Natural Convection Fluid Flow Research Articles

Natural Convection Fluid Flow and Heat Transfer in a Valley-Shaped Cavity

The phenomenon of natural convection is the subject of significant research interest due to its widespread occurrence in both natural and industrial contexts. This study focuses on investigating natural convection phenomena within triangular enclosures, specifically emphasizing a valley-shaped configuration. Our research comprehensively analyses unsteady, non-dimensional time-varying convection resulting from natural fluid flow within a valley-shaped cavity, where the inclined walls serve as hot surfaces and the top wall functions as a cold surface. We explore unsteady natural convection flows in this cavity, utilizing air as the operating fluid, considering a range of Rayleigh numbers from Ra = 100 to 108. Additionally, various non-dimensional times τ, spanning from 0 to 5000, are examined, with a fixed Prandtl number (Pr = 0.71) and aspect ratio (A = 0.5). Employing a two-dimensional framework for numerical analysis, our study focuses on identifying unstable flow mechanisms characterized by different non-dimensional times, including symmetric, asymmetric, and unsteady flow patterns. The numerical results reveal that natural convection flows remain steady in the symmetric state for Rayleigh values ranging from 100 to 7 × 103. Asymmetric flow occurs when the Ra surpasses 7 × 103. Under the asymmetric condition, flow arrives in an unsteady stage before stabilizing at the fully formed stage for 7 × 103 < Ra < 107. This study demonstrates that periodic unsteady flows shift into chaotic situations during the transitional stage before transferring to periodic behavior in the developed stage, but the chaotic flow remains predominant in the unsteady regime with larger Rayleigh numbers. Furthermore, we present an analysis of heat transfer within the cavity, discussing and quantifying its dependence on the Rayleigh number.

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

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

Transient natural convection flows and heat transfer in a thermally stratified air-filled trapezoidal cavity

This paper focuses on studying the transient behavior of natural convective heat and fluid flow in a two-dimensional trapezoidal cavity subjected to a heated bottom surface, cooling from the top, and thermally stratified inclined surfaces. The Finite Volume (FV) method is employed to numerically simulate the transient flow. The study considers a thermally stratified environment with a Prandtl number of Pr set to 0.71 (for stratified air), an aspect ratio (A) of 0.5, and a large array of Rayleigh numbers (Ra) ranging from 100 to 108. The research examines how the Rayleigh numbers affect the flow structures, transient phenomena, and heat transfer (HT) characteristics within the cavity. The transitional flow reveals several supercritical bifurcations. These include a changeover from symmetric to asymmetric states known as a Pitchfork bifurcation, as well as a shift from a steady-state to a periodic state referred to as a Hopf bifurcation. The Pitchfork bifurcation happens between Ra values of 105 and 2 × 105, while the Hopf bifurcation happens within the range of the Ra values from 4.7 × 105 to 4.8 × 105. Moreover, another bifurcation from a periodic to a chaotic state is observed between Ra of 3 × 107 and 4 × 107. To examine the transient flows during the changeover to chaos, various techniques such as power spectral density (PSD), limit points, limit cycles, trajectory in phase space, and the largest Lyapunov exponent (LLE) are used. Furthermore, convective heat transfer is computed, and its corresponding impact on the Ra values is explained. The flow phenomena within the cavity are measured and verified.

Effect of discrete heating on the key parameters and entropy generation in a corrugated enclosure filled with hybrid nanofluid

This research work aims to study the effect of discrete heating on natural convective heat transfer, fluid flow, and entropy generation within a corrugated enclosure filled with water-based molybdenum disulfide (MoS2)–silicon dioxide (SiO2) hybrid nanofluid. In the study, various heights of the discrete heaters in terms of aspect ratios ( AR = 0.2 , 0.4 , 0.6 , 0.8 ) are considered for various Rayleigh numbers ( Ra = 10 3 − 10 6 ) with varying nanoparticle volume fractions ( ϕ = 0 % − 4 % ). Stream function-vorticity formulations of two-dimensional (2D) Navier-Stokes equations and energy equation are used as the governing equations, and a higher-order compact (HOC) finite difference scheme is employed to discretize those equations. The results obtained from the current developed code are first validated with the existing numerical and experimental data. Finally, the present computed results are studied, both qualitatively and quantitatively, in terms of streamlines, isotherms, entropy generations, average Nusselt numbers, and Bejan numbers. At Ra = 10 6 and the aspect ratio of heater length AR = 0.2 , a different and interesting flow and heat transfer phenomenon is observed. The results show that an increase in the aspect ratio of heater length from 0.2 to 0.8 decreases the average Nusselt number and total entropy generation by 57.49% and 13.76%, respectively, for Ra = 10 6 and ϕ = 4 % . In addition, the effect of nanoparticle concentration on total entropy generation increases up to 73.40% when the aspect ratio of heater length increases to 0.8.

