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This study investigates the computational analysis of steady, incompressible, natural convection airflow in a 2D equilateral triangular cavity featuring two stationary cold circular cylinders. The convective phenomena within the cavity have been observed under the variation of uniform porosity. The convective flow has been modeled using the Darcy-Brinkman formulations for porous medium incorporated with the Boussinesq approximation. The governing equations have been simulated using the finite element method with non-uniform triangular meshing. The investigation was conducted with a fixed Prandtl number, Pr = 0.71, and different porosity by varying Darcy number, Da = 10-5 to 10-2. The convective strength has been varied with the Rayleigh number, Ra= 10³ to 106, and the length of the heated and cold segment, ε = 0.1 to 0.9. Results regarding the fluid flow and temperature distribution are visualized through streamlines and isotherms. The quantity and the quality of heat transfer (HT) have been investigated, respectively, by the Nusselt number (Nu) and the entropy generation (Egen). The results reveal that an increase in the length of the hot wall (ε) significantly reduces HT. Also, Egen increases with the length of active segments (ε), while the Bejan number (Be) consistently rises when the Darcy-Rayleigh (Da-Ra) number increases, i.e., Da-Ra ≥ 10². The maximum HT rate was obtained within the range of Da = 10-5 to 10-3 for a constant value of ε. Furthermore, the maximum HT was obtained for the smallest value ε for any value of Da or Ra. [ABSTRACT FROM AUTHOR]

In cold climates or winter countries, maintaining optimal room temperatures is essential for comfort and energy efficiency. Conventional square or rectangle‐shaped rooms often face challenges in achieving efficient heat transfer (HT) and uniform temperature distribution. To address these limitations, this study has been explored using curved corner cavities, varying their aspect ratio (AR = 1.0 and 0.5), and incorporating a circular shape cooler to enhance HT within the room. The curved corners promote better airflow circulation, creating a more efficient HT environment. The dimensionless governing equations and corresponding boundary conditions are solved numerically using the finite element method. This research aims to assess the optimized HT and entropy production within a curved corner cavity, varying their AR and enclosing a circular shape cooler to determine the most effective configuration for maximizing HT and energy efficiency in winter conditions. This study reveals that in the case without a cooler (WOC), the average Nusselt number (Nuavg $N{u}_{avg}$) is higher in the curved rectangle cavity compared with the curved square cavity for all Ra $Ra$ values. Using the curved square (AR = 1.0), Nuavg $N{u}_{avg}$ increases by 191.86%, while with the curved rectangle (AR = 0.5), Nuavg $N{u}_{avg}$ increases by 302.63% at Ra=106 $Ra=1{0}^{6}$. Additionally, in the case with a cooler (WC), Nuavg $N{u}_{avg}$ is higher than the case WOC and Nuavg $N{u}_{avg}$, and an average total entropy (Enavg) $(E{n}_{avg})$ increases for both the WOC and WC cases for all Ra $Ra$ values. Transitioning from a square to a curved rectangle (AR = 0.5) WC, Nuavg $N{u}_{avg}$ increases by 329.34% at Ra=106 $Ra=1{0}^{6}$. Furthermore, in the WOC case, the curved square cavity and, in the WC case, the curved rectangle show better energy efficiency and reduce environmental impact. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 103 to 106, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth‐shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency. [ABSTRACT FROM AUTHOR]

Numerical simulations have been performed to investigate the influence of constant volumetric heat generation and viscous dissipation on the unsteady natural convection flow of an incompressible Newtonian fluid contained in a rectangular cavity. The left vertical wall of the cavity is cooled, while the right vertical wall is heated, and the bottom and top walls are adiabatic. A numerical technique based on the implicit finite difference method (IFDM), along with an upwind finite difference scheme and an iterative successive over relaxation (SOR) technique, is employed to solve the governing equations numerically. The effect of physical parameters, namely the modified Rayleigh number ( 10 3 ≤ R a ≤ 10 7 ), aspect ratio ( 1 ≤ A ≤ 4 ), Prandtl number ( P r = 0.7 , 1.0 , 6.2 , 15), volumetric internal heat generation parameter ( Q λ = 0 , 1), and Eckert number ( 0 ≤ E c ≤ 10 − 6 ), on the streamlines and isotherms are discussed graphically. Variations of maximum stream function, as well as average and local Nusselt number, are also discussed. The results show that the increase in Eckert number from 0 to 10 − 4 causes the average heat transfer to decrease, while P r = 0.71 , R a = 10 4 , and Q λ = 0 . Additionally, the average heat transfer decreases as the cavity width increases from 1 to 4, while P r = 0.71 , R a = 5 × 10 4 , E c = 10 − 6 and Q λ = 1 . The results of the numerical model used here are in excellent accord with earlier findings. [ABSTRACT FROM AUTHOR]

