Steady-state Natural Convection Research Articles

Impact of variation in gap spacing and orientation of split baffles on thermodynamics optimization in naturally convective flow in corrugated enclosure

The fundamental aim of this research work is to examine the effect of heated split baffles and the influence of different corrugation frequencies on steady-state natural convection within a sinusoidal corrugated square cavity. The configuration of the present model maintains a constant temperature of T c for the horizontal wavy boundaries and vertical walls while the inner split baffles are heated at a constant temperature of T h . The finite element method is applied to the discretized equations representing the fluid behavior within the enclosure, with the aim to investigate the inclination angles, variation of space between the baffles, corrugation frequencies, and the impact of Rayleigh number on the fluid motion and heat transfer. The variation in velocity and temperature profile is illustrated through the streamlines and isotherm contours. Moreover, the numerical results are carried out in terms of local and average Nusselt numbers of the heat transfer, which are analyzed for inside space of baffles and line dip-angles of the baffle ( θ = 0 ° , 45 ° , 90 ° ) , and ( φ = 0 ° , 30 ° , 60 ° , 90 ° ) . The key findings indicate that increasing the space l s between the baffles enhanced the convective heat transfer by 8.5 % , moreover, elevating the baffle angle to right angle ( θ = 90 ° ) amplify the heat transfer rate increase by 19.17 % . The augmentation in corrugation frequency leads 7.15 % reduction in heat transfer efficiency. The comparison of the present numerical simulations revealing a satisfactory and reliable match with the literature precedents.

Local thermal nonequilibrium perspective of heat transfer and fluid flow in a slender anisotropic porous cavity due to lateral uniform heat flux

The influence of the local thermal nonequilibrium (LTNE) state on steady-state natural convection due to the heating and cooling of the side walls of the slender porous cavity has been addressed analytically and numerically. The porous medium is assumed to be hydrodynamically anisotropic. The Darcy model has been adopted. A closed-form solution, based on a parallel hypothesis, is reported for a slender cavity. The combined impact of media anisotropy and LTNE state on the heat transfer rate, as well as flow dynamics, have been analyzed. The help of boundary layer analysis is taken to report the boundary layer thickness and heat transfer rate of fluid flow analytically. It has been found that the maximum (minimum) heat transfer rate of the fluid phase as well as solid phase takes place at orientation angle, ϕ , equal to π / 2 when permeability along the horizontal (vertical) direction is higher than the same along vertical (horizontal) direction.

Natural Convection Heat Transfer In Heated Vertical Tube Without Internal Rings

An experimental investigation of natural convection heat transfer in heated vertical pipes dissipating heat from the internal surface is presented. The pipes are open-ended and circular in cross section. The test section is electrically heated imposing the circumferentially and axially constant wall heat flux. The purpose of this work is to study experimentally the natural convection pipe flows at different heating levels. The test section is a vertical, open-ended cylindrical pipe dissipating heat from the internal surface. The test section is electrically heated imposing the circumferentially and axially constant wall heat flux. Heat transfer experiment is carried out for four different channels of 45mm internal diameter and 3.8mm thickness with length 450 mm. Ratios of length to diameter of the channel is taken as L/D = 10. Wall heat fluxes are maintained at q// = 250 to 3341 W/m2. A systematic experimental database for the local steady state natural convection heat transfer behaviour is obtained. A correlation is developed for average Nusselt number and modified Rayleigh number and another correlation is also developed for modified Rayleigh number and modified Reynolds number.

Physics-informed graph convolutional neural network for modeling geometry-adaptive steady-state natural convection

This paper presents a novel deep learning-based surrogate model for steady-state natural convection problem with variable geometry. Traditional deep learning based surrogate models are more or less limited by the requirement for large amounts of training data, loss of accuracy due to pixelization of the original data, the low accurate prediction near the boundaries and low geometry adaptive capability. To overcome the above challenges, the proposed natural convection prediction framework is mainly composed of a physics-informed neural network (PINN) and a graph convolutional neural network (GCN), called natural convection prediction model based on physics-informed graph convolutional network (NCV-PIGN). The GCN serves as the prediction module, inferring and predicting natural convection phenomena by considering the interactions between unstructured nodes and their neighbor; the PINN incorporates the governing equations of natural convection into the loss function of the neural network, allowing the predictions from GCN to satisfy the constraints imposed by the physical laws. The advantages of this framework are twofold: the operation principles of the GCN better align with the development of the temperature field in real situations, and the embedding of physical information strengthens the model's understanding of the flow field, accurately describing the variations of temperature gradients at the boundary positions while reducing the model's reliance on training data. Finally, to validate the superiority of the NCV-PIGN, we analyze its geometric adaptability and accuracy of prediction using single and dual heat source cases. We compare the model's prediction results at different sampling point quantities and contrast them with those of purely data-driven models. The results demonstrate that the excellent geometric adaptability and prediction capability of the proposed model can be achieved with only 20 training data and once the fully trained the model can solve natural convection problems within 3 ms. The max and mean relative errors in predicting the temperature field are less than 2% and 0.4% for both single and dual heat source cases. Compared to the pure data-driven model, the proposed model has reduced the maximum error by 65.5% and the mean error by 72%. These results validate the effectiveness of the developed NCV-PIGN model, enabling better performance of the deep learning-based surrogate models for natural convection problems.

