Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field

In this study natural convection heat transfer of Cu–water nanofluid in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder in the presence of horizontal magnetic field is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Hartmann number, Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results indicate that in the absence of magnetic field, enhancement ratio decreases as Rayleigh number increases while an opposite trend is observed in the presence of magnetic field. Also it is found that the average Nusselt number is an increasing function of nanoparticle volume fraction, the number of undulations and Rayleigh numbers while it is a decreasing function of Hartmann number.     

Heat transfer in rectangular microchannels heat sink using nanofluids

The effect of using nanofluids on heat transfer and fluid flow characteristics in rectangular shaped microchannel heat sink (MCHS) is numerically investigated for Reynolds number range of 100–1000. In this study, the MCHS performance using alumina–water (Al₂O₃-H₂O) nanofluid with volume fraction ranged from 1% to 5% was used as a coolant is examined. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using finite volume method. The MCHS performance is evaluated in terms of temperature profile, heat transfer coefficient, pressure drop, friction factor, wall shear stress and thermal resistance. The results reveal that when the volume fraction of nanoparticles is increased under the extreme heat flux, both the heat transfer coefficient and wall shear stress are increased while the thermal resistance of the MCHS is decreased. However, nanofluid with volume fraction of 5% could not be able to enhance the heat transfer or performing almost the same result as pure water. Therefore, the presence of nanoparticles could enhance the cooling of MCHS under the extreme heat flux conditions with the optimum value of nanoparticles. Only a slight increase in the pressure drop across the MCHS is found compared with the pure water-cooled MCHS.     

Laminar pulsating flow of nanofluids in a circular tube with isothermal wall

In this study, two-dimensional pulsating flow of nanofluids through a pipe with isothermal walls is numerically investigated. In order to solve Navier–Stokes and energy equations, the finite volume approach with collocated grid is employed. The momentum interpolation technique of Rhie and Chow is applied in SIMPLE algorithm. Pulsating flows have potential for research as many aspects of such flows are still unclear and require further investigation because of many upcoming applications. In the past decade, nanofluids have attracted much interest because of their reported superior thermal performance and many potential applications. Pulsation in nanofluid is a new idea in case of fluid mechanics and heat transfer. The authors have not found any records similar to the present study. One of the advantages of using pulsation in nanofluid is a delay in nanoparticles sedimentation process. The simulation performed at with different pulse parameters (Amplitude, Strouhal and Reynolds numbers) and volume fractions of nanoparticles for unsteady flow. Increasing both the frequency and amplitude leads to a slight increase in Nusselt number but by increasing Reynolds and volume fraction, more rate of heat transfer is observed.     

Numerical investigations of flow and heat transfer enhancement in a corrugated channel using nanofluid

In this paper, heat transfer and pressure drop characteristics of copper–water nanofluid flow through isothermally heated corrugated channel are numerically studied. A numerical simulation is carried out by solving the governing continuity, momentum and energy equations for laminar flow in curvilinear coordinates using the Finite Difference (FD) approach. The investigation covers Reynolds number and nanoparticle volume fraction in the ranges of 100–1000 and 0–0.05 respectively. The effects of using the nanofluid on the heat transfer and pressure drop inside the channel are investigated. It is found that the heat transfer enhancement increases with increase in the volume fraction of the nanoparticle and Reynolds number, while there is slight increase in pressure drop. Comparisons of the present results with those available in literature are presented and discussed.     