Numerical findings of natural convection flows in a trapezoidal cavity are reported in this study. This study focuses on the shift from symmetric steady to chaotic flow within the cavity. This cavity has a heated bottom wall, a cooled top wall, and adiabatic inclined sidewalls. The unsteady natural convection flows occurring within the cavity are numerically simulated using the finite volume (FV) method. The fluid used in the study is air, and the calculations are performed for different dimensionless parameters, including the Prandtl number (Pr), which is kept constant at 0.71, while varying the Rayleigh numbers (Ra) from 100 to 108 and using a fixed aspect ratio (AR) of 0.5. This study focuses on the effect of the Rayleigh numbers on the transition to chaos. In the transition to chaos, a number of bifurcations occur. The first primary transition is found from the steady symmetric to the steady asymmetric stage, known as a pitchfork bifurcation. The second leading transition is found from a steady asymmetric to an unsteady periodic stage, known as Hopf bifurcation. Another prominent bifurcation happens on the changeover of the unsteady flow from the periodic to the chaotic stage. The attractor bifurcates from a stable fixed point to a limit cycle for the Rayleigh numbers between 4 × 106 and 5 × 106. A spectral analysis and the largest Lyapunov exponents are analyzed to investigate the natural convection flows during the shift from periodic to chaos. Moreover, the cavity's heat transfers are computed for various regimes. The cavity's flow phenomena are measured and verified. [ABSTRACT FROM AUTHOR]

In this study, we numerically investigate heat transfer enhancement in a partially thermally active rectangular enclosure. The enclosure is filled with a ternary hybrid nanofluid (water, Carbon Nanotube, A l 2 O 3 , and Graphene). It is subjected to a magnetic field and uniform internal heat generation. The study also investigates the effect of magnetic field strength and direction on the natural convection flow, which arises from density fluctuations caused by partial heating of the left vertical wall. To solve the dimensionless governing equations, the finite element approach is employed. The parameters studied in detail include Rayleigh number (R a) , Hartmann number (H a) , nanoparticle volume fraction (ϕ) , and heat generation coefficient (λ). The findings are presented graphically for the range of the parameters as follows: 10 3 ≤ R a   ≤ 10 6 ,   0 ≤ H a ≤ 20 , 0.01 ≤ ϕ ≤ 0.05 , and 0 ≤ λ ≤ 15 . It is noted that these parameters have an impact on heat transfer enhancement, flow patterns, and temperature fields. The results show that the average Nusselt number ( N u ¯ ) increases with an increasing value of ϕ . Moreover, it has been noted that N u ¯ decreases as the value of H a increases, and the impact becomes more obvious at higher R a values. Finally, the influence of the heat generation coefficient on the heat transfer rate inside an enclosure is examined. [ABSTRACT FROM AUTHOR]

The mixed convection and heat transfer in enclosures with inner heat sources widely exist in building ventilation, cooling of nuclear reactors and cooling of electronic components. In this study, the heat transfer characteristics of mixed convection in an open arc-shaped cavity with double heat sources under the condition of bottom heating and top wall cooling are studied by two-dimensional numerical simulation using ANSYS FLUENT. The influence of the Reynolds number on flow structures, transient characteristics and heat transfer characteristics in the arc cavity was studied by changing inlet wind speed. As the Reynolds number changes from 2.19 × 105 to 4.38 × 107, the flow in the fully developed stage will evolve from turbulent flow to periodic flow and then to steady state flow. In this study, the critical Reynolds number intervals for three different flow states are given. The increase in the Reynolds number enhances the heat convection in the cavity. The difference between heat convection and heat conduction is increased, which has a linear relationship with the Reynolds number. As the Reynolds number increases, the heat removal capacity in the middle region of the double heat sources is not always enhanced, which is due to the sudden change in flow structure and flow state around Re = 1.18 × 107. [ABSTRACT FROM AUTHOR]

