     

Flow behaviour of negatively buoyant jets in immiscible ambient fluid

In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting a jet of dyed fresh water through a nozzle in the base of a cylindrical tank containing rapeseed oil. The fountain inlet flow rate and nozzle diameter were varied to cover a wide range of Richardson Ri (8 × 10⁻⁴ < Ri < 1.98), Reynolds Re (467 < Re < 5,928) and Weber We (2.40 < We < 308.56) numbers. Based on the Re, Ri and We values for the experiments, we have determined a regime map to define how these values may control the occurrence of the observed flow types. Whereas Ri plays a stronger role when determining the maximum penetration height, the effect of the Reynolds number is stronger predicting the flow behaviour for a specific nozzle diameter and injection velocity.     

Convective transport of nanoparticles in multi-layer fluid flow

Technologically, multi-layer fluid models are important in understanding fluid-fluid or fluid-nanoparticle interactions and their effects on flow and heat transfer characteristics. However, to the best of the authors’ knowledge, little attention has been paid to the study of three-layer fluid models with nanofluids. Therefore, a three-layer fluid flow model with nanofluids is formulated in this paper. The governing coupled nonlinear differential equations of the problem are non-dimensionalized by using appropriate fundamental quantities. The resulting multi-point boundary value problem is solved numerically by quasi-linearization and Richardson’s extrapolation with modified boundary conditions. The effects of the model parameters on the flow and heat transfer are obtained and analyzed. The results show that an increase in the nanoparticle concentration in the base fluid can modify the fluid-velocity at the interface of the two fluids and reduce the shear not only at the surface of the clear fluid but also at the interface between them. That is, nanofluids play a vital role in modifying the flow phenomena. Therefore, one can use nanofluids to obtain the desired qualities for the multi-fluid flow and heat transfer characteristics.     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.     

Convective heat transfer of aqueous alumina nanosuspensions in a horizontal mini-channel

This work reports an experimental study of convective heat transfer of aqueous alumina nanofluids in a horizontal mini-channel under laminar flow condition 40 < Re < 1,000. The variation of local heat transfer coefficients, in both entrance and developed flow regimes, was obtained as a function of axial distance. The heat transfer coefficient of nanofluids was found to be dependent on not only nanoparticle concentration but also mass flow rate. Different to the behavior in conventional-sized channels, the major heat transfer coefficient enhancement is shown in the fully developed regime in the minichannel where up to 40% increase is observed. Discussions of the results suggest that apart from the need of a careful assessment of different thermo-physical properties of nanofluids, i.e., viscosity, specific heat and thermal conductivity, the heterogeneous nature of nanoparticle flow should be considered especially under high flow rate conditions.     

Free Convection Boundary Layer Flow from a Heated Upward Facing Horizontal Flat Plate Embedded in a Porous Medium Filled by a Nanofluid with Convective Boundary Condition

The steady laminar incompressible free convective flow of a nanofluid over a permeable upward facing horizontal plate located in porous medium taking into account the thermal convective boundary condition is studied numerically. The nanofluid model used involves the effect of Brownian motion and the thermophoresis. Using similarity transformations the continuity, the momentum, the energy, and the nanoparticle volume fraction equations are transformed into a set of coupled similarity equations, before being solved numerically, by an implicit finite difference numerical method. Our analysis reveals that for a true similarity solution, the convective heat transfer coefficient related with the hot fluid and the mass transfer velocity must be proportional to x ^−2/3, where x is the horizontal distance along the plate from the origin. Effects of the various parameters on the dimensionless longitudinal velocity, the temperature, the nanoparticle volume fraction, as well as on the rate of heat transfer and the rate of nanoparticle volume fraction have been presented graphically and discussed. It is found that Lewis number, the Brownian motion, and the convective heat transfer parameters increase the heat transfer rate whilst the thermophoresis decreases the heat transfer rate. It is also found that Lewis number and the convective heat transfer parameter enhance the nanoparticle volume fraction rate whilst the thermophoresis parameter decreases nanoparticle volume fraction rate. A very good agreement is found between numerical results of the present article for special case and published results. This close agreement supports the validity of our analysis and the accuracy of the numerical computations.     