An Experimental Study of Natural Convection Heat Transfer from a Horizontal and Slightly Inclined Plate-Fin Heat Sink

The steady-state natural convection from heat sink fin arrays was studied on horizontal, vertical, and inclined heat sinks. Under natural convection, horizontal and vertical heat sinks with parallel fins were tested by considering radiation heat transfer. The experiments were conducted with power inputs ranging from 60 W to 455 W in order to obtain different temperatures. According to the result, when heat input increases, the heat transfer coefficient increases by 38 %, 40.78 % for horizontal and vertical respectively. For horizontal and vertical cases, new correlations have been presented to calculate the Nusselt number influenced by the Rayleigh number. For the incline case, the effect of buoyancy force was studied by changing the inclination angles at 0, 30, 45, and 60 degrees from vertical position. According to comparisons between vertical and incline cases, Nusselt number and heat transfer coefficient were most improved at 30 degrees by 6 %.

Topology optimization using the lattice Boltzmann method for unsteady natural convection problems

This paper proposes a density-based topology optimization method for natural convection problems using the lattice Boltzmann method (LBM). As the LBM can be developed as a completely explicit scheme, its attractive features over the traditional ones, such as the finite element method, are (1) suitability for solving unsteady flow problems and (2) scalability for large-scale parallel computing. We develop an LBM code for solving unsteady natural convection problems and provide its sensitivity analysis based on the so-called adjoint lattice Boltzmann method. Notably, the adjoint equation is derived from the discrete particle velocity Boltzmann equation and can be solved similarly to the original LBM concerning unsteady natural convection problems. We first show that the proposed method can produce similar results to the previous work in a steady-state natural convection problem. We then demonstrate the efficacy of the proposed method through 2D numerical examples concerning unsteady natural convection. As a large-scale problem, we tackle a 3D unsteady natural convection problem on a parallel supercomputer. All the developed codes written in C++ are available at https://github.com/PANFACTORY/PANSLBM2.git.

Reduced order modelling of natural convection of nanofluids in horizontal annular pipes based on deep learning

Natural convection of nanofluids in annular pipes has been investigated in many studies due to its high occurrence in heat transfer systems. Solving natural convection problems numerically itself requires numerical discretization and iteration of differential equations, and introduction of nanofluids makes the solution process more complicated. In this paper, we propose and investigate a deep learning-based reduced-order model (ROM) for fast prediction of natural convection of nanofluids in annulus pipes. We construct the model using U-net structure of deep convolutional neural network and an end-to-end supervised learning method. The geometry presented by the Nearest Wall Signed Distance Function (NWSDF) is combined with numerical results to train the network model by minimizing model prediction error. The trained network model works as a ROM, which establishes the accurate mapping between the problem geometry, boundary conditions and the steady-state natural convection field. To validate the feasibility, stability and accuracy of the network model, current work studies the natural convection of nanofluids in single inner-ring annulus and multi-inner-ring annulus with different positions and diameters. The results show that the network model enables accurate predictions for natural convection of nanofluid with arbitrary inner-ring geometry, where an average accuracy of 99.9% for temperature field and 99% for velocity field are achieved; and the prediction speed of the proposed network model is more than three orders of magnitude faster than numerical solver. Furthermore, we also investigate and confirm the approach of setting the thermal boundary conditions in the neural network model, which will greatly enhance the applicability of the network model. The accurate and extremely fast prediction ability of the proposed network model proves that it can serve as a fast geometry optimization tool for design of heat exchangers or solar energy collectors of nanofluid in the future.