The transitional free convection flow and heat transfer within attics in cold climate are investigated using 3-D numerical simulations for a range of Rayleigh numbers from 103 to 106 and height-length ratios from 0.1 to 1.5. The development process of free convection in the attic could be classified into three-stages: an initial stage, a transitional stage, and a fully developed stage. Flow structures in different stages including transverse and longitudinal rolls are critically analyzed in terms of the location and strength of convection rolls and their impacts on the heat transfer. The transition unsteady flow and asymmetry flow in the fully developed stage is discussed for the fixed height-length ratio 0.5. Various flow regimes are given in a bifurcation diagram in the parameter space of Rayleigh numbers (10² < Ra < 107) for heightlength ratios (0.1 < A < 1.5). The time series of heat transfer rate through the bottom wall is quantified for different height-length ratios. The overall heat transfer rate for the low Prandtl fluid (Pr = 0.7) could be enhanced based on 3-D flow structure. [ABSTRACT FROM AUTHOR]

Natural convection is intensively explored, especially in a valley-shaped trapezoidal enclosure, because of its broad presence in both technical settings and nature. This study deals with a trapezoidal cavity, which is initially filled with linearly stratified air. Although the sidewalls remain adiabatic, the bottom wall is heated, and the top wall is cooled. For the stratified fluid (air), the temperature of the fluid adjacent to the top and the bottom walls is the same as that of the walls. Natural convection in the trapezoidal cavity is simulated in two dimensions using numerical simulations, by varying Rayleigh numbers (Ra) from 100 to 108 with constant Prandtl number, Pr = 0.71, and aspect ratio, A = 0.5. The numerical results demonstrate that the development of natural convection from the beginning is dependent on the Rayleigh numbers. According to numerical results, the development of transient flow within the enclosure owing to the predefined conditions for the boundary may be categorized into three distinct stages: early, transitional, and steady or unsteady. The flow characteristics at each of the three phases and the impact of the Rayleigh number on the flow's growth are quantified. Unsteady natural convection flows in the enclosure are described and validated by numerical results. In addition, heat transfer through the bottom and the top surfaces is described in this study. [ABSTRACT FROM AUTHOR]

Natural convection in a V-shaped section cavity heated from below and cooled from above is investigated experimentally for the first time in the literature. Temperature measurements using fast-response thermistors and flow visualization using the shadowgraph technology have been performed. The natural convection development in the cavity including the conductional, the transitional, and the fully developed stages is described. It is experimentally proven that the scaling law of the thermal boundary layer thickness is δT ∼ (κt)1/2 and the scaling law of the plume velocity is vp ∼ κRa7/15/l. Furthermore, the occurrence of Hopf bifurcation in the transition to chaos and the flow structure are also identified experimentally. The power spectral density of the temperature time series reveals that the dominant frequency of the oscillations of the unsteady flow depends on the Rayleigh number, which is quantified. [ABSTRACT FROM AUTHOR]

Conjugate natural convection heat transfer inside a differentially heated square cavity having a heat conducting and sinusoidal corrugated solid partition has been investigated numerically in the present study. The fluid flow and the heat transfer within the cavity are governed by two-dimensional Navier–Stokes and energy equations, and those are solved using the finite element method. Numerical simulation is carried out for a wide range of Rayleigh number (103 ≤ Ra ≤ 109) with a fixed Prandtl number (Pr = 0.71) since the working fluid in the cavity is considered as air. The variations of both corrugation amplitude and corrugation frequency of the sinusoidal partition wall on the average Nusselt number of the heated wall are observed in order to assess the influence of the roughness of the solid partition on the heat transfer characteristics of the cavity. Moreover, different types of partition material are selected to scrutinize the effect of thermal conductivity of the solid partition on the heat transfer performance. Finally, a correlation is proposed to predict the average Nusselt number of the heated wall of the cavity from the governing parameters (such as Rayleigh number, corrugation frequency and thermal conductivity ratio) within the selected range of the present investigation. [ABSTRACT FROM AUTHOR]

