Entropy generation and natural convection in square cavities with wavy walls

The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 10³ < Ra < 10⁵, irreversibility coefficients 10^?4 < φ < 10^?2, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

An experimental study of the effect of wall temperature nonuniformity on natural convection in an enclosure heated from the side

An experimental study of natural convection in a parallelepipedal enclosure induced by a single vertical wall is described. The upper half of this wall was warm and the lower half cold. The other enclosure walls were insulated. The temperature and flow measurements were performed in the high Rayleigh number regime (10¹⁰<Ra<5×10¹⁰) by using water as the working fluid. The Rayleigh number was based on the enclosure height and the temperature difference between the warm and the cold part of the driving wall. The flow field featured two flat cells, one filled with warm fluid along the top horizontal wall, and the other filled with cold fluid along the bottom horizontal wall. Each of these cells was surrounded by an additional cell as tall as half the enclosure height. The above flow structure prohibited extensive thermal contact between warm and cold fluid, thus limiting the role of convection on the heat transfer process in the cavity. The findings of this study differ significantly from the findings of previous studies based on the ‘classical’ enclosure model possessing two isothermal vertical walls, the one warm and the other cold, and support the view that the use of ‘more realistic‘ temperature boundary conditions in enclosure natural convection needs careful examination.     

Numerical comparison of conjugate and non-conjugate natural convection for internally heated semi-circular pools

In this numerical investigation, a detailed comparison of the conjugate and non-conjugate natural convection within a semi-cylindrical cavity has been presented. The cavity is assumed to be filled with a fluid containing uniformly distributed internal heating sources. The bottom circular wall of the cavity is taken to be thick with finite conductive properties, while the top wall is considered to be isothermal. The Navier–Stokes and energy equations are solved numerically by using the SIMPLER algorithm. A Rayleigh number range from 3.2×10⁶ to 3.2×10¹¹ has been investigated and the effects of solid-to-fluid conductivity ratios of 1.0, 5.0 and 23.0 have been analysed. The present numerical results for a semi-circular cavity with entirely isothermal walls are compared with known results from the open literature. It was found that these results for the non-conjugate problem are in very good agreement. The present results for a conjugate cavity show a remarkable difference from the non-conjugate analysis. The average Nusselt number for the solid–fluid interface shows a decrease while the top wall average Nu number has increased. It has been concluded that these effects increase for a system with a low solid-to-fluid conductivity ratio. It is evident from the present conjugate results that the assumption of isothermal enclosing walls gives somewhat different results when the walls are thick and the solid-to-fluid conductivity ratio is small.     

Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall

Natural convection in an open end cavity with a hot inclined wall is simulated based on the lattice Boltzmann method (LBM). The physics of flow and energy transfer in open end cavities are addressed when the hot wall is inclined. The combination of the two topics (open cavity and inclined walls) is the main novelty of the present study. The effects of the angle of the hot inclined wall on the flow field and heat transfer are thoroughly investigated. The Prandtl number is fixed to 0.71 (air). The Rayleigh number and the angle of the hot inclined wall are varied in the range of 10⁴ to 10⁶ and 60? to 85?, respectively. The results are presented for two different aspect ratios, i.e., A = 1 and 2. The results obtained with the LBM are also compared with those of the finite volume method (FVM). The predicted results of the LBM conform to those of the FVM. The results show that by increasing the angle of the hot inclined wall and the aspect ratio of the cavity, the average Nusselt number decreases. The trend of the local Nusselt number on the inclined wall is also discussed.     

Natural convection flow of water near its density maximum in a rectangular enclosure having isothermal walls with heat generation

We consider unsteady laminar natural convection flow of water subject to density inversion in a rectangular cavity formed by isothermal vertical walls with internal heat generation. The top and bottom horizontal walls are considered to be adiabatic, whereas the temperature of the left vertical wall is assumed to be greater than that of the right vertical wall. The equations are non-dimensionalized and are solved numerically by an upwind finite difference method together with a successive over-relaxation (SOR) technique. The effects of both heat generation and variations in the aspect ratio on the streamlines, isotherms and the rate of heat transfer from the walls of the enclosure are presented. Investigations are performed for water taking Prandtl number to be Pr=11.58 and the Rayleigh number to be Ra=10⁵.     

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

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

Investigation of Coulomb force effects on ethylene glycol based nanofluid laminar flow in a porous enclosure

Forced convection heat transfer of ethylene glycol based nanofluid with Fe_3O_4 inside a porous medium is studied using the electric field. The control volume based finite element method(CVFEM) is selected for numerical simulation. The impact of the radiation parameter(R_d), the supplied voltage(?φ), the volume fraction of nanofluid(?), the Darcy number(Da), and the Reynolds number(Re) on nanofluid treatment is demonstrated. Results prove that thermal radiation increases the temperature gradient near the positive electrode. Distortion of isotherms increases with the enhance of the Darcy number and the Coulomb force.     