Combined Effect of Magnetic Field and Nanofluid Variable Properties on Heat Transfer Enhancement in Natural Convection

The current work investigated, numerically, enhancement of heat transfer in natural convection using CuO-water nanofluid in the presence of a magnetic field. The governing equations were discretized using the control volume method and solved numerically via the SIMPLE algorithm. For the case of absence of a magnetic field and for low Rayleigh number, the heat transfer was almost insensitive to the presence of nanoparticles. For moderate and high Rayleigh numbers, the presence of nanoparticles had an adverse effect on heat transfer at high volume fraction of nanoparticles. The highest reduction in heat transfer was registered for the case of Ra = 10⁵. Contour maps are generated for the normalized Nusselt number (Nu*) to determine the optimum selection of volume fraction of nanoparticles and magnetic field that gives maximum heat transfer enhancement. The results demonstrated the effectiveness and practicality of using high values of magnetic field in enhancing heat transfer using nanofluids.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

Numerical investigation of non‐Newtonian nanofluid mixed convection in a two‐opposite direction lid‐driven cavity with variable properties

The mixed convection fluid flow in a square cavity filled with AL₂O₃‐water non‐Newtonian nanofluid is numerically analyzed. The left and right vertical boundaries of the enclosure have been kept in the constant temperature. Remaining walls of the cavity have been considered to have adiabatic boundary condition. Two different cases have been considered. In the first case, left and right side walls have been moved vertically with constant speed V_b in opposite directions. In the second case, the directions of their motions have been reversed. The transport equations, written in terms of the primitive variables for the non‐Newtonian nanofluid, have been solved numerically using the finite volume method. The shear stresses were calculated using the Ostwald‐de Waele model for the shear‐thinning nanofluid. The model introduced by Patel et al was used to obtain the thermal conductivity of the nanofluid. The variation of the fluid flow with respect to the Richardson number and volume fraction of the nanoparticles was investigated through a parametric study. Even though increasing the volume fraction of nanoparticles leads to heat transfer enhancement, for the second case of this study, for Ri = 1, the average Nusselt number initially drops sharply by increasing the volume fraction of nanoparticles, then remains constant.     

Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube

Turbulent heat transfer behavior of titanium dioxide/water nanofluid in a circular pipe was investigated experimentally where the volume fraction of nanoparticles in the base fluid was less than 0.25%. The experimental measurements have been carried out in the fully-developed turbulent regime for various volumetric concentrations. The results indicated that addition of small amounts of nanoparticles to the base fluid augmented heat transfer remarkably. There was no much effect on heat transfer enhancement with increasing the volume fraction of nanoparticles. The measurements also showed that the pressure drop of nanofluid was slightly higher than that of the base fluid and increased with increasing the volume concentration. In this paper, experimental results have been compared with the existing correlations for nanofluid convective heat transfer coefficient in turbulent regime. Finally, a new correlation of the Nusselt number will be presented using the results of the experiments with titanium dioxide nanoparticles dispersed in water.     

Nonequilibrium heat conduction in a nanofluid layer with periodic heat flux

Nonequilibrium heat conduction in a nanofluid layer with periodic heat flux on one side and specified temperature on the other side is studied numerically. The energy equations for the nanoparticles and base fluid are nondimensionalized and the problem is described by four dimensionless parameters: heat capacity ratio, volume fraction of nanoparticles, period of surface heat flux, and the Sparrow number. The Sparrow number is to describe the coupling between the energy equations for nanoparticles and base fluid. Nonequilibrium between nanoparticles and base fluid, as well as heat transfer enhancement in nanofluid, of three nanofluids (diamond–water, diamond–ethylene glycol, and copper–ethylene glycol) is investigated. The results showed that the nonequilibrium between the nanoparticles and base fluid exist for all three nanofluids at low Sparrow number and short period of surface heat flux. The results also showed that heat transfer in a liquid layer can be enhanced by adding nanoparticles to the base fluid, but the level of enhancement is not as high as those reported by using transient hot wire (THW) method.     

Numerical study of mixed convection in an inclined two sided lid driven cavity filled with nanofluid using two-phase mixture model

Mixed convection of a nanofluid consisting of water and SiO2 in an inclined enclosure cavity has been studied numerically. The left and right walls are maintained at different constant temperatures while upper and bottom insulated walls are moving lids. Two-phase mixture model has been used to investigate the thermal behaviors of the nanofluid for various inclination angles of enclosure ranging from θ = − 60° to θ = 60°, volume fraction from 0% to 8%, Richardson numbers varying from 0.01 to 100 and constant Grashof number 10⁴. The governing equations are solved numerically using the finite-volume approach. Results are presented in the form of streamlines, isotherms, distribution of nanoparticles and average Nusselt number. In addition, effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated. The results reveal that addition of nanoparticles enhances heat transfer in the cavity remarkably and causes significant changes in the flow pattern. Besides, effect of inclination angle is more pronounced at higher Richardson numbers.     