Numerical analysis of transient laminar forced convection of nanofluids in circular ducts

In this study, forced convection heat transfer characteristics of nanofluids are investigated by numerical analysis of incompressible transient laminar flow in a circular duct under step change in wall temperature and wall heat flux. The thermal responses of the system are obtained by solving energy equation under both transient and steady-state conditions for hydro-dynamically fully-developed flow. In the analyses, temperature dependent thermo-physical properties are also considered. In the numerical analysis, Al₂O₃/water nanofluid is assumed as a homogenous single-phase fluid. For the effective thermal conductivity of nanofluids, Hamilton–Crosser model is used together with a model for Brownian motion in the analysis which takes the effects of temperature and the particle diameter into account. Temperature distributions across the tube for a step jump of wall temperature and also wall heat flux are obtained for various times during the transient calculations at a given location for a constant value of Peclet number and a particle diameter. Variations of thermal conductivity in turn, heat transfer enhancement is obtained at various times as a function of nanoparticle volume fractions, at a given nanoparticle diameter and Peclet number. The results are given under transient and steady-state conditions; steady-state conditions are obtained at larger times and enhancements are found by comparison to the base fluid heat transfer coefficient under the same conditions.     

Opposing mixed convection and its interaction with radiation inside eccentric horizontal cylindrical annulus

In the present investigation, the coupled phenomenon of opposing mixed convection and radiation within differentially heated eccentric horizontal cylindrical annulus has been numerically simulated. The radiation transfer contributed from the participating medium is obtained by solving the nonlinear integro‐differential radiative transfer equation using discrete ordinate method. The participating gray medium is considered to be emitting, absorbing and isotropically scattering. The walls of the annulus are considered to be opaque, diffuse and gray. In the study it has been observed that the Richardson number ‘Ri’ has a small effect on the total Nusselt number ‘Nu’ in mixed convection heat transfer with or without radiation. From the present investigation it is found that substantial changes occur in isotherms as well as in flow patterns, when the Richardson number is allowed to vary in the range of 0.01–1. The influence of radiative parameters on the interaction phenomenon has been delineated through isotherm and streamline pattern. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of Brownian Motion and Thermophoresis on the Mixed Convection of Nanofluid in a Porous Channel Including Flow Reversal

This article is devoted to combined convection heat transfer of nanofluids through a vertical channel filled with a homogeneous and isotropic porous medium. The flow is assumed to be fully developed and the “Brinkman extended Darcy” model is used for the flow in the porous media and “clear compatible” viscous dissipation model is considered. Also the model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing momentum, energy, and nanopartices volume fraction equations are solved both analytically and numerically. The effects of the influential dimensionless parameters such as Brownian and thermophoresis parameters, mixed convection parameter (Gr/Re), Brinkman, Darcy and Lewis numbers on dimensionless velocity and temperature distributions and pressure drop are studied. Also, the results of the Nusselt number for the both left and right walls are presented and discussed.     

Electro-magneto-hydrodynamic flow of couple stress nanofluids in micro-peristaltic channel with slip and convective conditions

This study explores the effects of electro-magneto-hydrodynamics,Hall currents,and convective and slip boundary conditions on the peristaltic propulsion of nanofluids(considered as couple stress nanofluids)through porous symmetric microchannels.The phenomena of energy and mass transfer are considered under thermal radiation and heat source/sink.The governing equations are modeled and non-dimensionalized under appropriate dimensionless quantities.The resulting system is solved numerically with MATHEMATICA(with an in-built function,namely the Runge-Kutta scheme).Graphical results are presented for various fluid flow quantities,such as the velocity,the nanoparticle temperature,the nanoparticle concentration,the skin friction,the nanoparticle heat transfer coefficient,the nanoparticle concentration coefficient,and the trapping phenomena.The results indicate that the nanoparticle heat transfer coefficient is enhanced for the larger values of thermophoresis parameters.Furthermore,an intriguing phenomenon is observed in trapping:the trapped bolus is expanded with an increase in the Hartmann number.However,the bolus size decreases with the increasing values of both the Darcy number and the electroosmotic parameter.     

Numerical simulation of the nanoparticle diameter effect on the thermal performance of a nanofluid in a cooling chamber

The thermal performance of a nanofluid in a cooling chamber with variations of the nanoparticle diameter is numerically investigated. The chamber is filled with water and nanoparticles of alumina (Al₂O₃). Appropriate nanofluid models are used to approximate the nanofluid thermal conductivity and dynamic viscosity by incorporating the effects of the nanoparticle concentration, Brownian motion, temperature, nanoparticles diameter, and interfacial layer thickness. The horizontal boundaries of the square domain are assumed to be insulated, and the vertical boundaries are considered to be isothermal. The governing stream-vorticity equations are solved by using a secondorder central finite difference scheme coupled with the mass and energy conservation equations. The results of the present work are found to be in good agreement with the previously published data for special cases. This study is conducted for the Reynolds number being fixed at Re = 100 and different values of the nanoparticle volume fraction, Richardson number, nanofluid temperature, and nanoparticle diameter. The results show that the heat transfer rate and the Nusselt number are enhanced by increasing the nanoparticle volume fraction and decreasing the Richardson number. The Nusselt number also increases as the nanoparticle diameter decreases.     