Experimentation on Optimal Configuration and Size of Thin Cylinders in Natural Convection

In this paper, an experimental study of laminar, steady state natural convection heat transfer from heated thin cylinders in an infinite air medium has been reported. Two electrically heated cylinders having the same slenderness ratio (L/D) i.e. 6.1 but different diameters i.e. 3.8 cm and 5.08 cm were used. 105 experiments were carried out to study the effect of diameter and inclination angle of thin cylinder on natural convection heat transfer. After mandatory corrections of radiation and endcap heat losses, convective heat transfer results were presented in the form of local and average dimensionless numbers. For vertical configuration of thin cylinder, Nusselt number was varied from 52.99 to 95.10 corresponding to 1.28×108≤Ra*L≤1.08×1010. While for horizontal configuration,Nusselt number was varied from 10.74 to 17.78 corresponding to 9.42×104≤Ra*D≤8.17×106. Results were compared with the published data and found satisfactory as the maximum percentage difference was only 3.09%. The essence of research is that the heat transfer coefficient increases with decrease in diameter and increase in inclination angle. Smoke flow visualization was done to capture patterns of fluid flow. Finally, comparison was made to quantify increase in Nusselt number from slender cylinder as compared to the flat plate.

Impact of grooved cylinder on heat transfer by natural convection in cylindrical geometry

The current study reports a numerical analysis of a two-dimensional steady-state natural convection heat transfer from grooved heated cylinder for laminar flow regime. Two groove shapes are investigated in this work: circular and triangular groove. Simulations were carried out by varying the groove location, radius ratio f from 0.1 to 1, and the Rayleigh number over the range [103–106]. The thermal and dynamic behaviors are carefully analyzed and compared to the case of non-grooved cylinder (model 0). It is found that the heat transfer rate rises up with the increase of Rayleigh number. In addition, the groove locations φ = −90, and 80° provide the lowest heat transfer rate. A decrease of 9.4% in the heat transfer rate is detected for the case of triangular groove with f = 0.7 and Ra = 105. On the other hand, the highest heat transfer rate is provided at a position φ = −45° and 45° for f > 0.65. For these last groove locations, lower f present optimal configurations to accumulate heat on the cylinder. In fact, circular grooved cylinder with f = 0.1 decreases the heat loss by 9.3% and 12.4% for the locations φ = −45° and 45°, respectively compared to model 0. These results would be useful for engineering applications that are interested in the accumulation or transfer of heat through cylindrical ducts.

Natural convection heat transfer in PCM suspensions in a square enclosure with bottom heating and top cooling

Research on the use of phase change material (PCM) suspensions to improve the natural convection efficiency of thermal systems is booming; however, there are few studies on the transient behavior of PCM suspensions. In this study, numerical simulations were used to investigate transient and steady-state natural convection in a square enclosure containing a PCM suspension. The implicit finite-difference method was adopted. The left and right walls of the enclosure were adiabatic sections, the bottom was an isothermal heating, and the top was an isothermal cooling. The following parameters were considered: PCM = n-octadecane (C18H38), enclosure aspect ratio = 1, buoyancy ratio for mass-to-heat transfer = 1, Rayleigh number (RaT) = 103–104, Stefan number (Ste) = 0.005–0.05, subcooling factor (Sb) = 0–10, and initial mass fraction (cm,i) = 0–20%. The results show that all the parameters (RaT, Ste, Sb, and cm,i) affect the flow pattern, and convection oscillations occur at Sb = 0.5–1. The heat transfer rate increases with RaT. Both cm,i and Sb affect the heat transfer rate but in a case-specific manner, and no well-defined correlations are observed.

Natural convection in a horizontal annular sector containing heat-generating porous medium

PurposeThe purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium.Design/methodology/approachGITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost.FindingsThe effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium.Originality/valueThe strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.

The Effect of Fin Length on Free Convection Heat Transfer in Annular Space of Concentric Arrangement Using Shear-Thinning Fluids as a Thermal Medium

The two-dimensional steady-state natural convection of shear-thinning fluids is studied numerically between two concentric horizontal cylinders with different constant temperatures. The inner cylinder was put eccentrically into the outer one. The inner cylinder are held at constant temperatures with the inner one heated isothermally at temperature (Th) and the outer cylinder have one fin cooled isothermally at temperature Tc (Th > Tc). The simulations have been taken for the parameters 102 ≤ Ra ≤ 104, = 0.71 ≤ Pr ≤ 10 and 0.6 ≤ n ≤1.The effects of Rayleigh number and Prandtl number on the dimensionless velocity and temperature are investigated for both shear-thinning and Newtonian fluids. Also the mean Nusselt number for various values of governing parameters is obtained and discussed. Although huge researches were conducted for natural convection in non-circular enclosures, researches for annular enclosures are very limited, especially finned enclosures. The length of the fin is also studied. The results show that increase in the length of fin increases the effectiveness of heat transfer. Also, the increase in Ra number increases the heat transfer effectiveness.