Numerical Investigations on the Advantage of Nanofluids under DDMC in a Lid‐Driven Cavity

Double diffusive mixed convection in a lid‐driven cavity filled with Cu–water nanofluid is studied in detail. Various numerical experiments are conducted under horizontal thermal and concentration gradients. Flow equations were solved in velocity vorticity form using Galerkin's weighted residual finite element method. The Maxwell‐Garnett model and Brinkman models are applied to predict the thermal conductivity and dynamic viscosity of the nanofluid, respectively. The effectiveness of a nanofluid on heat transfer enhancement with respect to change in Richardson number has been studied at different Reynolds numbers for variation in particle volume fraction from 0 to 0.05. Similarly, the effect of buoyancy ratio on heat and mass transfer is presented for buoyancy ratio in the range of ?25 to 25. Detailed contour plots comparing the streamlines, temperature, concentration with and without nanoparticles were presented for all the range of parameters considered. The role of particle concentration and change in type of nanofluid has been reported. The average Nusselt number has increased in all the cases where as the Sherwood number slightly decreased with an increase in particle volume fraction. The Ag–water nanofluid showed better improvement in heat transfer characteristics compared to other nanofluids for all Reynolds numbers and particle volume fractions.     

Combined convection flow in triangular wavy chamber filled with water–CuO nanofluid: Effect of viscosity models

This work is focused on the numerical modeling of steady laminar combined convection flow in a vertical triangular wavy enclosure filled with water–CuO nanofluid. The left and right vertical walls of the cavity take the form of a triangular wavy pattern. The bottom and top horizontal walls are mechanically driven. The lower and upper surfaces move to the right and left direction at the same constant speed respectively. They maintain constant temperature lower than both vertical walls. Two different nanofluid models namely, the Brinkman model and the Pak and Cho correlation are employed. The developed equations are given in terms of the Navier Stokes and the energy equation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by the Galerkin's finite-element method. Comparisons with published work are performed and found to be in good agreement. A parametric study is conducted and a selective set of graphical results is presented. The effects of the Reynolds number, Richardson number and the nanoparticles volume fraction on the flow and heat transfer characteristics in the cavity are displayed to compare the predictions obtained by the two different nanofluid models. Heat transfer enhancement can be obtained significantly due to the presence of nanoparticles. The rate of heat transfer is accentuated moderately by falling the Richardson number and rising the Reynolds number as well as the solid volume fraction.     

Conjugate Heat Transfer from Sudden Expansion Using Nanofluid

Conjugate heat transfer from sudden expansion using nanofluid is studied numerically. The governing equations are solved using unsteady stream function-vorticity formulation method. Results are compared with zero nanoparticle fluid to exhibit the role of nanoparticle. The effect of volume fraction of nanoparticles and type of nanoparticles on heat transfer are examined and found to have a significant impact. Local Nusselt number and average Nusselt number are reported in connection with various nanoparticle, volume fraction, and Reynolds number for expansion ratio 2. Two dimensionality is more pronounced in the solid wall up to recirculation length. Local Nusselt number reaches peak values near the reattachment point and reaches asymptotic value in the downstream. Bottom wall eddy and volume fraction show significant impact on average Nusselt number. The wall thickness causes larger temperature gradient at the conjugate interface boundary, which leads to larger average Nusselt number.     

