Numerical Simulation Of Free Convection Research Articles

Three‐dimensional numerical simulation of free convection and entropy generation in a cubic cavity containing a heat source

AbstractThe present article provides a three‐dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from to . The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient , the analysis of the results showed that for low values of the Rayleigh number (), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of and , entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large (), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.

Numerical Simulation of Free Convection in Porous Media Modeled by Darcy-Brinkman Equation at Low Grashof Numbers

Numerical Simulation of Free Convection in Porous Media Modeled by Darcy-Brinkman Equation at Low Grashof Numbers

Numerical Simulation of Free Convection in a Three-Dimensional Enclosure Full of Nanofluid with the Existence a Magnetic Field

Blood glucose automatic regulation achievement depends on the robustness of the used control algorithm. However, some constraints were encountered due to the human glucose-insulin regulatory system’s complexity. It is proposed to tackle such a goal through the development of a robust synergetic control algorithm. An adaptive approach is integrated into this synergetic control scheme to handle disturbances and parameters variations. Multiple meal disturbances often occur daily as well as some other stochastic noises making efficient glucose regulation a tough challenge addressed in this paper via a new synergetic scheme. Simulation results show a robust function during multiple meal disturbances with good noise rejection.

Numerical Simulation of Free Convection in a Partially Heated Three-Dimensional Enclosure Filled with Ionanofluid ([C4mim][NTf2]-Cu)

A numerical analysis was performed to study free convection in a stationary laminar regime in a partially heated cube filled with ionanofluid. To numerically solve the dimensionless equations, we applied the finite volume method using the SIMPLEC algorithm for pressure correction. All walls are adiabatic, except for the left and right side walls which are partially heated differently. At the end of this simulation, several results are given in the form of current lines, isotherms, and variations in the Nusselt number. These results are obtained by analyzing the effect of a set of factors such as Rayleigh number, particle volume fraction, cold and source position on the dynamic and thermal fields, and heat transfer. It has been shown that the percentage of nanoparticles and high Rayleigh numbers significantly increase heat transfer by ionanofluid. Two comparisons have been made, between ionic fluid and ionanofluid at isotherms and streamlines, and between nanofluid and ionanofluid at Nusselt number, which show the advantage of using ionanofluid in heat transfer.

Numerical Simulation of Free Convection in a Three-Dimensional Enclosure Full of Nanofluid with the Existence a Magnetic Field

A numerical analysis was performed to study the influence of a magnetic field in free convection in a cube full with nanofluid. To solve the equation, we appeal to finite volume method. The SIMPLEC algorithm is used for pressure-velocity coupling. All walls are adiabatic, except for the left and right walls that are heated differently. The effects of the Rayleigh and Hartmann numbers, as well as the volume fraction of nanometric particles were studied. Results are conveyed in the form of isotherms, streamlines, velocity curves and Nusselt numbers. It has been shown that as the percentage of nanoparticles increases and the number of Rayleigh increases, heat transfer improves. Hartman number has considerable influence on hydrodynamic and thermal field.

Numerical simulation of free convection of MHD non-Newtonian nanofluid within a square wavy enclosure using Meshfree method

In this article, flow and heat transfer of nanofluids inside a wavy square enclosure filled with non-Newtonian (shear thinning) nanofluid under magnetic field has been simulated numerically. Single-phase model is used. The governing equations have been solved numerically using element free Galerkin method. The results are obtained for isotherms, streamlines, and average Nusselt number for various values of Hartmann number, Rayleigh number, nanoparticles volume fraction, and power-law index. Here, the main objective is to explore the effect of power-law index, Rayleigh number, Hartmann number, and volume fraction on average Nusselt number. It is found that in the absence of magnetic field, Nusselt number drops on increasing the value of power-law index whereas in the presence of magnetic field, heat transfer rate increases with increase in power-law index. With the increase in Rayleigh number and volume fraction of nanoparticles, the heat transfer rate increase in all cases. This type of problem has a direct application in the coolant systems, solar collector where the structure used is wavy in order to increase the rate of heat flow. Here, EFGM is efficiently applied for simulation due to irregular domain, which creates a novelty in the work.