THERMAL FIELD IN A HORIZONTAL WELL APPLIED TO THE DETERMINATION OF FLUID FLOW BY ACTIVE THERMOMETRY

Today, in the context of falling oil production and increasing water cut, the importance of geophysical control over field development is increasing. A promising method of production logging is active thermometry, it is based on the creation of a thermal disturbance area in the wellbore, for example, due to induction heating of a section of a metal pipe (liner or casing, depending on the design of the well). As a result of heat exchange with a locally heated pipe section, heat marks are formed in the liquid, moving along the wellbore. The article presents the results of physical modeling of thermal processes during local induction heating of a section of a horizontal well. It has been experimentally established that with an induction heater power of about 1 kW and flow rates in the pipe up to 50 m3/day, the heating of the pipe wall reaches 12 K. As part of the experimental studies, the movement of heat marks was monitored using two modules of temperature sensors distributed over the pipe cross section. It is shown that the nature of temperature change in time is determined by the position of the temperature sensor in the pipe section. The greatest thermal anomalies are noted for sensors pressed against the pipe in its upper part, the smallest - for sensors located in the lower part of the pipe. The fluid flow rate in the pipe was estimated from the rate of passage of the heat mark between the temperature modules. It is shown that the calculated flow rate is overestimated relative to the actual one due to the influence of natural thermal convection, which causes the occurrence of a natural convective fluid flow in addition to the forced movement with a given flow rate. A new analytical solution has been obtained for calculating the dynamics of the pipe temperature in the induction heating section, a comparison of the results of calculations using the analytical model with the experimental results showed good agreement. The results of experimental studies can be used in interpreting the results of field logging wells using active thermometry, in particular, the sensitivity of the pipe temperature in the induction heating section to the flow rate can be used to solve inverse problems of estimating the flow rate in a pipe by measuring its surface temperature using the obtained analytical solution.

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.

Natural convective Power law fluid flow in a crown cavity with heated cylinder: Application to energy transfer

The present study investigates heat transfer characteristics of power law fluid flow and energy transfer in a crown cavity with adjustment of the heated cylinder. The flow distribution is generated by the response of the heated cylinder. Additionally, the enclosure is partially adiabatic and the influence of cold interfaces is also taken. This whole setup generates a partial differential system in its mathematical translation. The numerical simulation is performed for the mathematical formulation by adopting the Galerkin Finite element method. The obtained results are analyzed against pertinent parameters of interest and presented via line graphs and contour maps for better explanation. The findings indicate that the K.E (energy motion) and Nu (Nusselt number) are higher for shear thinning While K.E energy motion) and Nu (Nusselt number) are higher is minimum for shear thickening.

Investigation of the heat transfer coefficient for a red clay brick

AbstractThere is a need for the development of materials for thermal isolation. Heat energy is used in different ways, for example, for house warming or production of electricity from solar power plants. However, to use the heat energy efficiently isolating materials are needed. There are different materials available to isolate houses and heat storage containers. However, those materials are expensive and some are over engineered. The best available material for thermal isolation would be air that has the thermal coefficient . Thus, materials that trap a large amount of air are good isolators. On the other hand, some isolating materials are harmful for the environment, for example, glass wool, asbestos. An alternative are red clay bricks because red clay is a natural product that is present everywhere on the planet. But the thermal coefficient of red clay bricks is high . To reduce the thermal coefficient cavities can be added in the brick. The cavities trap air and reduce the thermal coefficient of the brick.We simulate the heat transfer through a hollow brick. The holes in the brick are cavities. In order to determine the heat transfer coefficient we solve the heat flux through the hollow brick. For that a model of the brick is formulated as sequence of a solid and a fluid part. In the solid part only heat conduction is present and in the fluid heat transfer is present in form of conduction, convection and radiation. The flow field in the fluid part is modelled with the velocity‐vorticity formulation of the incompressible Navier‐Stokes. It is assumed that the Rayleigh number is below 106, hence, natural convective laminar fluid flow is present in the cavities. The cavities are also heated by heat radiation of the surrounding walls.The numerical realisation is done with the Boundary‐Domain Integral Method (BDIM). To handle suitable geometries the complexity of the BDIM is reduced from quadratic to logarithmic or almost linear by applying the ‐methodology. M is the number of unknown domain nodes. Numerical studies will be presented.