Asymmetric Forced Convection of Nanofluids in a Channel with Symmetrically Mounted Rib Heaters on Opposite Walls

Laminar forced convection of nanofluids in a vertical channel with symmetrically mounted rib heaters on surfaces of opposite walls is numerically studied. The fluid flow and heat transfer characteristics are examined for various Reynolds numbers and nanoparticles volume fractions of water-Al₂O₃ nanofluid. The flow exhibits various structures with varying Reynolds number. Even though the geometry and heating is symmetric with respect to a channel vertical mid-plane, asymmetric flow and heat transfer are found for Reynolds number greater than a critical value. Introduction of nanofluids in the base fluid delays the flow solution bifurcation point, and the critical Reynolds number increases with increasing nanoparticle volume fraction. A skin friction coefficient along the solid-fluid interfaces increases and decreases sharply along the bottom and top faces of the heaters, respectively, due to sudden acceleration and deceleration of the fluid at the respective faces. The skin friction coefficient, as well as Nusselt numbers in the channel, increase with increasing volume fraction of nanoparticles.     

Effects of wall confinement and rheology of non‐Newtonian nanofluids on mixed convection phenomenon of a square cylinder in a vertical channel

The mixed convective momentum and heat transfer phenomena of confined square cylinders in non‐Newtonian nanofluids are numerically investigated. The experimental thermophysical properties of alumina‐water‐based nanofluids are adopted from literature and these nanofluids obey shear‐thinning power‐law type non‐Newtonian behavior. The square cylinder is confined in a vertical channel with a confinement ratio of 0.1333. The flow is assumed to be two‐dimensional and the fluid is allowed to flow in upward direction across the confined square cylinder in the vertical channel. The aiding/opposing buoyancy in the flow is incorporated in terms of Richardson number (Ri ) in the range of –2 to 2. The ranges of other dimensionless parameters considered are: Reynolds number, Re : 1 to 40; and volume fraction of nanoparticles, ?: 0.005 to 0.045. This range of volume fraction of nanoparticles (i.e., ? = 0.005 to 0.045) corresponds to the power‐law index (n ) of a non‐Newtonian nanofluid in the range of n = 0.88 to 0.5, respectively. Prior to obtaining new results, the solution methodology is validated with existing literature counterparts. Finally, effects of the Reynolds number, Richardson number, and the rheology of non‐Newtonian nanofluids on streamline patterns, surface pressure, surface vorticity, drag coefficients, isotherm contours, local and average Nusselt numbers are delineated.     

Buoyancy-Aided Mixed Convection Between Shear-Thinning Non-Newtonian Nanofluids and Unbounded Elliptic Cylinders in a Vertical Channel

Abstract

This work presents buoyancy-driven mixed convective flow and heat transfer phenomena of an isothermally heated horizontal elliptic cylinder in vertically upward unbounded flow of power-law type non-Newtonian nanofluids using ANSYS Fluent. The governing continuity, momentum and energy equations for the shear-thinning power-law nanofluids along with suitable boundary conditions are simultaneously solved within the limitations of Boussinesq approximation. The semi implicit method for pressure-linked equations algorithm along with the quadratic upstream interpolation for convective kinematics scheme for discretizing the convective terms in both momentum and energy equations are adopted. The ranges of parameters considered for this study are: volume fraction of nanoparticles, 0.005–0.045; aspect ratio of elliptic cylinder, 0.5–2.5; and Richardson number, 0–40; and a representative Reynolds number of 20. The streamline patterns, surface pressure coefficient distributions, total drag coefficients, isotherm contours, and Nusselt numbers are presented for better understanding of heat transfer and flow phenomena around elliptic cylinders. Briefly results indicate that the total drag coefficient is found to increase with the increasing Richardson number whereas it decreases with the increasing volume fraction of nanoparticles. The average Nusselt numbers are found to increase with increasing Richardson number and increasing volume fraction of nanoparticles.     