Highlights • A numerical model deals with heat transfer and air flow in a V-shaped enclosure. • Transition to a chaotic flow is presented in details based on Rayleigh number. • The Lyapunov exponent of periodic and chaotic flows have been described. • The power spectral density and the phase space trajectory are also presented. Abstract Natural convection in a V-shaped cavity heated from below and cooled from top is investigated owing to its extensive presence in industrial systems and in nature such as in a valley. Two dimensional numerical simulation is performed for natural convection in the cavity using a Finite Volume Method. A wide range of Rayleigh numbers of Ra = 100 to 108 for the aspect ratio of A = 0.5 and the Prandtl number of Pr = 0.71 is considered. A set of supercritical bifurcations in a transition to a chaotic flow are described, which include a Pitchfork bifurcation from symmetric to asymmetric state and a Hopf bifurcation from steady to unsteady state. It is found that the Pitchfork bifurcation occurs between Ra = 7.5 × 103 and 7.6 × 103 and the Hopf bifurcation occurs between Ra = 1.5 × 107 and 1.6 × 107. Additionally, a further bifurcation from periodic to chaotic state occurs between Ra = 5 × 107 and 6 × 107. The power spectral density, the phase space trajectory and the largest Lyapunov exponent of unsteady flows in the transition to a chaotic state have been described. Further, heat transfer in the cavity is calculated and the corresponding dependence on the Rayleigh number is discussed and quantified. [ABSTRACT FROM AUTHOR]

Natural convection from a duct into the quiescent ambient is investigated. Heat transfer and dynamics of natural convection from the duct are discussed using a simple scaling analysis and the corresponding scaling relations are obtained. Additionally, numerical simulation for a wide range of Rayleigh numbers from 100 to 106 and the duct aspect ratios from 0 to 4 with the Prandtl number of 0.71 (air) is performed. The development of natural convection may approach a steady or an unsteady state in a fully developed stage, which is determined by the Rayleigh number and the duct aspect ratio. It is demonstrated that heat transfer of natural convection is improved by the duct for high Rayleigh numbers but depressed for low Rayleigh numbers. The scaling relations of natural convection from the duct have been validated in comparison with numerical results. The scaling predictions are consistent with the numerical results. Furthermore, the formulae of the Nusselt number, the Reynolds number, and the flow rate quantifying natural convection from the duct are presented. [ABSTRACT FROM AUTHOR]

Natural convection within an attic space under diurnal temperature condition on the sloping wall and a heat source located on the insulated bottom wall have been studied to show the basic flow features in the attic space over diurnal cycles. The finite volume numerical method has been employed to solve the governing equations. Effect of Rayleigh number ( Ra ), attic aspect ratio, heater location and its size are discussed on the transient flow pattern and heat transfer phenomenon after grid independency and time interval selection tests with a fixed prandtl number of 0.72 (air). Results are presented as a form of isotherms and streamlines. Also, heat transfer is presented as a form of Nusselt number. The numerical experiments show that, the flow in the attic space is stratified during the daytime heating stage; whereas the flow becomes unstable at the night-time cooling stage. [ABSTRACT FROM AUTHOR]

Numerical investigation of free convection heat transfer in an attic shaped enclosure with differentially heated two inclined walls and filled with air is performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is uniformly cooled. There is a heat source placed on the right side of the bottom surface. Rest of the bottom surface is kept as adiabatic. Finite volume based commercial software ANSYS 15 (Fluent) is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 10 3 to 10 6 , heater size from 0.2 to 0.6, heater position from 0.3 to 0.7 and aspect ratio from 0.2 to 1.0 with a fixed Prandtl number of 0.72. Outcomes have been reported in terms of temperature and stream function contours and local Nusselt number for various Ra , heater size, heater position, and aspect ratio. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement. [ABSTRACT FROM AUTHOR]

The transition from a steady to an unsteady flow induced by an adiabatic fin on the sidewall of a differentially heated air-filled cavity is numerically investigated. Numerical simulations have been performed over the range of Rayleigh numbers from Ra=105–109. The temporal development and spatial structures of natural convection flows in the cavity with a fin are described. It has been demonstrated that the fin may induce the transition to an unsteady flow and the critical Rayleigh number for the occurrence of the transition is between 3.72×106 and 3.73×106. Furthermore, the peak frequencies of the oscillations triggered by different mechanisms are obtained through spectral analysis. It has been found that the flow rate through the cavity with a fin is larger than that without a fin under the unsteady flow, indicating that the fin may improve the unsteady flow in the cavity. [ABSTRACT FROM AUTHOR]

Abstract: Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 105 to 108 with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq’s approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency. [Copyright &y& Elsevier]

