Two-dimensional Natural Convection Research Articles

Numerical study of magneto-hydrodynamics natural convective flow in a porous-corrugated enclosure using a higher-order compact finite difference scheme

This study explores the numerical investigation of two-dimensional natural convection in a porous corrugated enclosure with heat sources of different heights and electrically conducting fluids. The governing equations are solved using a higher-order compact finite difference scheme. Boundaries on the top and sides are subject to thermal cooling and adiabatic conditions, respectively. Numerical results are presented for wide range of Rayleigh (103 to 106), Darcy (10−5 to 10−1), Hartmann (25 to 150), and Prandtl (0.015 to 10) numbers. For fixed high Rayleigh-Darcy values, the porous medium has higher permeability. Most significant possible multiple steady solutions can be found in the case 1 at Ra=106,Da=10−2,Ha=50, and Pr=10.0. In the low to moderate critical values of Prandtl numbers, it encompasses a wide range of fluid flow phenomena, from stable to unstable. The maximum enhancement of the averaged Nusselt numbers on the boundaries in increasing and decreasing trends are viz. Ra(139.13% and 54.37%), Da(46.14% and 74.25%), Ha(633.04% and 74.73%), and Pr(142.52% and 45.92%) for case 1, Ra(129.64% and 0.32%), Da(40.68% and 69.66%), Ha(46.65% and 80.85%), and Pr(18.41% and 18.23%) for case 2, and Ra(163.98% and 77.20%), Da(8.25% and 58.68%), Ha(81.38% and 59.17%), and Pr(30.60% and 22.46%) for case 3.

Similar Solutions for Changing Characteristics of Natural Convection Laminar Flow around a Vertical Rectangular Inclined Plane Surface

The study investigates laminar natural convection flow around a vertical rectangular inclined plane surface, specifically focusing on the effects of viscous and pressure stress work. Previous research primarily addressed these effects in two-dimensional natural convection flow scenarios, while this study extends the analysis to encompass three exterior situations, accounting for variations in fluid properties outside compressible boundary layers. Employing numerical methods, the study aims to predict essential flow parameters including Prandtl’s number (Pr), controlling parameter (C), and additional parameters (A, B, D, E, ∅). The investigation yields velocity profiles (F'(0), S'(0)), temperature profiles , skin frictions (F''(0), S''(0)), and heat transfer coefficients θ'(0). Numerical results are presented to illustrate the impact of different parameters on these flow characteristics. Additionally, tabulated data in Tables-2 and Tables-3 offer further insights into the predicted flow parameters and their variations under varying conditions.

Unsteady Two-Dimensional Natural Convection Fluid Flow in a Valley Shaped Cavity

Unsteady Two-Dimensional Natural Convection Fluid Flow in a Valley Shaped Cavity

MHD natural convection flow in a porous medium-filled corrugated enclosure: Effect of heat sources with different heights

A two-dimensional natural convection flow problem in a porous medium-filled enclosure with electrically conducting fluids and solid heat sources of different heights is numerically investigated in this study. The top boundary is cold, and the vertical side boundaries are insulated, while rectangular-shaped corrugations at the lower boundary are generated by placing heat sources. Three distinctive cases are considered concerning the height of the solid rectangular-shaped heat sources. The nonlinear coupled transport equations are discretized by using a higher-order compact (HOC) finite difference scheme. First, existing numerical and experimental data are used to validate the developed code. Then, the effect of key parameter values, like Hartmann number (25–150), Rayleigh number (103–106), Darcy number (10−5–10−1), and Prandtl number (0.015–10), on the convective flow in the corrugated enclosure is analysed. The influence of the permeability of the porous medium is abundantly seen for a range of significant parameter values with a fixed high Rayleigh-Darcy number. The formation of primary, secondary, tertiary, and quaternary vortices affects the thickness of the thermal boundary layer on both hot and cold surfaces in both symmetric and asymmetric patterns. In addition, possible multiple steady states are observed in the Case 2 at Pr=10.0. The local and average Nusselt numbers remains constant on the bottom cold surfaces of the corrugated enclosure, while significant variations are observed on the upper surfaces of the heat sources. These findings are analysed by conducting stream-function (ψ), isotherms (T), local (Nuh,Nuv), and average (Nū) Nusselt number plots. The intensities of heat transfer rate are also examined by analysing Nusselt numbers as a function of Prandtl, Darcy, Rayleigh and Hartmann numbers. Analysing natural convective heat transfer fluid flow in an enclosure with heat sources is prominent for ample engineering applications such as solar collectors, designing nuclear reactors, chemical energy production systems, building constructions and microelectronic equipment, to name a few.

