Aspect ratio effect on side and basal melting in fresh water

An experimental investigation on natural convection of non-covalently functionalized MWCNTs nanofluids: Effects of aspect ratio and inclination angle

ABSTRACTIn this paper we describe the results of various numerical simulations of sideways or horizontal convection. Specifically, a two-dimensional Boussinesq fluid is both heated and cooled from its upper surface, but the walls and the bottom of the tank are insulating and have no flux of heat through them. We perform experiments with a range of Rayleigh numbers up to 1011, obtained by systematically reducing the diffusivity. We also explore the effects of a nonlinear equation of state and of a mechanical force imposed on the top surface at a fixed Rayleigh number. We find that, when there is no mechanical forcing, both the energy dissipation and the strength of the circulation itself monotonically fall with decreasing diffusivity. At Rayleigh numbers greater than 1010 the flow is unsteady; however, the eddying flow is still much weaker than the steady flow at smaller Rayleigh numbers. At high Rayleigh numbers, the stratification and the mean circulation are increasingly confined to a thin layer at the upper surface, with the layer thickness decreasing according to Ra−1/5. There is no evidence that the flow ever enters a regime that is independent of Rayleigh number. Using a nonlinear equation of state makes little difference to the flow phenomenology at a moderate Rayleigh number. The addition of an imposed stress at the upper surface makes a significant difference in the flow. A strong, energy-dissipating circulation can be maintained even at Ra = 109, and the stratification extends more deeply into the fluid than in the unstressed case. Overall, our results are consistent with the notion that in the absence of mechanical forcing a fluid that is heated and cooled from above cannot maintain a deep stratification or a strong sustained flow at high Rayleigh numbers, even if the interior flow is unsteady.

PurposeThe purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model.Design/methodology/approachIn this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 103 < Ra < 105), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10).FindingsResults show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects.Originality/valueThis paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.

Two new results are presented on the development of convective flow in a finite Hele-Shaw cell. First, it is shown that within a certain range of Rayleigh numbers there exist three regions in the fluid layer: the center region having a steady flow and the two end regions exhibiting time-dependent flow. Second, in the two end regions each flow oscillation is always found to be monoperiodic and the two are not correlated. Transition to a more complicated oscillation is not observed, and the flow never becomes chaotic. The time-dependent flow regime is bounded at low and high Rayleigh number by transitions to steady-state flow.

Overall heat transfer and mean temperature distribution measurements have been made of turbulent thermal convection in horizontal water layers heated from below. The Nusselt number is found to be proportional to Ra0·278 in the range 2·76 × 105 &lt; Ra &lt; 1·05 × 108. Eight discrete heat flux transitions are found in this Rayleigh number range. An interferometric method is used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 105 and 1·86 × 107. Direct visual and photographic observations of the fluctuating interferogram patterns show that the main heat transfer mechanism is the release of thermals from the boundary layers. For relatively low Rayleigh numbers (up to 5 × 105) many of the thermals reach the opposite surface and coalesce to form large masses of relatively warm fluid near the cold surface and masses of cold fluid near the warm surface, resulting in a temperature-gradient reversal. With increasing Rayleigh numbers, fewer and fewer thermals reach the opposite bounding surface and the thermals show persistent horizontal movements near the bounding surfaces. The central region of the layer becomes an isothermal core. The mean temperature distributions for the high Rayleigh number range are found to follow a Z−2 power law over a considerable range, where Z is the distance from the bounding surface. A very limited agreement with the theoretically predicted Z−1 power law is also found.

Free convection with MWCNT/water nanofluid having varying aspect ratio of MWCNT nanoparticle in thermally undulated enclosures

Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls

Oscillatory natural convection in a square enclosure containing a PCM suspension

Turbulent Rayleigh–Bénard convection in low Prandtl–number fluids

A numerical analysis has been performed for the steady-state temperature and stream function distributions in a finite vertical cylinder, having an isothermal side and top and an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid. The non-dimensionalized momentum and energy equations were solved for a wide range of Rayleigh numbers (10 to 10 x 10^6) and solutions for the streamlines and isotherms were obtained using a transient explicit finite-difference approximation. The isotherms and streamlines were followed while varying the heat generation rate, bulk thermal conductivity, permeability, boundary temperature and cylinder size. Conduction was prominent at low Rayleigh numbers and convection predominated at high Rayleigh numbers. Within the convective heat transfer realm, several different flow patterns were observed.

