Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid

Heat transfer enhancement has been investigated in a square cavity subject to different side wall temperatures using water/SiO₂ nanofluid. An experimental setup has been used to extract the conductivity value of nanofluid. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra_f = 10⁵–10⁷ and the volumetric fraction of nanoparticle between 0 and 4%. The comparisons show that the mean Nusselt number increases with volume fraction for the whole range of Rayleigh numbers. Although by using the theoretical formulations for conductivity no enhancement has been observed.     

Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid

This paper presents a numerical study of natural convection cooling of a heat source horizontally attached to the left vertical wall of a cavity filled with copper-water nanofluid. The left vertical wall is kept at the constant temperature, while the other ones are kept adiabatic. The numerical approach is based on the finite volume method with a collocated grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. In this study, the influence of some effective parameters such as: Rayleigh number, location and geometry of heat source and solid concentration are studied and discussed. Results are presented in the form of streamlines, isotherms, and average Nusselt number. The results show that dimension of the heat source is an important parameter affecting the flow pattern and temperature field, so that the average Nusselt number decreases with an increase in the length of the heater. It is also observed that at a given Rayleigh number and definite heat source geometry, the average Nusselt number increases linearly with the increase in the solid volume fraction of nanofluid. The increase of Rayleigh numbers strengthens the natural convection flows which leads to the decrease in heat source temperature. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.     

Entropy generation due to natural convection cooling of a nanofluid

In the present work, entropy generation due to natural convection of a nanofluid that consists of water and Cu in a cavity with a protruded heat source has been studied. To investigate both the First and the Second Law of Thermodynamics for this considered problem the numerical scheme carried out based on finite volume method with the SIMPLE algorithm for pressure-velocity coupling. In this study, the effect of Rayleigh number, solid concentration and heat source location on entropy generation have been revealed. Consequently the optimum case has been selected since the thermal system could have the least entropy generation and the best heat transfer rate. The results have shown the maximum value of Nusselt number and minimum entropy generation are obtained when heat source mountains in the bottom horizontal wall.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid

A numerical investigation of mixed convection flows through a copper–water nanofluid in a square cavity with inlet and outlet ports has been executed. The natural convection effect is attained by heating from the constant flux heat source which is symmetrical located at the bottom wall and cooling from the injected flow. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Reynolds number in the range 50 ≤ Re ≤ 1000, with Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction 0 ≤ ? ≤ 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. Results are presented in the form of streamlines, isotherms, average Nusselt number and average bulk temperature. In addition, the effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated and discussed. The results indicate that increase in solid concentration leads to increase in the average Nusselt number at the heat source surface and decrease in the average bulk temperature.     

Mesoscopic simulation of CuOH2O nanofluid in a porous enclosure with elliptic heat source

In this article, mesoscopic approach has been utilized to investigate magnetic field impact on CuOH₂O nanofluid free convection inside a porous cavity with elliptic heat source. Simulations have been done via LBM. KKL model is employed to consider Brownian motion impact on nanofluid properties. Influences of Rayleigh number (Ra), nanofluid volume fraction (?), Hartmann number (Ha), Darcy number (Da) on heat transfer treatment are demonstrated. Outputs demonstrate that temperature gradient reduces with increase of Ha while it increases with augment of Da,Ra.     

Natural convection investigation in square cavity filled with nanofluid using dispersion model

A cooling achieved with compact and efficient device is one of the major challenges encountered in the promising technique of fuel cell stacks. The safe and reliable use of such a system is highly dependent on the efficiency of the assured heat transfer and consequently on the quality of the coolant used. To test the possible improvement of the coolant performances, laminar natural convection in square cavity filled with copper-water nanofluid is numerically carried out taking into account the thermal dispersion effect on the heat transfer intensity. The finite element method is used to solve the governing equations. The hydrodynamic structure of the flow and its thermal behavior are studied for a wide range of Rayleigh numbers. The obtained results showed an enhancement of heat transfer with an increase in nanoparticle volume fraction for all examined Rayleigh numbers. However, it is found that an increase in nanoparticle diameter enhances heat transfer only when thermal dispersion is significant. Correlation with 99.94% confidence coefficient is proposed to quantify the heat transfer intensity according to the Rayleigh number and particle diameter and concentration.     

Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid

In this study, natural convection in a concentric annulus between a cold outer square and heated inner circular cylinders in presence of static radial magnetic field is investigated numerically using the lattice Boltzmann method. The inner and outer cylinders are maintained at constant uniform temperatures and it is assumed that all walls are insulating the magnetic field. The numerical investigation is carried out for different governing parameters namely; the Hartmann number, nanoparticles volume fraction and Rayleigh number. The effective thermal conductivity and viscosity of nanofluids are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. Also, the multi-distribution-function (MDF) model is used for simulating the effect of uniform magnetic field. The results reveal that the average Nusselt number is an increasing function of nanoparticle volume fraction as well as the Rayleigh number, while it is a decreasing function of the Hartmann number.     

Natural convection of water-CuO nanofluid in a cavity with two pairs of heat source-sink

Natural convection in a two-dimensional square cavity filled with a water-CuO nanofluid is numerically studied. Two pairs of heat source-sink are considered to cover the entire length of the bottom wall of the cavity while the other walls are thermally insulated. The nanofluid is assumed to be homogenous and Newtonian. The governing differential equations are discretised by the control volume approach and the coupling between velocity and pressure is solved using the SIMPLE algorithm. A comparison study is presented between two cases with different arrangements of the two pairs on the bottom wall. The effects of Rayleigh number and solid volume fraction of the nanofluid on the heat transfer rate have also been examined. The results show that regardless of the position of the pairs of source-sink, the heat transfer rate increases with an increase of the Rayleigh number and the solid volume fraction.     

Natural convection heat transfer in a nanofluid filled semi-annulus enclosure

To investigate natural convection heat transfer in a semi-annulus enclosure filled with nanofluid, the Control Volume based Finite Element Method (CVFEM) is used. The fluid in the enclosure is Cu–water nanofluid. The inner and outer semi circular walls are maintained at constant temperatures while the two other walls are thermally insulated. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern and isotherms. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and the angle of turn for the enclosure. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The results reveal that there is an optimum angle of turn in which the average Nusselt number is maximum for each Rayleigh number. Moreover, the angle of turn has an important effect on the streamlines, isotherms and maximum or minimum values of local Nusselt number.     

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

Mixed convection in a lid-driven triangular enclosure filled with nanofluids

This paper presents the results of a numerical study on the mixed convection in a lid-driven triangular enclosure filled with a water–Al₂O₃ nanofluid. A comparison study between two different scenarios of upward and downward left sliding walls is presented. The effects of parameters such as Richardson number, solid volume fraction and the direction of the sliding wall motion on the flow and temperature fields as well as the heat transfer rate are examined. The results show that the addition of Al₂O₃ nanoparticles enhances the heat transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the downward sliding wall motion results in a stronger flow circulation within the enclosure and hence, a higher heat transfer rate.     

Free convection in a square cavity filled with a bidisperse porous medium

The classical problem of steady Darcy free convection in a square cavity filled with a porous medium has been extended to the case of a bidisperse porous medium (BDPM) by following the recent model proposed by Nield and Kuznetsov [D.A. Nield, A.V. Kuznetsov, Natural convection about a vertical plate embedded in a bidisperse porous medium, Int. J. Heat Mass Transfer 51 (2008) 1658–1664] and Rees et al. [D.A.S. Rees, D.A. Nield, A.V. Kuznetsov, Vertical free convective boundary-layer flow in a bidisperse porous medium, ASME J. Heat Transfer 130 (2008) 1–9]. The transformed partial differential equations in terms of the dimensionless stream function and temperature are solved numerically using a finite-difference method for some values of the governing parameters when the Rayleigh number Ra is equal to 10² and 10³. Results are presented for the flow field with streamlines, temperature field by isotherms and heat transfer by local and mean Nusselt numbers are presented for both the f- and p-phases. It is found that the most important parameters that influence the fluid flow and heat transfer are the inter-phase heat transfer parameter H and the modified thermal conductivity ratio parameter γ.     