FLT-HPM for Two-dimensional Transient Natural Convection in a Horizontal Cylindrical Concentric Annulus

FLT-HPM for Two-dimensional Transient Natural Convection in a Horizontal Cylindrical Concentric Annulus

FLT-HPM for Two-dimensional Transient Natural Convection in a Horizontal Cylindrical Concentric Annulus

FLT-HPM for Two-dimensional Transient Natural Convection in a Horizontal Cylindrical Concentric Annulus

Efficient monolithic immersed boundary projection method for incompressible flows with heat transfer

Efficient monolithic immersed boundary projection methods (MIBPMs) with staggered time discretization have been proposed for incompressible viscous flows with heat transfer. The main idea is to use a two-step approximate lower-upper decomposition technique to decouple the momentum and energy equations, including immersed boundary forcing. The momentum and energy forcing are treated as Lagrangian multipliers to impose divergence-free constraints and no-slip conditions at the immersed boundary surfaces. A staggered time discretization is applied with the Crank-Nicolson scheme to decouple the temperature and velocities, which means that the velocity fields are described at integer time levels (n+1), while the temperature fields are described at half-integer time levels (n+1/2). To investigate the effect of forcing schemes in monolithic formulation, several MIBPM variants based on forcing schemes are formulated and evaluated numerically. The proposed MIBPM presents an accurate imposition of no-slip conditions on the immersed boundary surface and exhibits good stability for two-dimensional forced and natural convection problems. Further, simulations with the proposed MIBPM are implemented for the three-dimensional natural convection problem. Numerical simulation results for single- and multi-particle sedimentation demonstrate the robustness of the proposed method for complex heat transfer flows over moving objects.

A natural convection conjugate heat transfer of Nano-Encapsulated Phase Change Materials (NEPCMs) in an inclined blocked square enclosure

The current investigation deals numerically with a two-dimensional steady laminar flow natural convection heat transfer of a dilute suspension of a base fluid and suspension of Nano Encapsulated Phase Change Materials (NEPCMs) nanoparticles saturated inside an inclined square enclosure with a centered internal conducting square block with a ratio of 0.5. The enclosure inclination angle varies from 0° to 90° with increments of 15°, and block thermal conductivity to the host fluid has been chosen to be 0.2 and 5. The obtained results are in excellent agreement with those available in the literature for validation. The findings reveal that the heat transfer depends considerably on the inclination angle, block thermal conductivity ratio, and Stefan number for all considered ranges. The present results suggest that the average Nusselt number rate is notably enhanced as the inclination angle rises from 0° to 90° for thermal conductivity KR = 0.2 and KR = 5; this enhancement is more evident as the Rayleigh number is increased. The average Nusselt number improves by 5%, 153%, 558%, and 1120% for Rayleigh numbers of 103, 104, 105, and 106, respectively, when the inclination angle varies from 0° to 90° for a thermal conductivity ratio of 0.2. This improvement is somewhat reduced in the case of a thermal conductivity of 5, where the average Nusselt number grows by around 0.4%, 27%, 213%, and 537% for Rayleigh numbers 103, 104, 105, and 106, respectively. The higher value of the latent heat capacity of encapsulated particles enhances the heat transfer rate; the decreased Stefan number induces a notable improvement in the average Nusselt number. This enhancement is more evident as the inclination angle increases. The findings clearly show a considerable influence on the isotherms and heat capacity ratio distributions for all considered block thermal conductivities and Rayleigh numbers.

Study of the Impacts of Different Geometry and Aspect Ratio Hot Body on Natural Convection Heat Transfer

This work deals with a two-dimensional laminar natural convection heat flow, based on the temperature difference between the cold outer corrugated cylinder and three different cross-sectional areas, i.e. circular, square, and triangle configuration at the steady-state condition. The free region between two surfaces has been filled by a fluid with (Pr=7.0), and CFD finite volume method has been employed to solve the main equations. The simulations have been performed based on the dimensionless parameters: (Ra=104-105-106), (D/Dbase, and L/Dbased), while θ=0°-90°-180° has been applied for square and triangle configuration. The results are displayed in terms of isothermal contours and stream function and the heat transfer is recognized by both local and average Nusselt number. Firstly, the ANSYS 19.2 code validation has been performed by the comparisons of the outer data with previously theoretical papers, and good agreements have been detected. It is initiated from the local and average Nusselt number that the heat transfer from the inner hot surface has been affected by the above governing parameters at a certain fixed value of Ra. In all the results of the valve of average Nu approximately constant for the same configuration when Ra<106 also, flow lines become fewer symmetrical when Ra=106. It is detected that both the cylinder aspect ratio and coordinations have a significant effect on the thermal fields and flow distribution. Moreover, the results that designate the changing of D/Dbase to 0.3 cause improvement in heat transfer by 23.3% at Ra=106, and also the circular cylinder is better than the other configurations.