Fully Resolved Numerical Simulation of Free Convection of Falling Spherical Particles in Sedimentation Transports Using Immersed Boundary Method

In this research, the direct numerical simulations are applied to study the sedimentation of spherical particles in an unsteady thermal condition in a viscous flow. The immersed boundary method is used to fully resolve the hydrodynamic interactions of solid–fluid phases, and a volume of fluid approach is employed to account the heat transfer both inside and outside the solid particles. The Boussinesq approximation is used to consider the density variation of the fluid. The behavior of particles is examined under different thermal conductivity ratios ($$k_{\mathrm{r}}$$) ranging between 0.1 to 10 and various Grashof numbers (Gr) up to 5000. The results indicate that for the Grashof and Galilean (Ga) numbers less than 5000 and 50, respectively, the threshold of $$k_{\mathrm{r}}$$ to solve the energy equation inside the particles is $$k_{\mathrm{r}}=0.1,$$ and for the thermal conductivity ratio higher than this value, the heating/cooling of the particles is fast enough to assume that the temperature over the solid particle changes uniformly. Furthermore, we investigate the well-known drafting–kissing–tumbling (DKT) phenomenon for a pair of spherical particles in an enclosed space at different $$k_{\mathrm{r}}$$ and Gr numbers. It is observed that the DKT motion of two particles with varied temperature is proceeded with any values of $$k_{\mathrm{r}}$$ and Grashof number; however, the natural convection delays this process.

Reconciling estimates of the ratio of heat and salt fluxes at the ice-ocean interface

The ratio of heat and salt flux is employed in ice-ocean models to represent ice-ocean interactions. In this study, this flux ratio is determined from direct numerical simulations of free convection beneath a melting, horizontal, smooth ice-ocean interface. We find that the flux ratio at the interface is three times as large as previously assessed based on turbulent-flux measurements in the field. As a consequence, interface salinities and melt rates are overestimated by up to 40\% if they are based on the three-equation formulation. We also find that the interface flux ratio depends only very weakly on the far-field conditions of the flow. Lastly, our simulations indicate that estimates of the interface flux ratio based on direct measurements of the turbulent fluxes will be difficult because at the interface the diffusivities alone determine the mixing and the flux ratio varies with depth. As an alternative, we present a consistent evaluation of the flux ratio based on the total heat and salt fluxes across the boundary layer and reconcile the determinations of the ice-ocean interface conditions.

Three-dimensional numerical simulations of free convection in a layered porous enclosure

Three-dimensional numerical simulations are carried out for the study of free convection in a layered porous enclosure heated from below and cooled from the top. The system is defined as a cubic porous enclosure comprising three layers, of which the external ones share constant physical properties and the internal layer is allowed to vary in both permeability and thermal conductivity. The model is based on Darcy’s law and the Boussinesq approximation. A parametric study to evaluate the sensitivity of the Nusselt number to a decrease in the permeability of the internal layer shows that strong permeability contrasts are required to observe an appreciable drop in the Nusselt number. If additionally the thickness of the internal layer is increased, a further decrease in the Nusselt number is observed as long as the convective modes remain the same, if the convective modes change the Nusselt number may increase. Decreasing the thermal conductivity of the middle layer causes first an increment in the Nusselt number and then a drop. On the other hand, the Nusselt number decreases in an approximately linear trend when the thermal conductivity of the layer is increased.

Thermal convection of temperature‐dependent viscous fluids within three‐dimensional faulted geothermal systems: Estimation from linear and numerical analyses

AbstractLinear stability analysis and numerical simulations of density‐driven flow are presented in order to estimate the effects of temperature‐dependent fluid viscosity variation on the onset of free thermal convection within a three‐dimensional fault embedded into impermeable rocks. The strongly coupled equations of density‐driven flow are linearized. The solution was obtained through expansion into Fourier series. Simple polynomial expressions fitting the neutral stability curves are given for a range of fault aspect ratios, fluid viscosity properties, and thermal conductivity heterogeneity, providing a new tool for the estimation of critical Rayleigh numbers in faulted systems. The results are validated against the limiting case of temperature‐invariant viscosity (i.e., constant). 3‐D numerical simulations of free convection within a fault are run using the finite element technique in order to verify the theoretical results. It turned out that at average geothermal temperature conditions, thermal convection can develop within faults which permeability is up to 4 times lower than the case of a fluid with constant viscosity, in agreement with the developed linear theory. The polynomial expressions of this study can be applied to any numerical model for testing the feasibility of fault convection in 3‐D geothermal basin.