Natural convection in a parabolic enclosure with an internal vertical heat source filled with Cu–water nanofluid

The numerical investigation of the natural convection in concave and convex parabolic enclosures with a nanofluid consisting of water and copper nanoparticles is carried out by using the finite volume method. The upper and lower walls of the enclosures are adiabatic while the sidewalls are isothermal at a cold temperature. An internal heat source of constant length (ε = 0.2) and negligible thickness is placed at various vertical positions along the center of the enclosure. It was found that the increase in the location of the heat source leads to a drop in the water and nanofluid flow circulation in both types of enclosures. For both considered Cases I and II, the average Nusselt number increases when the Rayleigh number and solid volume fraction increase. Moreover, it was concluded that Case I with δ = 0.8 is the optimum case for heat transfer enhancement for Ra = 10³ and Ra = 10⁴. Case II with δ = 0.5 is optimum for Ra = 10⁵. Both cases are satisfied when the nanofluid is used with ? = 0.2.     

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.     

Heat transfer enhancement in a cubical cavity filled with a hybrid nanofluid

Mixed convection heat transfer in a cubical cavity with an isothermally heated blockage inside filled with a hybrid nanofluid (HBNF) is numerically studied. The natural convection is created by the temperature difference between the hot block and the cold lateral walls, while the forced convection is generated by moving the upper wall. The influence of some variables, like the aspect ratio (0.1 ≤ r ≤ 0.5), Richardson number (0 ≤ Ri≤ 20), Reynolds number (50 ≤ Re ≤ 200), volume concentration of nanoparticles (0 ≤ ϕ ≤ 0.06), and the concentration ratio (2:8, 5:5, and 8:2) on the flow field and heat transfer is analyzed. A comparison between hybrid and mono nanofluids (NFs) is realized to investigate the energy transport enhancement. Results show that the increase of each parameter causes an increase of average Nusselt number Nu_avg and improves the heat transfer; besides the use of HBNF gives better Nu_avg values. Three correlations of the effect of r, ϕ, Ri, and Re on Nu_avg are determined for both hybrid and mono NFs.     

Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations

In this model, a numerical study of two dimensional steady natural convection is performed for a uniform heat source applied on the inner circular cylinder in a square air (Pr = 0.7) filled enclosure in which all boundaries are assumed to be isothermal (at a constant low temperature). The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of vertical cylinder locations and Rayleigh numbers on fluid flow and heat transfer performance are investigated. Rayleigh number is varied from 10³ to 10⁶ and the location of the inner cylinder is changed vertically along the centerline of the enclosure from − 0.25 L to 0.25 L upward and downward, respectively. It is found that at small Rayleigh numbers does not have much influence on the flow field while at high Rayleigh numbers have considerable effect on the flow pattern. In addition, the numerical solutions yield a two cellular flow field between the inner cylinder and the enclosure. Also, the total average Nusselt number behaves nonlinearly as a function of locations. Results are presented in terms of the streamlines, isotherms, local and average Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.     

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.     

Boiling heat transfer on a high temperature silver sphere in nanofluid

To investigate boiling heat transfer characteristics of nanofluids, transient quenching experiments of a high temperature silver sphere in water-based nanofluids with Ag and TiO₂ nanoparticles were performed. A silver sphere with a diameter of 10 mm and an initial temperature of 700 °C was quenched in these nanofluids at a temperature of 90 °C. The results showed a considerable reduction in the quenching ability of nanofluids compared to that of pure water. The presence of nanoparticles in water caused the film boiling mode to vanish at lower temperatures depending on the mixture concentration. Calculated heat transfer rates in nanofluids were lower than those in pure water. In the quenching experiments with an unwashed heated sphere, the film boiling mode did not appear and the hot sphere quenched more rapidly through nucleate boiling. In this case the sphere surface was covered by a thin layer of nanoparticles. It was evident that nanoparticle deposition on the sphere surface prevented vapor film from forming around it and resulted in quick quenching of the hot sphere.