Natural convective heat transfer and fluid flow in a porous medium filled corrugated enclosure: Effect of discrete heat sources

AbstractIn this work, we investigate the two‐dimensional unsteady natural convective fluid flow problem in a porous‐corrugated enclosure with a fixed sinusoidal heated upper wall. The corrugations of the enclosure are discretely heated while vertical walls are maintained isothermally cold. Subject to where the heat sources are located, five different cases are taken into consideration. The vorticity–streamfunction equations are discretized using a transformation‐free higher order compact approach, and the hybrid BiCGSTAB technique is used to solve the system of algebraic equations that derives from the numerical discretization. To validate our findings, we first compare them to previously published numerical and experimental data. The numerically simulated outcomes are then examined over a variety of essential parameters, such as the Darcy (10−5 ≤ Da ≤ 10−1), Rayleigh (103 ≤ Ra ≤ 106), and Prandtl (0.1 ≤ Pr ≤ 10) numbers. Symmetric and asymmetric fluid flow phenomena are observed. Asymmetric flow phenomenon can be caused by miscible or non‐miscible movements of lighter fluids by heavier fluids, or almost exclusively by nonuniform buoyancy‐driven forces caused by density variations that have arisen because of variations in fluid temperature. The averaged Nusselt value for Case 1 and Case 5 exhibits the highest percentage ratio. The thermal boundary layer is strongly affected by compression, dispersion, suppression, the zone of stratification, and the outweighing of isotherms. The simulated results are visualized by stream functions, isotherms, local and averaged Nusselt number plots.

Numerical Analysis of Heating Technique in Corium Melt Pool Convection Flow Field & Thermal Interaction in a Volumetrically Heated Molten Pool

In-Vessel Retention (IVR) is one of the existing strategies of severe accident management of LWR, which intends to stabilize and isolate corium & fission products inside the reactor pressure vessel (RPV) and primary containment structure. Since it has become an important safety objective for nuclear reactors, it is therefore needed to model and evaluate relevant phenomena of IVR strategy in assessing safety of nuclear power reactors. One of the relevant phenomena during accident progression in the oxidic pool is non-uniform high heat generation occurring at large scale. Consequently, direct experimental studies at these scales are not possible. The role computer codes and models are therefore important in order to transpose experimental results to reactor safety applications. In this paper, the state-of-the-art ANSYS FLUENT CFD code is used to simulate Non-uniform heat generation in the lower plenum by the application of Cartridge heating under severe accident conditions to derive the basic accident scenario. However, very few studies have been performed to simulate non-uniform decay heat generation by Cartridge heaters in a pool corresponding lower plenum of power reactor. The current investigation focuses on non-uniform heating in the fluid domain by Cartridge heaters, which has been done using ANSYS FLUENT CFD code by K-epsilon model. The computed results are based on qualitative assessment in the form of temperature and velocity contour and quantitative assessment in terms of temperature and heat flux distribution to assess the impact of heating method on natural convective fluid flow and heat transfer.

Fluid Flow and Heat Transfer of Natural Convection around Heated Horizontal Square Cylinder —Air Case—

Fluid Flow and Heat Transfer of Natural Convection around Heated Horizontal Square Cylinder —Air Case—

Machine Learning based algorithms for modeling natural convection fluid flow and heat and mass transfer in rectangular cavities filled with non-Newtonian fluids

The importance of studying double-diffusive fluid flows along with the significance of non-Newtonian fluids have been well recognized in the fluid dynamics field for scientific and practical purposes. However, and given the ever-rising complexity of such non-linear flows, the conventional simulation methods are confronted with problems related to accuracy and required computation time and resources. As a result, the Machine Learning approach qualifies as a promising solution to said limitations. The present study investigates the application of Machine Learning models to study double-diffusive natural convection in rectangular cavities filled with non-Newtonian fluids. The flow is governed by four dimensionless parameters, namely: thermal Rayleigh number RaT, Lewis number Le, buoyancy ratio N, and power-law behavior index n, employed as input features. To precisely model fluid flow, three characteristics are predicted: flow intensity |ψc|, average Nusselt number Nu¯, and average Sherwood number Sh¯ using four machine learning models: Artificial Neural Networks (ANN), Random Forests (RF), Gradient Boosted Decision Trees (GBDT), and Extreme Gradient Boosting (XGBoost). The analysis of investigated models’ fine-tuned architectures using various tools confirms the non-linear complexity of the problem and allows to explore and discuss in details the inner-workings of each model. The ANN predicts the test data with R2=0.9999,R2=0.9996, and R2=0.9999 followed by XGBoost with R2=0.9979,R2=0.9802, and R2=0.9979, and that for |ψc|, Nu¯, and Sh¯, respectively. The study shows the strong and correlated effects of RaT and n on the flow characteristics. The models’ generalization is further examined using fluids with power-law behavior indexes outside the learning range. The present paper validates the choice of Machine Learning approach as a promising solution to model non-Newtonian double-diffusive fluid flows and encourages future works in this direction.