Effect of adiabatic wall on the natural convection heat transfer from a wavy surface created by attached horizontal cylinders

The effect of a vertical adiabatic wall on the natural convection heat transfer from vertical array of attached cylinders, which can be considered as wavy surface, was investigated experimentally and numerically. The experiments were carried out using Mach-Zehnder interferometer and the commercial FLUENT code was used for numerical study. This paper focuses on the effect of wall-wavy surface spacing and Rayleigh number variation on the local and average free convection heat transfer coefficients from the each cylinder and the wavy surface. Rayleigh number ranges from 2400 to 10,000 and from 300,000 to 1,250,000 based on cylinder diameter and wavy surface height respectively. The local and average Nusselt numbers were determined for the different Rayleigh numbers, and the ratio of wall- wavy surface spacing to cylinder diameter 0.75, 1, 1.5, 2, 3, 4, 5, and ∞. Results are indicated with a single correlation which gives the average Nusselt number as a function of the ratio of the wall-wavy surface spacing to cylinder diameter and the Rayleigh numbers. There is an optimum distance between the wall and wavy surface in which the Nusselt number attain its maximum value. This optimum distance depends on the Rayleigh number.     

Effect of Thermal Modulation on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid

The effect of time-periodic temperature modulation at the onset of convection in a Boussinesq porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. The perturbation method is applied for computing the critical Rayleigh and wave numbers for small amplitude temperature modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, concentration Rayleigh number, porosity, Lewis number, and thermal capacity ratio. It has been shown that it is possible to advance or delay the onset of convection by time-periodic modulation of the wall temperature. The nanofluid is found to have more stabilizing effect when compared to regular fluid. Low frequency is destabilizing, while high frequency is always stabilizing for symmetric modulation. Asymmetric modulation and only lower wall temperature modulation is stabilizing for all frequencies when concentration Rayleigh number is greater than one.     

Instability of binary nanofluids with magnetic field

The present paper investigates the effects of a vertical magnetic field on the double diffusive nanofluid convection. The effects of the Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of the Dufour and Soret parameters due to the presence of solute are included in the investigated model. The normal mode technique is used to solve the conservation equations. For the analytical study, valid approximations are made in the complex expression for the Rayleigh number to get useful and interesting results. The bottom heavy binary nanofluids are more stable than the regular binary fluids, while the top heavy binary nanofluids are less stable than the regular binary fluids. The critical wave number and the critical Rayleigh number increase whereas the frequency of oscillation (for the bottom heavy configuration) decreases when the Chandrasekhar number increases. The numerical results for the alumina-water nanofluid are studied by use of the MATHEMATICA software.     

Non-homogeneous model for a side heated square cavity filled with a nanofluid

A side heated two dimensional square cavity filled with a nanofluid is here studied. The side heating condition is obtained by imposing two different uniform temperatures at the vertical boundary walls. The horizontal walls are assumed to be adiabatic and all boundaries are assumed to be impermeable to the base fluid and to the nanoparticles. In order to study the behavior of the nanofluid, a non-homogeneous model is taken into account. The thermophysical properties of the nanofluid are assumed to be functions of the average volume fraction of nanoparticles dispersed inside the cavity. The definitions of the nondimensional governing parameters (Rayleigh number, Prandtl number and Lewis number) are exactly the same as for the clear fluids. The distribution of the nanoparticles shows a particular sensitivity to the low Rayleigh numbers. The average Nusselt number at the vertical walls is sensitive to the average volume fraction of the nanoparticles dispersed inside the cavity and it is also sensitive to the definition of the thermophysical properties of the nanofluid. Highly viscous base fluids lead to a critical behavior of the model when the simulation is performed in pure conduction regime. The solution of the problem is obtained numerically by means of a Galerkin finite element method.     

ISPH modeling of natural convection heat transfer with an analytical kernel renormalization factor

The objective of this study is to extend the attention of the incompressible smoothed particle hydrodynamics method (ISPH) in the heat transfer field. The ISPH method for the natural convection heat transfer under the Boussinesq approximation in various environments: pure-fluid, nanofluid, and non-Darcy porous medium is introduced. We adopted the improved analytical method for calculating the kernel renormalization factor and its gradient based on a quintic kernel function for the wall boundary treatment in the ISPH method. The proposed method requires no dummy particle layer to meet the impermeability condition and makes the heat flux over the wall boundary easy to implement. We performed four different numerical simulations of natural convection in cavities with increasing complexity in modeling and implementation: the natural convection in a square cavity with constant differentially heated wall temperature, natural convection with the heat flux from the bottom wall for a wide range of Rayleigh numbers, natural convection in a non-Darcy porous cavity fully filled with nanofluid in different flow regimes, and natural convection in a partially layered porous cavity. The results showed excellent agreement with results from literatures and the in-house P1–P1 finite element method code.     