Abstract: A scaling analysis is performed for the transient boundary layer established adjacent to an inclined flat plate following a ramp cooling boundary condition. The imposed wall temperature decreases linearly up to a specific value over a specific time. It is revealed that if the ramp time is sufficiently large then the boundary layer reaches quasi-steady mode before the growth of the temperature is finished. However, if the ramp time is shorter then the steady state of the boundary layer may be reached after the growth of the temperature is completed. In this case, the ultimate steady state is the same as if the start up had been instantaneous. Note that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh–Bénard instability if the Rayleigh number exceeds a certain critical value for this cooling case. The onset of instability may set in at different stages of the boundary layer development. A proper identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is presented in this study. Different flow regimes based on the stability of the boundary layer have also been discussed with numerical results. [ABSTRACT FROM AUTHOR]

Abstract: The heat transfer through the attics of buildings under realistic thermal forcing has been considered in this study. A periodic temperature boundary condition is applied on the sloping walls of the attic to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution is seen for relatively low Rayleigh numbers. However, as the Ra gradually increases, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage. [ABSTRACT FROM AUTHOR]

Abstract: The natural convection thermal boundary-layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary-layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady-state time, the layer reaches a quasi-steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating. [Copyright &y& Elsevier]

Abstract Free convection studies in a section-triangular prismatic enclosure with different aspect ratios (depth-width ratios, A) is conducted using three-dimensional numerical modeling approach. The Rayleigh number (Ra) covers a broad range from 100 to 107. Transient free convection is characterized under top cooled and bottom heated boundary conditions. The flow structure of transverse rolls and longitudinal rolls is described. The critical Rayleigh numbers for the transition of the flow from driven by the baroclinic to Rayleigh-Bénard instability and from a steady to an unsteady state have been obtained for different aspect ratios. Free convection in the section-triangular prismatic enclosure could be divided into three regimes, which are presented in a Ra-A space. The quantitative relationship between heat transfer and the aspect ratio as well as the Rayleigh number has been obtained numerically. [ABSTRACT FROM AUTHOR]

The transition to a chaotic plume from a two-dimensional (2D) open cavity heated from below has been investigated using numerical simulation. A large range of Rayleigh numbers (Ra) pertaining to an aspect ratio of A = 1, and Prandtl number (Pr) of Pr = 0.71 (air) is numerically investigated. It is shown that there exists a complex transition of the plume from a steady reflection symmetry to a chaotic flow with a sequence of bifurcations. As the Rayleigh number increases, the plume from the open cavity undergoes a supercritical pitchfork bifurcation from a steady reflection symmetry to a steady reflection asymmetry flow. Once the Rayleigh number exceeds 7 × 10 3 , the plume appears as a distinct flapping namely, a Hopf bifurcation, and then as a distinct puffing. The chaotic plume has the possibility to exhibit an alternate appearance of flapping and puffing in the event the Rayleigh number exceeds 8 × 10 4 . Moreover, the dynamics of the plume from the open cavity is discussed, and the dependence on the Rayleigh number of heat and mass transfer of the plume from the open cavity is quantified. [ABSTRACT FROM AUTHOR]

Flows and heat transfer of the transition to an unsteady state in a finned cavity are studied for Prandtl numbers ( Pr ) from 0.1 to 100 and Rayleigh numbers ( Ra ) from 10 7 to 10 10 . Transient flows are described in the finned cavity. Critical Rayleigh numbers of the transition to an unsteady state are obtained for different Prandtl numbers and the relation between two dimensionless parameters is given. The spectral analysis is applied for the oscillations of unsteady flows and the dominant frequency dependent on governing parameters is presented. Heat transfer of the transition to an unsteady flow is quantified and the corresponding relations dependent on the Prandtl number and Rayleigh number are gained. It is demonstrated that the flow rate and the Nusselt number of the finned cavity significantly increase due to the presentence of the fin, which depend on the Prandtl number and the Rayleigh number. [ABSTRACT FROM AUTHOR]

Natural convection in a prismatic enclosure of triangular section with the top cooling and the bottom heating is investigated using three dimensional (3D) numerical simulations for a wide range of Rayleigh numbers from 10 0 to 1.25 × 10 6 . The numerical result has been compared with the experiment. The development of natural convection flows in the cavity following sudden heating and cooling involves three stages: an initial stage, a transitional stage and a fully developed stage. Transition to unsteady natural convection flow in the fully developed stage, dependent on the Rayleigh number, is described. The flow structure including transversal and longitudinal rolls is characterized and the corresponding mechanism is discussed. The critical Rayleigh number for the transition to unsteady natural convection flow is obtained. The dependence of heat transfer on the Rayleigh number is quantified. [ABSTRACT FROM AUTHOR]