Transient natural convective heat transfer and fluid flow in an undulated cavity: Effects of localized heat sources

AbstractThe purpose of this research work is to investigate two‐dimensional transient natural convective heat transfer and fluid flows in an undulated cavity by placing solid objects with isolated heated surfaces on the bottom wall. We discretize the coupled nonlinear transport equations using a higher‐order compact finite‐difference scheme. First, we test our scheme using existing experimental and numerical data. Then, we analyze the transient and steady‐state natural convective flow phenomena for distributed heat sources on corrugations on the lower wall for a range of the Rayleigh number and Prandtl number . These simulated outcomes are presented in the form of central‐line velocity , local and averaged Nusselt numbers, streamlines , dispersion of isotherms , and so forth. It is found that the transient fluid flow behavior is more magnificent than the steady‐state solutions and shows the dominant behavior of the prominent primary cells over secondary cells, where it influences the heat transfer rates inside the entire enclosure. In steady states, at high Rayleigh numbers; convection dominates, formation of thermal boundary layers, compression of isotherms, and stratification of isotherms are significantly observed. Our results show many interesting flow phenomena that have not been analyzed previously.

Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

AbstractThe article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left‐inclined, right‐inclined, L‐shaped, wavy, corrugated, and square‐wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full‐length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom‐wall and top‐wall attached conditions. Some of the notable findings are that for smaller‐sized partitions (B < 0.5), L‐shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger‐sized partitions (L > 0.5), square‐wave‐shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.

Time‐dependent natural convection fluid flow of stably stratified fluid in an asymmetrically heated vertical channel filled with an anisotropic porous material

AbstractThis paper presents a theoretical analysis of the combined effects of anisotropic porous material and thermal stratification on the transient natural convection fluid flow in an asymmetrically heated vertical parallel channel. The solutions of the governing equations for the temperature and velocity fields are obtained using Laplace transform technique, Riemann sum approximation, and the D'Alembert method. The choice of the D'Alembert method is to provide a simple decoupling procedure for the coupled governing equations while still retaining their original orders. The research established that owing to the layering effect induced by the thermal stratification , the temperature and the velocity distributions of the fluid are found to be attenuated with an increase in thermal stratification. It is also observed that the inclusion of anisotropic parameters in the transport equations aids in regulating the fluid velocity, temperature, Nusselt number, skin friction, and mass flow rate. In addition, by neglecting the anisotropic parameter and taking into account the adiabatic stratification of the fluid, the numerical values for the mass flow rate of the present research favorably compared with the numerical results obtained by Singh et al.

Exploring the dynamics of natural convective Prandtl fluid flow subjected to induced magnetic field

In the present study, Prandtl fluid flows naturally under the action of buoyancy in a vertical microchannel. The channel proliferates the fluid to the surrounding through small pores in the channel. Fluid flow properties are explored and heat transfer analysis is carried out theoretically via mathematical modeling using fluid dynamic conservative laws. Magnetohydrodynamics effect is also made a part of the study so that the induced magnetic field impact can be investigated. The mathematical form of the conservative laws leads to a differential system nonlinear in nature. The complexity of the mathematical system demands its solution to be carried out numerically. For this purpose, the finite difference-based Keller box method is utilized. Interpretation of the results is carried out in the form of graphs and tables of numerical values of the skin friction coefficient and the Nusselt number. The results show that the Prandtl number coupled with the suction velocity parameter results in an exponential growth in the heat transfer rate in Prandtl fluid. Graphical representations confirm the fact that skin friction coefficient peaks when the value of Hartmann number is minimum and that of Grashof number is maximum.

