Velocity Flux Research Articles

Design and Experimental Investigation of a Self-Powered Fan Based on a Thermoelectric System

Providing electricity for isolated areas or emergencies (snowstorms, earthquakes, hurricanes, etc.) is an important challenge. In this study, a prototype of a self-powered fan based on a thermoelectric system was built to enhance the heat dissipation of the thermoelectric generator (TEG) systems using household stoves as heat sources. To improve output performance of the system, a heat collector consisting of a heat-conducting flat plate and a heat sink with fan cooling was designed to integrate several thermoelectric modules (TEM). The effects of the fan operating conditions (airflow velocity), number of thermoelectric modules, electrical connection mode under different heat flux among the performance of the TEG system are studied. The data obtained showed a higher heat flux and lower flow velocity are required to realize self-sustained cooling of the system. The maximum electric power is more sensitive to the heat flux than the fan operation conditions. It is also observed that more modules provide a higher power output but lower efficiency. The maximum power of four modules in series is larger than that in parallel, and the difference between them increases with increasing heat flux of the heat collector. In the case of self-sufficiency: the maximum output power and maximum net power with four thermoelectric modules are 10.92 W and 5.26 W, respectively, at a heat flux of 30,000 W/m2. Additionally, the maximum conversion efficiency of 1.8% is achieved for two modules at a heat flux of 14,000 W/m2, providing an effective strategy for the installation of TEMs and cooling fans in TEG.

Experiment on local convective heat transfer for successive droplets impacting on heated cylindrical surface

An experiment was conducted to investigate the underlying heat transfer mechanism when successive droplets impacting on the heated cylindrical surface. The hydrodynamics of droplets were captured by visual method and the local convective heat transfer characteristics were obtained by combining direct measurement and numerical solution of three-dimensional differential equation of heat conduction. The influences of impact frequency, impact velocity and input heat flux were experimentally discussed. It is found that, based on the evolution of local wall temperature, there are three zones along the circumference, i.e., impingement zone, heat diffusion zone and tail detachment zone. Increasing the impact frequency and input heat flux enhances the convective heat transfer performance. However, when the impact frequency is high enough, continuously increasing the impact frequency, the degree of convective heat transfer improvement gradually decreases. The increase of impact velocity mainly enhances the convective heat transfer on the impingement zone and heat diffusion zone, but has little effect on the tail detachment zone. The continuous increase of impact velocity results in the splashing phenomenon and the decrease of convective heat transfer performance. Furthermore, some dimensionless correlations were proposed for predicting the droplet splashing threshold and the local convective heat transfer performance along circumference, respectively.

Modelling the 2021 East Asia super dust storm using FLEXPART and FLEXDUST and its comparison with reanalyses and observations

The 2021 East Asia sandstorm began from the Eastern Gobi desert steppe in Mongolia on March 14, and later spread to northern China and the Korean Peninsula. It was the biggest sandstorm to hit China in a decade, causing severe air pollution and a significant threat to human health. Capturing and predicting such extreme events is critical for society. The Lagrangian particle dispersion model FLEXPART and the associated dust emission model FLEXDUST have been recently developed and applied to simulate global dust cycles. However, how well the model captures Asian dust storm events remains to be explored. In this study, we applied FLEXPART to simulate the recent 2021 East Asia sandstorm, and evaluated its performance comparing with observation and observation-constrained reanalysis datasets, such as the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) and CAMS global atmospheric composition forecasts (CAMS-F). We found that the default setting of FLEXDUST substantially underestimates the strength of dust emission and FLEXPART modelled dust concentration in this storm compared to that in MERRA-2 and CAMS-F. An improvement of the parametrization of bare soil fraction, topographical scaling, threshold friction velocity and vertical dust flux scheme based on Kok et al. (Atmospheric Chemistry and Physics, 2014, 14, 13023–13041) in FLEXDUST can reproduce the strength and spatio-temporal pattern of the dust storm comparable to MERRA-2 and CAMS-F. However, it still underestimates the observed spike of dust concentration during the dust storm event over northern China, and requires further improvement in the future. The improved FLEXDUST and FLEXPART perform better than MERRA-2 and CAMS-F in capturing the observed particle size distribution of dust aerosols, highlighting the importance of using more dust size bins and size-dependent parameterization for dust emission, and dry and wet deposition schemes for modelling the Asian dust cycle and its climatic feedbacks.

Influence of fin thickness variation on the thermal performance of metallic foam heat sink laminar condition

In recent years, open-pore metallic foams have been employed in a wide variety of applications owing to the essential qualities that they possess. In the present study, the thermal performance of a finned heat sink made from open-cell copper foam was investigated numerically under laminar forced conditions. The influence of fin thickness, air velocity, and heat fluxes on the average heat sink base temperature to ambient temperature difference, the Nusselt number, and pressure drop were investigated. Fin thickness was generally taken as 2, 5, 7, and 10 mm. Heat fluxes were taken from (600 to 3000) W/m2, while the air velocity was taken from 0.04 to 0.16 m/s. The findings of laminar flow indicate that straight fins with a thickness of 10 mm minimize the temperature difference between the heat sink's base and the surrounding air the most, followed by fins with thicknesses of 7 mm, 5 mm, and 2 mm. At 3000 W/m2, a change in velocity from 0.04 to 0.16 m/s increases the average base temperature difference (i.e. (Tbase-Tamb)) by 118.9% for a heat sink with 10 mm straight fins. . At a heat flow of 600W/m2, the Nusselt number grew by 72.6%, 60.7%, and 45.7% when fin thickness was raised from 2 mm to 10 mm, 2 mm to 7 mm, and 2 mm to 5 mm, respectively. The results also demonstrate that the pressure drop rises with increasing fin thickness.