Impingement heat transfer at a circular cylinder due to a submerged slot jet of water

An experimental investigation was carried out on the heat transfer due to a submerged slot jet of water impinging on a circular cylinder in crossflow. The cylinder diameter and the slot width are of the same order of magnitude, specifically D_s = 2.0 and 3.0 mm and D_c = 2.5 and 3.0 mm. The experimental apparatus allowed variation of the slot width, the cylinder diameter, and the distance from nozxle exit to heater. Conditions of impingement from the bottom (ascending flow) were taken into consideration as well as impingement from above (descending flow). The Nusselt number was determined as a function of Reynolds and Prandtl numbers in the range 1.5 × 10³ < Re < 2.0 × 10⁴, 2.7 < Pr < 7.0, and 1.5 ≤ z/D_s ≤ 10. The experimental data were correlated with a simple equation that fits 90% of the data with a precision of 20%.     

Low dimensional chaos in Boussinesq convection

Three-dimensional time-dependent Boussinesq convection has been simulated numerically and analyzed based on the theory of the dynamical system. The dynamical development of the system is simulated numerically with Rayleigh number Ra=2.10⁴ and the aspect ratio Γ_x=Γ_y=2; a chaotic solutions is obtained for the Prandtle number Pr=1, whereas the case Pr=3 gives a periodic solution. The chaotic solution has an initial transient state of quasi-periodicity which turns into a non-periodic state characterized by a large degree of asymmetry in the flow pattern and a large vertical vorticity compared with that of the periodic solution. It is found that the total heat flux averaged over the time is somewhat smaller in the non-periodic state than in quasi-periodicity. Using the velocities and temperatures at a few particular points, the phase space has been constructed for studying the dynamical behavior of the system. The dimension of the chaotic attractor is found to be 3.3 with two positive and one possibly zero Lyapunov exponents. These chaos characteristics are considered to be consistent with the appearance of the asymmetry of the flow pattern and of the vertical vorticity in the chaotic flow.     

Experimental study on the magnetic convection in a vertical cylinder

The flow of paramagnetic fluid inside a cylinder placed in a bore of a superconducting magnet was studied experimentally. Single-phase closed thermosyphon configuration was employed. The lower side wall of the cylindrical enclosure was heated while the upper side wall was cooled with the thin adiabatic interface in between. The experiment was carried out with an aqueous solution of glycerol. The magnetic susceptibility of the working fluid was increased by adding Gd(NO₃)₃ × 6H₂O and was measured by a magnetic susceptibility balance. The encapsulated liquid crystal slurry (KWN-2025, Japan Capsular Product Inc.) dispersed in the working fluid was illuminated in the middle height horizontal cross-section of the enclosure to visualize the temperature field. The color images of flow mode were taken by a digital camera. The average heat transfer rates were also measured. Depending on the Rayleigh number, different spoke patterns were observed. The number of angular structures (spokes) increased with increase not only in the Rayleigh number but also in the strength of magnetic field. The heated fluid was repelled by the magnetic field, while the cooled fluid was attracted. The magnetic field enhanced the heat transfer rate.     

Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³–10⁵, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 10⁵). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.     

Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure

This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. 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, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.     

Turbulent forced convection of nanofluid in a wavy channel using two phase model

Two phase mixture model is used to numerically simulate the turbulent forced convection of Al₂O₃-Water nanofluid in a channel with corrugated wall under constant heat flux. Both mixture and single phase models are implemented to study the nanofluid flow in such a geometry and the results have been compared. The effects of the volume fraction of nanoparticles, Reynolds number and amplitude of the wavy wall on the rate of heat transfer are investigated. The results showed that with increasing the volume fraction of nanoparticles, Reynolds number and amplitude of wall waves, the rate of heat transfer increases. Also the results showed that the mixture model yields to higher Nusselt numbers than the single phase model in a similar case.     

Aspect ratio effect on natural convection in water near its density maximum temperature

The effect of the aspect ratio on natural convection in water subjected to density inversion has been investigated in this study. Numerical simulations of the two-dimensional, steady state, incompressible flow in a rectangular enclosure with a variety of aspect ratios, ranging from 0.125 to 100, have been accomplished using a finite element model. Computations cover Rayleigh numbers from 10³ to 10⁶. Results reveal that the aspect ratio, A, the Rayleigh number, Ra, and the density distribution parameter, R, are the key parameters to determine the heat transfer and fluid flow characteristics for density inversion fluids in an enclosure. A new correlation for predicting the maximum mean Nusselt number is proposed in the form of , with the constants a and b depending on density distribution number R. It is demonstrated that the aspect ratio has a strong impact on flow patterns and temperature distributions in rectangular enclosures. The stream function ratio Ψ_inv/|Ψ_reg| is introduced to describe quantitatively the interaction between inversional and regular convection. For R=0.33, the density inversion enhancement is observed in the regime near A=3.