Natural convection heat transfer and fluid flow in a thermal chimney with multiple horizontally-aligned cylinders

To address the scarcity of natural convection research for the tube array with three or more columns of horizontally-aligned cylinders, this paper conducts RANS/URANS simulations for multiple cylinder columns in one or two rows, validated by particle-image velocimetry and heat transfer measurements. Parametric study with varying horizontal and vertical pitches is implemented by RANS with transition SST model. Key findings are then substantiated and examined by URANS. It is found that the horizontal pitch influences the balance between the chimney effect and the blockage effect, thus has an optimum with respect to the natural draft velocity. For all the vertical distances computed in the two-row thermal chimney model, the flow pattern stays in a plume-dominant mode at the large horizontal pitch and a chimney-dominant mode at the small horizontal pitch. Interestingly, at the intermediate horizontal pitch (pitch/diameter≈2.5), the flow pattern switches from plume-dominant to chimney-dominant over a minor increase of the vertical pitch (from 4.5 to 6 diameters), leading to significant augmentation in natural draft velocity and heat transfer on cylinder surfaces. This distinct thermo-flow behavior, identified for the first time to the authors’ knowledge, may be harnessed to improve the performance of passive heat exchangers.

Natural convection phenomena in a liquid metal pool due to relocated and heap of heat-generating core debris: Numerical study

In the present numerical study, authors have investigated the natural convection heat transfer and fluid flow characteristics in a pool due to the heat generating core debris, i.e. decay heat in a typical fast breeder reactor. Two significant aspects of decay heat removal from debris under core disruptive accidents have been analyzed. These key aspects are (i) relocation of heat-generating core debris at the different locations inside the main vessel and (ii) effect of debris heap on heat transfer from source to ambient. These cases are analyzed extensively on full-scale three-dimensional reactor model with all major components. Multiple tray-type core catcher has incorporated with passive pipes over one collection tray. The present numerical study provides a robust and practical feasible core debris retention arrangement after a severe accident in fast breeder reactors. Also, the study is focused on a feasible array of core collection trays that maintained heat-generating debris and heat shield trays under safe thermal designed limit (∼1200 K for debris and ∼ 923 K for trays). This eliminates the further advancement of accidents and leakage of radioactive material into environments. During our analysis, it has been found that single tray with passive pipes maintained the heat-generating debris and tray under safe thermal limit for a fraction of 50 % destroyed core relocated to lower plenum while remaining heat-generating debris is present in its original position. Multiple tray arrangements accommodate the whole core debris within safe thermal design limits. With the possibility of debris heap after its relocation to the lower plenum, it has been found that heap angle less than 3° does not affect the integrity of core catcher.

Study of special types of boundary layer natural convection flow problems through the clique polynomial method

AbstractThis study proposed a new novel approach called the clique polynomial method (CPM) and applied it to the system of highly nonlinear ordinary differential equations (ODEs) associated with different cases of boundary layer natural convection fluid flow problems. Here, three specific problems are considered: (1) laminar film condensation of a fluid‐saturated flow with isothermal vertical plate; (2) natural convection boundary layer fluid flow; and (3) heat transfer boundary layer flow due to a stretching sheet. CPM results, which do not need small parameters, are compared with numerical results, and the outcomes are established to be in good agreement. The CPM is hugely proficient and a sensible choice for finding outcomes to this type of coupled nonlinear ODEs. The work is in outstanding accord for coupled nonlinear ODEs in engineering applications.

Numerical simulation on double diffusion natural convection of a power-law nanofluid within double wavy cavity

In the present paper, the effect of double diffusion natural convection fluid flow inside the double wavy enclosure using the mesh-free method is investigated. The enclosure is filled with nanofluid whose base fluid is non-Newtonian. The results are obtained for the variation in Brownian motion parameter (0.2–0.8), buoyancy ratio parameter (0.2–1), power-law index (0.2–1), thermophoresis parameter (0.2–0.8), Rayleigh number (103–105), and Lewis number (1–5) on mass and heat transfer. It is explored that the mass and heat transfer rate increases with increase in the Rayleigh number and buoyancy ratio. Heat transfer rate decreases with increase in the thermophoresis parameter, Lewis number, Brownian motion, and power-law index, whereas mass transfer rate increases. Such type of enclosure has direct application in heat exchanger devices, the double-wall thermal insulation system, and microelectronic devices. Parallel implementation with the hybrid [EFGM (element free Galerkin method)/FEM (finite element method)] method has been used for the reduction of the running cost to ensure efficiency, which is the novel contribution of the author.