Heat Transfer by Natural Convection in a Square Enclosure Containing PCM Suspensions

Research on using phase change material (PCM) suspension to improve the heat transfer and energy storage capabilities of thermal systems is booming; however, there are limited studies on the application of PCM suspension in transient natural convection. In this paper, the implicit finite difference method was used to numerically investigate the transient and steady-state natural convection heat transfer in a square enclosure containing a PCM suspension. The following parameters were included in the simulation: aspect ratio of the physical model = 1, ratio of the buoyancies caused by temperature and concentration gradients = 1, Raleigh number (RaT) = 103–105, Stefan number (Ste) = 0.005–0.1, subcooling factor (Sb) = 0–1.0, and initial mass fraction (or concentration) of PCM particles (ci) = 0–0.1. The results showed that the use of a PCM suspension can effectively enhance heat transfer by natural convection. For example, when RaT = 103, Ste = 0.01, ci = 0.1, and Sb = 1, the steady-state natural convection heat transfer rate inside the square enclosure can be improved by 70% compared with that of pure water. With increasing Sb, the Nusselt number can change nonlinearly, resulting in a local optimal value.

Periodic unsteady natural convection in square enclosure induced by inner circular cylinder with different vertical locations

The periodic unsteady natural convection flow and heat transfer in a square enclosure containing a heated circular cylinder with different vertical locations is numerically studied. The temperature of the enclosure keeps lower constant while the temperature of the inner circular cylinder oscillates periodically with time at higher averaged value, the natural convection in the enclosure is driven by the temperature difference. The two-dimensional natural convection is simulated with high accuracy temporal spectral method and local radial basis functions method at Rayleigh number Ra = 105. The location of inner circular cylinder varies from −0.25 to 0.25 vertically, the temperature pulsating amplitudes are a = 0.5, 1.0 and 1.5 and the temperature pulsating period ranges from 0.01 to 100. Numerical results show that the heat transfer is strongly dependent on the vertical location and the pulsating temperature of inner cylinder. The heat transfer is enhanced generally for the time-periodic unsteady natural convection comparing with its steady state natural convection, and the local maximum heat transfer rate is observed for some locations. Moreover, the phenomenon of backward heat transfer is discussed and the quantity of back heat transfer rate is presented. Finally, the influence of the vertical locations and pulsating temperature on the unsteady fluid flow and heat transfer are discussed and analyzed.

Conjugate Natural Convection in a Square Porous Cavity Filled with a Nanofluid in the Presence of Two Isothermal Cylindrical Sources

In this work, a numerical study has been performed for the problem of steady-state natural convection in a square porous cavity having a solid wall of finite thickness and conductivity filled by a nanofluid in the presence of two isothermal cylindrical sources. The external walls of the cavity are considered adiabatic and the circular sources are maintained at a hot and cold uniform temperatures. The internal thick wall has been a conducting solid. The governing dimensionless equations are solved using Galerkin finite element method and Darcy-Brinkman model assumed to be adopted. The results are presented as isotherms, streamlines, stream function values, average and local Nusselt number for various combinations of Rayleigh and Darcy numbers, concentration of nanoparticles, Thermal conductivity ratio, and dimensionless wall thickness of the solid portion. The convection heat transfer can be enhanced by increasing of these parameters except for the wall thickness.

Lattice Boltzmann Modeling for Natural Convection in Power-Law Fluids Within a Partially Heated Square Enclosure

Abstract This paper reports the numerical investigations for steady-state natural convection in power-law fluids inside a square enclosure embedded with bottom discrete heaters. The lattice Boltzmann method (LBM) is employed to model the flow and heat transfer phenomenon at different combinations of power-law index, Rayleigh number, and heat source length for a constant Prandtl number. The buoyancy force is incorporated in the collision term of the LBM through Boussinesq approximation. Simulation outcomes are furnished using streamlines, temperature contours, velocity profiles, and variation of heat transfer on the nonadiabatic walls to probe natural convection phenomena. The results indicate that the temperature and the flow fields in the enclosure are symmetric about the vertical centerline. The detailed physical interpretations have been provided for the reported results. Further, the increase in the power-law index means a rise in viscosity and a decrease in thermal energy transport for other constant parameters. The outcomes also specify that the intensity of circulation and heat transfer enhances with the increase of Rayleigh number and size of the localized heater. Finally, though, a rise in the size of the confined heat source enhances the rate of total thermal transport, it does not change the trend of fluid flow and local heat transfer rate.