• An increase of 57.1% heat transfer rate modulator is observed from re = 100 to re = 103. • The modulator best serves its purpose at the lowest ra and the highest re. • The effect of blade number on the thermal performance improvement is trivial. • Thermal effectiveness and storage capacity have inverse relationship with each other. The transient analysis of the thermal response and frictional loss characteristics for flow-modulated conjugate heat transfer phenomena has been investigated in the present study. The flow domain is a partitioned cavity of a hexagonal structure equipped with a multi-blade flow modulator. The clockwise rotating blade is adiabatic and stirrers the internal flow along with the natural convection caused by the bottom heated floor of uniform heat flux. The conjugate behavior is introduced through the solid subdomains consisting of two brick-made partitions and one glass partition of uniform thickness. The material of the partition wall reflects the physical aspects of industrial applications. The two-dimensional unsteady continuity, momentum, and energy equations are expressed in a non-dimensional form where the buoyant force is modeled through the Boussinesq approximation. The Arbitrary Lagrangian Euler (ALE) finite element is adopted to solve the moving mesh problem by formulating a free triangular discretization scheme. Parametric computational investigations are carried out for air as the working fluid (Pr = 0.71) and 3 different configurations of the rotating modulator while varying the other parameters, i.e., Reynolds number (Re) and Rayleigh number (Ra) for a fixed Biot number (Bi = 104). This dynamic mesh problem encompasses a wide range of parameters, i.e., (100 ≤ Re ≤ 103), and (104 ≤ Ra ≤ 106) for Bi = 104 to evaluate the thermodynamic response of the present thermo-fluid system. Various thermo-fluid system responses are visualized through the spatially average Nusselt number evaluated on the heated surface, system effectiveness, average thermal storage capacity, and frictional power loss of the flow domain. The thermal response is fragmented into individual responses in terms of component signal frequency by the Fast Fourier Transform (FFT) analysis. According to the current analysis, increasing the number of blades increases the rate of heat transfer by a negligible amount. On the other hand, among three different types of modulators, the three-blade modulator shows the lowest power loss coefficient and the lowest power instability. Thus, a three-blade modulator qualifies as the optimum design to impart external motion to the working fluid to introduce forced convection. This research has some scope for improvement. Future studies can be conducted on the improvement of blade designs, thickness, and size of the blades. The present study can shed light on the modeling of a better storage system where heat transfer and moisture control are integrated for the proper functioning of the storage, such as food storage, cold storage, garment inventory, etc. This study is original, and no previous research has been conducted considering the hexagonal domain and variation of the number of blades. The present study reveals that a modulator best serves its purpose at low Rayleigh and high Reynolds numbers. Moreover, the three-blade modulator has the lowest power loss coefficient and lowest power instability, making it the most suitable modulator to impart external excitation to the working fluid. [ABSTRACT FROM AUTHOR]

– Forced convection heat transfer in a cavity is of great importance due to its strong relevance to the practical aspects. Most of the studies focus on this topic from a steady perspective. But adding a flow modulator enhances a system's thermodynamic performance and makes such a system more realistic and widens the field of application. Such studies are unsteady and often quite expensive. As a result, only a few literatures are available with very idealistic geometric configuration and boundary conditions. – Two-dimensional unsteady continuity, momentum and energy equations are used for the mathematical modeling of the problem incorporating the Boussinesq approximation. A free triangular discretization scheme is adopted to solve the moving mesh problem by formulating the Arbitrary Lagrangian Euler (ALE) finite element approach. – Numerical studies are carried out for a fixed Prandtl number (Pr = 0.71) and fixed geometry of the rotating blade while varying the other parameters i.e. Rayleigh number, Reynolds number and Biot number. This dynamic boundary problem encompasses a wide range of parameters i.e. (100 ≤ Re ≤ 103), (103 ≤ Bi ≤ 104) and (104 ≤ Ra ≤ 107) to evaluate the thermodynamic behavior of the thermo-fluid system. External flow condition is taken into consideration in terms of Biot number. Effects of these parameters are visualized through streamlines, heatlines, spatially average Nusselt number evaluated on the heated surface and system effectiveness. – Present computational study focuses on the transient analysis of the conjugate forced convection flow and heat transfer characteristics in a hexagonal, air filled cavity. This cavity is equipped with a floor heater of constant heat flux under the rotational influence of an adiabatic flow modulator. And the blade is placed in the central position of the cavity which is rotating in the clockwise direction. Also, the whole computational domain is composed of four different domains, one convective domain and three solid domains. The solid domains are made of brick and glass as per their practical aspects. – A Fast Fourier Transform (FFT) analysis is presented to comprehend the thermo-oscillating system response. FFT plots indicate that for all of the cases the fundamental frequency of the system response conforms to the blade frequency. Moreover, present numerical results show that the heat transfer effectiveness has an inverse relationship with the Biot and Rayleigh numbers while improves significantly with the increase of Reynolds number and reaches a critical state for Re cr = 650. Higher Reynolds number also attenuates the degree of power spectrum. – To attain a higher heat transfer effectiveness the thermo – fluid system should be operated at low Rayleigh number with higher Reynolds number. [ABSTRACT FROM AUTHOR]