We report the existence of two new limiting turbulent regimes in horizontal convection (HC) using direct numerical simulations at intermediate to low Prandtl numbers. In our simulations, the flow is driven by a step-wise buoyancy profile imposed at the surface, with free-slip, no-flux conditions along all other boundaries, except along the spanwise direction, where periodicity is assumed. The flow is shown to transition to turbulence in the plume and the core, modifying the rate of heat and momentum transport. These transitions set a sequence of scaling laws that combine theoretical arguments from Shishkina, Grossmann and Lohse (SGL) and Hughes, Griffiths, Mullarney and Peterson (HGMP). The parameter range extends through Rayleigh numbers in the range [ $6.4\times 10^5, 1.92\times 10^{15}$ ] and Prandtl numbers in the range [ $2\times 10^{-3},2$ ]. At low Prandtl numbers and intermediate Rayleigh numbers, a core-driven regime is shown to follow a Nusselt-number scaling with $Ra^{1/6}Pr^{7/24}$ . For Rayleigh numbers larger than $10^{14}$ , the Nusselt number scales with $Ra^{0.225}Pr^{0.417}$ . For these particular regimes, the Reynolds number is found to scale as $Ra^{2/5}Pr^{-3/5}$ for the low-Prandtl-number regime and $Ra^{1/3}Pr^{1}$ for Rayleigh numbers larger than $10^{14}$ . These results embed the HGMP model in the SGL theory and extend the known regime diagram of HC at high Rayleigh numbers. In particular, we show that HC and Rayleigh–Bénard share similar turbulent characteristics at low Prandtl numbers, where HC is shown to be ruled by its core dynamics and turbulent boundary layers. This new scenario confirms that fully turbulent HC enhances the transport of heat and momentum with respect to previously reported regimes at high Rayleigh numbers. This work provides new insights into the applicability of HC for geophysical flows such as overturning circulations found in the atmosphere, the oceans, and flows near the Earth's inner core.

This study investigates the flow and heat transfer characteristics of microencapsulated phase change material suspensions in a square cavity by developing a coupled two-phase flow model that integrates the lattice Boltzmann method and discrete element method. The partially saturated cell method is employed to simulate the solid–liquid interface, while the effective specific heat method is adopted to capture the phase change behavior of microcapsule particles. A comprehensive analysis is conducted to examine the effects of microcapsule concentration, Rayleigh number, phase change temperature, and particle size on the suspension's flow and heat transfer performances. The results reveal that the inclusion of microcapsule particles significantly enhances the effective specific heat capacity of the suspension. Particle aggregation behavior is primarily influenced by the Rayleigh number. At lower Rayleigh numbers, particles are randomly distributed, while rapid aggregation occurs due to thermophoretic forces at high Rayleigh numbers. At a certain microcapsule concentration, the suspension achieves an optimal balance between heat capacity enhancement and flow stability. The results indicate that the microcapsule particles with a diameter of 75 μm can effectively release latent heat while avoiding the pronounced fluctuations associated with larger particles. Furthermore, the highest latent heat release efficiency is observed when the phase change temperature is close to the average cavity temperature. This study demonstrates that the Rayleigh number plays a pivotal role in governing the transition of the flow regime from laminar to turbulent by modulating the buoyancy-to-viscous force ratio, which in turn influences particle aggregation and heat transfer intensity of microencapsulated phase change material suspensions.

Buoyancy effects in plane Couette flow heated uniformly from below with constant heat flux

Laminar flow in shallow horizontal cavities (aspect ratio a &lt; &lt; 1) at high Rayleigh numbers (&gt; 106) is investigated using an approximate analysis based on first principles, and also with numerical solutions to the full equations. A Prandtl number of approximately one is assumed. It is found that the flow regime at such high values of Ra is characterized by boundary layers lining both vertical as well as horizontal walls of the enclosure, and is qualitatively different from the flow regimes at lower Rayleigh numbers. The internal region of the core (near to the horizontal centerline) exhibits linear velocity and temperature profiles. Typical isotherms and streamlines characteristic of this flow regime are presented, based on the numerical solutions. The velocity and temperature profiles predicted from the approximate analysis are found to compare well with those obtained from the numerically obtained solutions. The Nusselt numbers predicted from the analysis are also in good agreement with the numerical solutions, and with the limited experimental data in the literature. The various physical processes in this type of flow are discussed based on the findings of the analytical and numerical studies.

PurposeThe purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper, which is solely devoted to three-dimensional calculations. Results also indicate that optimal average heat transfer rate is obtained for both high Rayleigh number of 106 and high inclination of 90° for the two cases of the inner cylinder and cubical enclosure.Design/methodology/approachThe manuscript deals with prediction of the three-dimensional natural convection phenomena in a cubical cavity induced by an isothermal cylinder at the center with different inclinations by simulating the flow using highly numerical methods such as finite volume method.FindingsIt is found that the local Nusselt number through active walls for titled inclination set at 90°, the symmetry of the flow is conserved and the area containing the maximum heat transfer is divided into three smaller areas situated near the upper portion of the wall, taking the maximum value. That may be due to the preparation of local occurrence of instabilities and bifurcation phenomena that appear for Ra > 107, which is not included in the present paper to save journal space. It was found also that an optimal heat transfer appears when the cylinder orientation becomes vertical (a = 90°). For this inclination, buoyancy forces act upward, corresponding to an aiding situation. In addition, heat transfer rate is increasing with Rayleigh numbers, so correlations of average Nusselt through the cubical cavity and the cylinder are established as function of two parameters (Ra, a). Comparisons of the numerical results with those obtained from all correlations show good agreements.Originality/valueTo the author’s knowledge, studies have thus far adressed three-dimensional cuboids enclosures induced by an inner shape which the location is changed. However, no study has examined three-dimensional natural convection between the inner isothermal cylinder and outer cooled cubical enclosure when the outer enclosure is tilted.