MAGNETOHYDRODYNAMIC FREE CONVECTION FLOW OF FLUID OF A VERTICAL PLANE WITH VISCOSITY AND THERMAL CONDUCTIVITY DEPENDING ON TEMPERATURE

A two-dimensional natural convection flow of a viscous incompressible and electrically conducting fluid with both the viscosity and the thermal conductivity depending on temperature past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to non-similar boundary layer equations by introducing coordinate transformations appropriate to the cases (i) near the leading edge (ii) in the region far away from the leading edge and (iii) for the entire regime from leading edge to down stream. The governing equations for the flow in the upstream regime are investigated by perturbation method for smaller values of x, the stream-wise distributed magnetic field parameter. The equations governing the flow for large x and for all x, have been investigated by employing the implicit finite difference method with Keller box scheme. The effects of the viscosity variation parameter, e and the thermal conductivity variation parameter g, on the skin friction as well as the rate of heat transfer for the fluid for low Prandtl number are shown graphically.

Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array

AbstractThis study numerically investigates the two-dimensional natural convection in a square enclosure with an isothermal diamond elliptic array at Rayleigh numbers of 104≤ Ra ≤ 107. Three cases are considered, i.e., case 1 where two pairs of circular heating bodies are used inside the cavity, one is placed on the vertical centerline (VC) of the cavity and the other on the horizontal centerline (HC), case 2 where one pair of horizontal elliptic heating bodies is placed on the VC of the cavity and the other on the HC and case 3 where the horizontal elliptic heating bodies are replaced by vertical elliptic heating bodies. Numerical simulation was carried out based on the mesoscopic approach (LBM). The effects of the horizontally and vertically heated arrays were investigated. We demonstrate that, only when the Rayleigh number increases to Ra = 107, the numerical solutions reach an unsteady state for all cases. The transition of the flow regime from the unsteady state to the steady state depends on the variation in the ratio of the elliptical cylinder.

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.

Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method

Modal global linear stability analysis of thermal convection is performed with the linearized lattice Boltzmann method (LLBM). The onset of Rayleigh–Bénard convection in rectangular cavities with conducting and adiabatic sidewalls and the instability of two-dimensional (2-D) and three-dimensional (3-D) natural convection in cavities are studied. The method of linearizing the local equilibrium probability distribution function that was first proposed by Pérez et al. (Theor. Comp. Fluid Dyn., vol. 31, 2017, pp. 643–664) is extended to solve the coupled linear Navier–Stokes equations together with the linear energy equation in this work. A multiscale analysis is also performed to recover the macroscopic linear Navier–Stokes equations from the discrete lattice Boltzmann equations for both the single and multiple relaxation time models. The present LLBM is implemented in the framework of the Palabos library. It is validated by calculating the linear critical value of 2-D natural convection that the LLBM with the multiple relaxation time model has an error less than 1 % compared with the spectral method. The instability mechanism of the flow is explained by kinetic energy transfer analysis. It is shown that the buoyancy mechanism and inertial mechanism tend to stabilize the Hopf bifurcation of the 2-D natural convection at Pr < 0.08 and Pr > 1, respectively. For 3-D natural convection, subcritical bifurcation of the Hopf type is found for low-Prandtl-number fluids (Pr < 0.1).

MHD natural convective flow in a porous corrugated enclosure: Effects of different key parameters and discrete heat sources

Present work deals with an unsteady two-dimensional magneto-hydrodynamics natural convection flow problem in a porous-corrugated enclosure. The vertical side walls are insulated, and the top wall is non-uniformly heated; while square-shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending on the discrete heat sources and various key parameters. A transformation-free higher-order compact (HOC) scheme is used to discretize the non-linear coupled transport equations, and an advanced iterative solver, like the hybrid-bi-conjugate-gradient stabilized technique, is used to solve the system of algebraic equations generated from the numerical discretization. Present higher-order compact scheme is fourth-order accurate in space coordinates and second-order accurate in the time variable. At first, the developed code is validated with existing experimental and numerical computed results for the case of a square enclosure associated with and without a heat source. Then, the computed results are analysed over a range of key parameters, like Rayleigh number (103≤Ra≤106), Darcy Number (10−5≤Da≤10−1), Hartmann number (25≤Ha≤150), with a fixed Prandtl number (Pr=6.1), to study the effects of these key parameters on the fluid flow behaviour and isotherm patterns in the porous-corrugated enclosure. It is found that at high Rayleigh–Darcy numbers with different Hartmann numbers, the effect of the permeability of the porous medium is significant; whereas the flow resistance from the boundary friction is gradually reduced, and the flow behaviour is similar to the pure buoyancy-induced flow. These simulated results are presented in the form of streamlines, isotherms, local and averaged Nusselt number plots, etc. The presented results show various flow features that have not been analysed before.