Fog is omnipresent in the natural environment, namely valleys and mountains. A strong comprehension of the fluid flow dynamics pertaining to fog formation is of crucial importance. In the present study, the two-dimensional numerical method is used to investigate the transient natural convection in a valley-shaped triangular cavity initially filled with stratified water. A wide range of Rayleigh numbers (2.26 × 10 5 –2.26 × 10 9 ) and aspect ratios (0.1–1.0) are considered. The numerical results are verified against experimental results. The development of natural convection flows in the cavity from the start up to the steady state is classified into two stages: an early stage and a transitional stage. Transient natural convection flows in the cavity are described. Spectral analysis is performed for different governing parameters. A simple scaling analysis is performed for the thermal boundary layer and the time scale of the stratification breakup describing the disappearance of fog in the valley is obtained and validated by numerical results. Additionally, mass and heat transfer in the cavity is measured and the scaling relation between the Nusselt number and the Rayleigh number for different aspect ratios are presented. [ABSTRACT FROM AUTHOR]

In this study magneto-hydrodynamic convection in a half-moon shaped cavity filled with ferrofluid has been analyzed numerically. The cavity has two semi-circular bottom heaters and effect of the distance between these two heaters ( λ = 0.1 , 0.4 ) has been thoroughly investigated. Numerical simulation has been carried out for a wide range of Rayleigh number ( Ra = 10 3 ∼ 10 7 ), Hartmann number ( Ha = 0 ∼ 100 ) and inclination angle of magnetic field ( γ = 0 ° ∼ 90 ° ) to understand the flow field, thermal field and entropy generation respectively. Cobalt-kerosene and Fe 3 O 4 -water ferrofluids are used for the present investigation and considered as a single phase fluid. Galerkin weighted residual method of finite element analysis has been used for numerical solution. The code validation and grid independency test have been carried out to justify the numerical accuracy. It has been observed that increment of magnetic field reduces the heat transfer rate, whereas increment of heater distance augments the heat transfer rate significantly. Results are discussed on the basis of Nusselt number ( Nu ), Bejan number ( Be ) and shown by contours and 3D plots. It has also been found that λ = 0.4 always shows better heat transfer rate and entropy optimization. [ABSTRACT FROM AUTHOR]

The changes from steady-state to chaotic natural convection in a V-shaped differentially heated enclosure have been studied numerically because of their importance in nature, such as in a river or lake. The finite volume method (FVM) is applied to simulate the Navier-Stokes and Energy equations with proper boundary conditions. The working fluid is considered water with the Prandtl number, Pr = 7.0 for various Rayleigh numbers ranging from Ra = 100 to 106 with a fixed aspect ratio, A = 0.5. A group of bifurcations in the transitional flow is investigated, including a Pitchfork and a Hopf bifurcations. The occurrence of Pitchfork bifurcation happens between Ra = 1.3 × 104 and 1.4 × 104 and of Hopf bifurcation happens between Ra = 1.6 × 105 and 1.7 × 105. Moreover, another bifurcation occurs between Ra = 2.6 × 105 and 2.7 × 105 for the changeover from intervallic state to chaotic state. Power spectral density of temperature time series, phase space trajectories, and the largest Lyapunov exponents of the unsteady chaotic flows are also investigated. Additionally, heat and mass transfer are measured and explained elaborately with physical significance. [ABSTRACT FROM AUTHOR]