Natural convection of SiO_2-water nanofluid in square cavity with thermal square column

A square with a thermal square column is a simple but nontrivial research prototype for nanofluid research. However, until now, the effects of the temperature of the square column on the heat and mass transfer of nanofluids have not been revealed comprehensively, especially on entropy generation. To deepen insight into this important field, the natural convection of the SiO_2-water nanofluid in a square cavity with a square thermal column is studied numerically in this study. The effects of the thermal column temperature(T = 0.0, 0.5, 1.0, 1.5), the Rayleigh number(ranging from 10~3 to 10~6),and the volume fraction of the nanoparticle(varying from 0.01 to 0.04) on the fluid flow,heat transfer, and entropy generation are investigated, respectively. It is found that, no matter at a low or high Rayleigh number, the volume fraction of the nanoparticle shows no considerable effects on the flow field and temperature field for all the temperatures of the thermal column. With an increase in the volume fraction, the mean Nusselt number increases slightly. At the same time, it is found that, with an increase in the temperature of the thermal column, the average Nusselt number gradually decreases at all values of the Rayleigh number. Meanwhile, it is found that, at a high Rayleigh number, the heat transfer mechanism is the main parameter affecting the increase in the total entropy generation rather than the volume fraction. In addition, no matter at a high or low Rayleigh number, when T = 0.5, the total entropy generation is the minimum.     

The effect of real viscosity on the heat transfer of water based Al2O3 nanofluids in a two-sided lid-driven differentially heated rectangular cavity

The heat transfer and fluid flow behavior of water based Al₂O₃ nanofluids are numerically investigated inside a two-sided lid-driven differentially heated rectangular cavity. Physical properties which have major effects on the heat transfer of nanofluids such as viscosity and thermal conductivity are experimentally investigated and correlated and subsequently used as input data in the numerical simulation. Transport equations are numerically solved with finite volume approach using SIMPLEC algorithm. It was found that not only the thermal conductivity but also the viscosity of nanofluids has a key role in the heat transfer of nanofluids. The results show that at low Reynolds number, increasing the volume fraction of nanoparticles increases the viscosity and has a deteriorating effect on the heat transfer of nanofluids. At high Reynolds number, the increase in the viscosity is compensated by force convection and the increase in the volume fraction of nanoparticles which results in an increase in heat transfer is in coincidence with experimental results.     

Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects

The effect of double-diffusive natural convection of water in a partially heated enclosure with Soret and Dufour coefficients around the density maximum is studied numerically. The right vertical wall has constant temperature θ_c, while left vertical wall is partially heated θ_h, with θ_h > θ_c. The concentration in right wall is maintained higher than left wall (C_c < C_h) for case I, and concentration is lower in right wall than left wall (C_h > C_c) for case II. The remaining left vertical wall and the two horizontal walls are considered adiabatic. Water is considered as the working fluid. The governing equations are solved by control volume method using SIMPLE algorithm with QUICK scheme. The effect of the various parameters (thermal Rayleigh number, center of the heating location, density inversion parameter, Buoyancy ratio number, Schmidt number, and Soret and Dufour coefficients) on the flow pattern and heat and mass transfer has been depicted. Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters mentioned above.     

Investigation of the different base fluid effects on the nanofluids heat transfer and pressure drop

A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with a constant heat flux condition has been performed. The effect of Al₂O₃ volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids, and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid, solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover, this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper nanofluids.     

Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under laminar flow in a helically dimpled tube

An experimental investigation on the convective heat transfer and friction factor characteristics in the plain and dimpled tube under laminar flow with constant heat flux is carried out with distilled water and CuO/water nanofluids. For this, CuO nanoparticles with an average size of 15.3 nm were synthesized by sol–gel method. The nanoparticles are then dispersed in distilled water to form stable suspension of CuO/water nanofluid containing 0.1, 0.2 and 0.3% volume concentration of nanoparticles. It is found that the experimental Nusselt numbers for 0.1, 0.2 and 0.3% volume concentration of CuO nanoparticles are about 6, 9.9 and 12.6%, respectively higher than those obtained with distilled water in plain tube. However, the experimental Nusselt numbers for 0.1, 0.2 and 0.3% volume concentration of CuO nanoparticles are about 3.4, 6.8 and 12%, respectively higher than those obtained with distilled water in dimpled tube. The friction factor of CuO/water nanofluid is also increased due to the inclusion of nanoparticles and found to increase with nanoparticle volume concentration. The experimental results show that there exists a difference in the enhancement levels of Nusselt numbers obtained with nanofluids in plain tube and dimpled tube. Hence it is proposed that the mechanism of heat transfer enhancement obtained with nanofluids is due to particle migration from the core of fluid flow to tube wall.