Heat Transfer in Horizontal Copper Tube Heated by Electric Heating Process

Heat transfer from electrical and electronics component is essential for better performance of that electrical system, The maximum heat transfer from that system results long period durability. In most of the system base provided for equipments are very small and placed in a very complicated position. so heat transfer by forced convection is not easy for that purpose.The heat transfer by natural convection is the familiar technique used in electronics cooling; there is huge group of apparatus that lends itself to natural convection .This category consist of stand-alone correspondence such as modems and small computers having an array of printed circuit boards (PCB) accumulate within an area. Natural convection heat transfer in heated horizontal duct drive away heat from the interior surface is offered. The duct is open-ended and round in cross section. The test section is heated by provision of heating coils, where constant wall heat flux mentioned. Heat transfer experiment is carried out for channel of 50 mm. internal diameter and 4 mm thickness with length 600 mm. Ratios of length to diameter of the channel are taken as L/D = 12. Wall heat fluxes maintained at q// = 300 W/m2 to 3150 W/m2 . A methodical investigational record for the localsteady state natural convection heat transfer activities is obtained. The wall heating condition on local steady-state heat transfer phenomena are studied.The present experimental data is compared with the existing theoretical and experimental results for the cases of vertical smooth tubes.

A new mixed-FEM for steady-state natural convection models allowing conservation of momentum and thermal energy

In this work we present a new mixed finite element method for a class of steady-state natural convection models describing the behavior of non-isothermal incompressible fluids subject to a heat source. Our approach is based on the introduction of a modified pseudostress tensor depending on the pressure, and the diffusive and convective terms of the Navier–Stokes equations for the fluid and a vector unknown involving the temperature, its gradient and the velocity. The introduction of these further unknowns lead to a mixed formulation where the aforementioned pseudostress tensor and vector unknown, together with the velocity and the temperature, are the main unknowns of the system. Then the associated Galerkin scheme can be defined by employing Raviart–Thomas elements of degree k for the pseudostress tensor and the vector unknown, and discontinuous piece-wise polynomial elements of degree k for the velocity and temperature. With this choice of spaces, both, momentum and thermal energy, are conserved if the external forces belong to the velocity and temperature discrete spaces, respectively, which constitutes one of the main feature of our approach. We prove unique solvability for both, the continuous and discrete problems and provide the corresponding convergence analysis. Further variables of interest, such as the fluid pressure, the fluid vorticity, the fluid velocity gradient, and the heat-flux can be easily approximated as a simple postprocess of the finite element solutions with the same rate of convergence. Finally, several numerical results illustrating the performance of the method are provided.

Computation of Metallic Nanofluid Natural Convection in a Two-Dimensional Solar Enclosure with Radiative Heat Transfer, Aspect Ratio and Volume Fraction Effects

As a model of nanofluid direct absorber solar collectors (nano-DASCs), the present article describes recent numerical simulations of steady-state nanofluid natural convection in a two-dimensional enclosure. Incompressible laminar Newtonian viscous flow is considered with radiative heat transfer. The ANSYS FLUENT finite volume code (version 19.1) is employed. The enclosure has two adiabatic walls, one hot (solar receiving) and one colder wall. The Tiwari–Das volume fraction nanofluid model is used and three different nanoparticles are studied (Copper (Cu), Silver (Ag) and Titanium Oxide (TiO2)) with water as the base fluid. The solar radiative heat transfer is simulated with the P1 flux and Rosseland diffusion models. The influence of geometrical aspect ratio and solid volume fraction for nanofluids is also studied and a wider range is considered than in other studies. Mesh independence tests are conducted. Validation with published studies from the literature is included for the copper–water nanofluid case. The P1 model is shown to more accurately predict the actual influence of solar radiative flux on thermal fluid behaviour compared with Rosseland radiative model. With increasing Rayleigh number (natural convection, i.e. buoyancy effect), significant modification in the thermal flow characteristics is induced with emergence of a dual structure to the circulation. With increasing aspect ratio (wider base relative to height of the solar collector geometry), there is a greater thermal convection pattern around the whole geometry, higher temperatures and the elimination of the cold upper zone associated with lower aspect ratio. Titanium Oxide nanoparticles achieve slightly higher Nusselt number at the hot wall compared with Silver nanoparticles. Thermal performance can be optimized with careful selection of aspect ratio and nanoparticles and this is very beneficial to solar collector designers.

Two-Grid Stabilized FEMs Based on Newton Type Linearization for the Steady-State Natural Convection Problem

Two-Grid Stabilized FEMs Based on Newton Type Linearization for the Steady-State Natural Convection Problem