Convective Heat Transfer in a Vertical Rectangular Duct Filled with a Nanofluid

An analysis is performed to study natural convective heat transfer in a vertical rectangular duct filled with a nanofluid. One of the vertical walls of the duct is cooled by a constant temperature, while the other wall is heated by a constant temperature. The other two sides of the duct are thermally insulated. The transport equations for a Newtonian fluid are solved numerically with a finite volume method of second‐order accuracy. The influence of pertinent parameters such as Grashof number, Brinkman number, aspect ratio and solid volume fraction on the heat transfer characteristics of natural convection is studied. Results for the volumetric flow rate and skin friction for Copper and Diamond nanoparticles are also drawn. The Nusselt number for various types of nanoparticle such as silver, copper, diamond and titanium oxide are also tabulated. The results indicate that inclusion of nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximizes the heat transfer rate.     

Thermal and hydraulic characteristics of turbulent nanofluids flow in a rib–groove channel

Thermal and hydraulic characteristics of turbulent nanofluids flow in a rib–groove channel are numerically investigated. The continuity, momentum and energy equations were solved by means of a finite volume method (FVM). The top and bottom walls of the channel are heated at a constant temperature. Nine different rib–groove shapes are considered in this study, which are three different rib shapes with three different groove shapes including rectangular, triangular and trapezoidal and they are interchanged with each other. Four different types of nanoparticles Al₂O₃, CuO, SiO₂, and ZnO with different volume fractions in the range of 1% to 4% and different nanoparticle diameters in the range of 25 nm to 80 nm, are dispersed in different base fluids (water, glycerin, engine oil) are used. In this study, several parameters such as different Reynolds numbers in the range of 5000 < Re < 20000, and different rib–groove aspect ratios in the range of 0.5 ≤ AR ≤ 4 are also examined to identify their effects on the heat transfer and fluid flow characteristics. The results indicate that the rectangular rib–triangular groove has the highest Nusselt number among other rib–groove shapes. The SiO₂ nanofluid has the highest Nusselt number compared with other nanofluid types. The Nusselt number increased as the nanoparticle volume fraction, Reynolds number and aspect ratio increased; however, it decreased as the nanoparticle diameter increased. It is found that the glycerin–SiO₂ shows the best heat transfer enhancement compared with other tested base fluids.     

Numerical Investigation of Heat Transfer by CuO–Water Nanofluid in Rectangular Enclosures

This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO–water nanofluid and differentially heated. Conservation of mass, momentum, and energy equations are solved numerically by a control volume finite-element method using the SIMPLER algorithm for pressure–velocity coupling. The Prandtl number is fixed at 7.02, corresponding to water. Aspect ratio and solid volume fraction are varied from 0.5 to 4 and from 0% to 4%, respectively. The inclination angle is varied from 0° to 90° and used as a control parameter to investigate flow mode-transition and the accompanying hysteresis phenomenon (multi-steady solutions). It is found that the efficiency of heat transfer is improved by the addition of nanoparticles into base fluid; however, there is an optimum solid volume fraction that maximizes the heat transfer rate. Numerical results show also that the diameter of solid particle is an important parameter that affects the heat transfer efficiency; its impact is more important than the concentration itself. Effects of inclination angle on streamlines and on thermal boundary layer are presented. Combined effects of aspect ratio and inclination angle on heat transfer and hysteresis region are analyzed.     

Boundary Layer Flow of Rotating Two Phase Nanofluid Over a Stretching Surface

An analysis is carried out to discover the influence of a rotating nanofluid over a stretching surface. The two phase nanofluid model is used for this study. Two types of nanoparticles, namely copper and titanium oxide are used in our analysis with water as the base fluid. The governing system of partial differential equations along with the corresponding boundary conditions are presented and then transformed into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically by means of an iterative procedure called the midpoint integration scheme along with Richardson extrapolation. The results for flow and heat transfer characteristics are presented through graphs against nanoparticle volume fraction and rotation parameter for both types of nanoparticles. Quantities of physical interest such as local skin friction coefficients and local heat flux rate at the stretching surface are computed and analyzed. Numerical values for skin frictions and local heat flux rate are computed in the absence of nanoparticle volume fraction and rotation and they are found to be in very good agreement with the existing published literature.