Numerical simulation of free convection within an eccentric annulus filled with micropolar fluid using spectral method

In this paper, the problem of natural convection in a circular eccentric annulus filled with micropolar fluid has been numerically investigated using Fourier Spectral Method. The annulus inner wall is heated and maintained at constant temperature while the outer wall is cooled and kept at constant temperature. The full governing equations of momentum, angular momentum and energy have been solved to give the details of flow and thermal fields. The heat convection process in the annulus is mainly controlled by Rayleigh number Ra, Prandtl number Pr, radius ratio Rr, eccentricity, e and material parameters of micropolar fluid. The material parameters are dimensionless spin gradient viscosity λ, dimensionless micro-inertia density B and dimensionless vortex viscosity D. This study considers Ra up to 5×104 and the eccentricity is varied between −0.6 and +0.6 while dimensionless material parameters D of micropolar fluid is considered between 0 and 10. Both Pr, and Rr are fixed at 0.7, 2.6, respectively while B and λ are assigned the value of 1. The study considers the effect of controlling parameters on flow and thermal fields with emphasis on the effect of these parameters on mean Nusselt number. The study has shown that for certain controlling parameters the heat transfer in the annulus is minimum at a certain eccentricity. The study also has shown that as parameter D increases the rate of heat transfer through the annulus decreases.

Direct numerical simulation of free convection over a heated plate

AbstractDirect numerical simulations of free convection over a smooth, heated plate are used to investigate unbounded, unsteady turbulent convection. Four different boundary conditions are considered: free-slip or no-slip walls, and constant buoyancy or constant buoyancy flux. It is first shown that, after the initial transient, the vertical structure agrees with observations in the atmospheric boundary layer and predictions from classical similarity theory. A quasi-steady inner layer and a self-preserving outer layer are clearly distinguished, with an overlap region between them of constant turbulent buoyancy flux. The extension of the overlap region reached in our simulations is more than 100 wall units$ \mathop{ ({\kappa }^{3} / {B}_{s} )}\nolimits ^{1/ 4} $, where${B}_{s} $is the surface buoyancy flux and$\kappa $the corresponding molecular diffusivity (the Prandtl number is one). The buoyancy fluctuation inside the overlap region already exhibits the$\ensuremath{-} 1/ 3$power-law scaling with height for the four types of boundary conditions, as expected in the local, free-convection regime. However, the mean buoyancy gradient and the vertical velocity fluctuation are still evolving toward the corresponding power laws predicted by the similarity theory. The second major result is that the relation between the Nusselt and Rayleigh numbers agrees with that reported in Rayleigh–Bénard convection when the heated plate is interpreted as half a convection cell. The range of Rayleigh numbers covered in the simulations is then$5\ensuremath{\times} 1{0}^{7} \text{{\ndash}} 1{0}^{9} $. Further analogies between the two problems indicate that knowledge can be transferred between steady Rayleigh–Bénard and unsteady convection. Last, we find that the inner scaling based on$\{ {B}_{s} , \hspace{0.167em} \kappa \} $reduces the effect of the boundary conditions to, mainly, the diffusive wall layer, the first 10 wall units. There, near the plate, free-slip conditions allow stronger mixing than no-slip ones, which results in 30 % less buoyancy difference between the surface and the overlap region and 30–40 % thinner diffusive sublayers. However, this local effect also entails one global, substantial effect: with an imposed buoyancy, free-slip systems develop a surface flux 60 % higher than that obtained with no-slip walls, which implies more intense turbulent fluctuations across the whole boundary layer and a faster growth.

Role of data processing in measuring temperature gradients with DOE Schardin's schlieren #2

Flows having a variable fluid density can be visualized with optical methods. Recently, a background distortion technique, which can be considered a type of Schardin's schlieren #2, was proposed to study the refractive index variation in fluid and hence to measure the convective heat transfer. The background is a fringe pattern generated by a diffractive optical element (DOE). However, this system may exhibit poor performance when using air as a working fluid. Different strategies were proposed for improving sensitivity, such as modifying the experimental setup or increasing the frequency of the projected fringe pattern. In this paper the performance of the system is evaluated, by using different data processing methods, through a numerical simulation of free convection from a vertical plate in air. In particular, we found that the use of windowed Fourier transform method for data processing enhances both the accuracy and the sensitivity of the temperature gradient measurements.