Heat transfer in a square cavity filled by nanofluid with sinusoidal wavy walls at different wavelengths and amplitudes

This study's main purpose is to investigate the wavy wall effect with a sinusoidal function on two-dimensional natural convection in a cavity with Cu-Water nanofluid. The SIMPLE algorithm is used to solve the FVM discretized governing Equations of velocity field and heat transfer. The effect of wall wavelength, amplitude, and volume fraction (VF) of nanoparticles, is investigated at a Rayleigh number of 10000 to find the optimal heat transfer mode. The amplitude varied from 0 to 0.15, the wavelength from 0.25 to 1, and the concentration of nanoparticles is changed from 0 to 0.04. The effect of all three parameters is determined separately by statistical analysis using the signal-to-noise ratio. According to the results, the most important parameter that can affect heat transfer is VF. As the VF increases from 0 to 0.04, the average Nusselt number (Num) increases by about 2.5 times. For example, at amplitude A = 0.05, wavelength B = 0.25, with increasing VF from 0 to 0.04, the null number increases from 35.30086 to 90.4793. In contrast, wall wavelength has the least effect on it. Three steps of −1, 0, and +1 are defined for further investigation of heat transfer. The wavy wall's Num increases with increasing VF and wavelength from step −1 to +1. The surface heat transfer coefficient also shows an increasing trend.

HEAT-TRANSFER BEHAVIORS OF A SLIGHTLY HORIZONTAL VENTILATED ROOF UNDER VARIABLE CLIMATIC CONDITIONS

This paper illustrates a numerical study to evaluate thermal and fluid dynamic behaviors of natural convection inside a slight inclined ventilated roof for residential building in Mediterranean area. The system is studied considering a roof with a length equal to 6.0 m and three different inclinations with respect to the horizontal plane (0°, 2°, 5°). The ventilated channel, under the roof, has a distance between the flat plates equal to 10 cm. A two-dimensional natural convection with surface radiation model is considered assuming a turbulent air flow. Different conditions are applied on the top wall and the bottom wall of the roof to simulate summer and winter conditions. Different values of solar heat fluxes are applied on the top wall of the ventilated cavity together with heat transfer with the external ambient. Along the bottom wall there is a heat transfer toward an internal ambient by means a thermal conductance. The problem is solved by means of the commercial code Ansys-Fluent. Results are given in terms of temperature and pressure distributions, air velocity and temperature profiles. The increase in inclination of the pitched roof determines a better performance of the component. In fact, during the summer, the efficiency of the system improves because the high heat flux produces an optimal air-convective condition into the ventilated channel. In the winter, the effect of the ventilated layer is more significant to fulfill optimal thermal and hygrometric conditions.

Development of unsteady natural convection in a square cavity under large temperature difference

To investigate how the nonuniform fluid density distribution caused by large temperature variations affects the development of unsteady natural convection, we perform a series of direct numerical simulations of two-dimensional compressible natural convection in an air-filled square cavity. The cavity has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The simulations are done using a kinetic approach based on a modeled Boltzmann equation, from which the fully compressible Navier–Stokes–Fourier equations are recovered. No Boussinesq approximation or low Mach number approximation is made. An extra source term is introduced to adjust the fluid Prandtl number. Simulations are performed for a range of Rayleigh numbers (107−109) with a fixed dimensionless temperature difference of ε=0.6 to determine the critical Rayleigh number and study the development of unsteady flow. To illustrate the instability mechanism, instantaneous fluctuation field, time trace of temperature, and velocity at selected monitoring points, the spectrum and other statistics are presented and discussed. As expected, significant differences are observed between the instability of compressible natural convection and the Boussinesq-type natural convection. With a large temperature difference, the transition to unsteady flow is asymmetric for the flows near the hot wall and cold wall. For the Rayleigh number range we studied, the cold wall region is dominated by low-frequency impact instability of the boundary thermal jet at the bottom corner. For the hot wall region, besides the upper corner impact instability, a boundary layer instability featuring high-frequency oscillations is 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.

Classification of Flow Modes for Natural Convection in a Square Enclosure with an Eccentric Circular Cylinder

The present study investigated the natural convection for a hot circular cylinder embedded in a cold square enclosure. The numerical simulations are performed to solve a two-dimensional steady natural convection for three Rayleigh numbers of 103, 104 and 105 at a fixed Prandtl number of 0.7. This study considered the wide range of the inner cylinder positions to identify the eccentric effect of the cylinder on flow and thermal structures. The present study classifies the flow structures according to the cylinder position. Finally, the present study provides the map for the flow structures at each Rayleigh number (Ra). The Ra = 103 and 104 form the four modes of the flow structures. These modes are classified by mainly the large circulation and inner vortices. When Ra = 105, one mode that existed at Ra = 103 and 104, disappears in the map of the flow structures. The new three modes appear, resulting in total six modes of flow structures at Ra = 105. New modes at Ra = 105 are characterized by the top side secondary vortices. The corresponding isotherms are presented to explain the bifurcation of the flow structure.