Numerical simulation of free convection of nanofluid in a square cavity with an inside heater

In the present paper, free convection fluid flow and heat transfer of various water based nanofluids in a square cavity with an inside thin heater has been investigated numerically. The left and right walls of the cavity are maintained at constant temperature T c, while its top and bottom walls are insulated. A thin heater with the temperature of T h ( T h > T c) is located inside the cavity which its location and length is varying. The governing equations were discretized using the finite volume method and SIMPLER algorithm. Using the developed code, a parametric study was undertaken, and the effects of pertinent parameters, such as, Rayleigh number, the position and location of the heater, the volume fraction of the nanoparticles, and various types of the nanofluids on the fluid flow and heat transfer inside the cavity were investigated. It was observed from the results that at low Rayleigh numbers the horizontal positioned heater have higher Nusselt number compared to the vertical positioned heater while at high Rayleigh numbers the position of the heater does not affect the heat transfer rate. For a horizontal heater when it is located in lower half of the cavity, more heat transfer occurs compared to the case of heater located in upper half of the cavity. Moreover, it was found that at high Rayleigh numbers, the Ag–water nanofluid is more effective to enhance the heat transfer rate while at low Rayleigh numbers the type of nanofluids does not affect the heat transfer rate.

Numerical simulation of free convection of a nanofluid in L-shaped cavities

The present paper focuses on problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside L-shaped cavities. The governing equations are discretized using the finite volume method while the SIMPLER algorithm is employed to couple velocity and pressure fields. Using the developed code, the effects of the Rayleigh number, the aspect ratio of the L-shaped cavity, and the volume fraction of the Cu nanoparticles on the flow and thermal fields and heat transfer inside the cavity are investigated. The obtained results show that the average Nusselt number for all rage of cavity aspect ratio increases with increase in the Rayleigh number and the solid volume fraction of the nanofluid. Also the Rayleigh number in which transition from conduction to convection occurs postpones with decreasing the aspect ratio of cavity. Moreover it is found that the rate of heat transfer increases with decreasing the aspect ratio of the cavity.

Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO 2 nanofluid

Heat transfer enhancement has been investigated in a square cavity subject to different side wall temperatures using water/SiO 2 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 = 10 5–10 7 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 simulation of free convection of a heat-releasing fluid in an axisymmetric closed volume

A simplified computing method has been developed and on its basis the problem on laminar free convection of a heat-releasing fluid in a cylindrical and a hemispherical volumes with an isothermal lateral (in the case of a hemisphere, lower) and adiabatic upper bounds has been solved. On the basis of the results obtained the influence of the temperature stratification in the volume and geometry on the heat transfer characteristics has been investigated. It has been established that neglecting the temperature stratification leads to a considerable overestimation of the density of heat flow to the boundary in the lower part of the volume.

On the validity of the Millionshchikov quasi‐normality hypothesis for open‐ocean deep convection

Data from numerical simulations of free convection in the ocean with rotation are used to explore the validity of the Millionshchikov quasi‐normality hypothesis. The parameterizations of fourth‐order moments according to a universal model proposed by Gryanik et al. are found to be far more accurate than their corresponding Gaussian parameterizations, which are based on the Millionshchikov hypothesis. The universal model is marginally improved by fitting the model parameters to the data. The present results extend previous results that discuss shallow convection in the planetary boundary layer to rotationally controlled deep convection.

Direct numerical simulations of free convection beneath an air–water interface at low Rayleigh numbers

Direct numerical simulations of a cooling air–water interface were employed to determine the structure of the temperature, velocity, and vorticity fields in the thin thermal boundary layer formed at the free surface. The simulations were performed at low to moderate Rayleigh numbers. In this flow, the turbulence is initiated by the Rayleigh instability at the interface and is maintained by buoyant production. Visualizations of the flow reveal that the temperature field at the interface is composed of large warm patches surrounded by cooler dense fluid which accumulates in thin bands. The cool fluid associated with the bands initially falls in sheets, but rapidly forms descending tubes and plumes. The turbulence statistics were scaled both with outer and inner variables. The latter scaling is based on the so-called surface strain model which is essentially consistent with Townsend’s inner scaling. It is found that the temperature statistics collapse well using inner variables. On the other hand, the vertical velocity scales well with inner variables within the thermal boundary layer, but at greater depths it becomes more appropriate to use outer scaling. The anisotropic nature of the velocity statistics in the core of the flow is ascribed to the relatively low Rayleigh numbers used in the simulations. An explanation for this anisotropy is offered based on a detailed examination of the turbulence kinetic energy balances.

Numerical simulations of free convection about a vertical flat plate embedded in a porous medium

We consider the free convection about a vertical flat plate embedded in a porous medium within the framework of a boundary layer approximation. In some cases, similarity solutions arise in the modelization of such phenomena, allowing a reduction of the dimension of the problem. We suggest two complementary and rather simple numerical methods to compute such solutions. When possible, the numerical analysis for the two discretizations is performed and convergence results are given. Numerical experiments with a physical model are presented to confirm the efficiency of both approaches.