Experimental study on droplet behavior and mechanisms during reflooding in a Single-rod channel

• The complete vapor-liquid interface behavior during reflooding is observed. • Discovery and interpretation of the bimodal distribution of droplets. • The three main mechanisms of droplet formation and breakup are discussed. A high-temperature surface reflooding visualization experiment in a single-rod channel was conducted to investigate the transient droplet behavior, which is considered to be critical for heat transfer in Dispersed Flow Film Boiling (DFFB). After the zirconium alloy cladding was heated to the preset temperature, the specimen was subjected to a continuous flow of deionized water under varying input heat flux, coolant subcooling, and apparent reflooding velocity. The temperature history during reflooding was recorded, and the quench behavior was visualized using a high-speed camera. The experimental results show the typical transition mode of inverted annular flow-dispersive flow; at the same time, although the size distribution of droplets conforms to the form of log-normal distribution, the probability of large droplets will increase significantly at higher input heating power. Furthermore, to provide physical support for building droplet distribution models containing more physical mechanisms in the future, several droplet formations and breakup mechanisms, which include the Helmholtz instability, capillary breakage, and rewetting area sputter, have been discussed in this paper.

CFD simulation of circumferential crack in low pressure water pipelines

Detection of the pipeline leakage and its repair at an early stage is very crucial as leaks can cause significant destruction to the surrounding infrastructures. This paper demonstrates the change in flow characteristics of a low-pressure water pipeline with the existence of a narrow circumferential crack of three different sizes. The steady state simulations have shown clear indications in the velocity and mass flux variations along the pipe and at the crack surface. These results show that the crack causes measurable differences in fluid flow properties at different inlet pressure. Predicted results were analysed to assess the effect of leakage on the pressure field and maximum mass flux. The study intends to contribute in the development of pipe crack leakage detection in various industrial and commercial purposes.

ANALYSIS OF ENTROPY PRODUCTION OF IMMISCIBLE MICROPOLAR AND NEWTONIAN FLUIDS FLOW THROUGH A CHANNEL: EFFECT OF THERMAL RADIATION AND MAGNETIC FIELD

This paper aims to analyze the thermal characteristics, entropy production, flow velocity and Bejan number profile for immiscible nature of micropolar and Newtonian viscous fluid within a channel. Here, the authors emphasize the influence of thermal radiation and oriented magnetic field on the thermal profile and entropy generation of two different types of non-miscible and incompressible micropolar and Newtonian fluids in a channel. The viscous dissipation and thermal radiation effect are also considered in the thermal energy equation. In this work, the entropy production is analyzed within a channel due to oriented magnetic field and thermal radiation. A constant pressure gradient acts on the entry zone of flow domain and static walls of the channel are isothermal. In this problem, we tried to simulate thermal radiation in energy equation by adopting the Rosseland’s diffusion approximation. According to geometrical configuration of the problem, the conditions of no-slip at the walls of the channel and continuity of thermal exchange, microrotation, shear stress, flow velocity and heat flux at the interface of immiscible fluids are used. The governing equations for the flow of immiscible fluids are solved by reliable technique and exact solution for thermal characteristics and flow field are evaluated. The mathematical results of thermal profile and flow characteristics are used to obtain the Bejan number profile as well as the entropy production number profile. The influence of various thermo-physical governing parameters such as radiation parameter, Reynolds number, inclination angle parameter, viscous dissipation parameter, micropolarity parameter and Hartmann number, which describe the physical significance of the present model, on the flow and thermal characteristics of the model are discussed graphically. The newly obtained results of this study are verified with previous published results.

Numerical study on the heat and mass transfer in charging and discharging processes of a triangular honeycomb thermochemical energy storage reactor

• A triangular honeycomb reactor has been designed and experimentally investigated. • A 3-D numerical model of this reactor has been developed and validated. • Relationships between heat transfer and mass diffusion are determined. • The thermal efficiency of triangular honeycomb reactor can achieve around 20% Adsorption heat storage based on porous adsorbents attracts considerable attention for the high energy storage density and long storage duration compared to sensible and latent heat storage methods. However, one of the critical challenges is the poor heat and mass transfer performance of thermochemical reactors. This study presents a triangular honeycomb reactor using zeolite 13X-H 2 O working pair and investigates the heat and mass transfer performance. To do this, a three-dimensional transient heat and mass transfer model has been built in COMSOL to simulate the adsorption and desorption processes of the new reactor. A detailed numerical model and the corresponding modelling methods are critical to the investigation while most of the recent studies are based on one-dimensional and two-dimensional models. The model has been experimentally validated thoroughly to a close agreement in both adsorption and desorption processes (mean sum of percent errors of 0.6% to 8.91% for air temperature and relative humidity). The reactor thermal efficiency from the simulation and experiment are 19.57% and 21.93%, respectively, which are achieved by the fast and controllable charging and discharging performance along with the reduced air pressure drop benefited from the reactor design. To add value of the charging and discharging details, this study also presents the contour diagrams with detail discussions for the air velocity, temperature, water concentration, and heat and mass flux variations of the triangular honeycomb channel during desorption and adsorption processes. The results show that the side of triangle channel has larger and stronger moisture desorption in a charging process and stronger moisture adsorption in a discharging process than that of the triangle corner areas.

EFFECT OF NON-AXISYMMETRIC INLET PORTS AND OPERATING CONDITIONS ON DROP DYNAMICS OF AN INTERNAL MIXING ATOMIZER

The effect of a non-axisymmetric inlet ports configuration of an internal-mixing twin-fluid atomizer on the spray characteristics is experimentally investigated. Inside the atomizer, two water jets are impinged on each other and are further disrupted by a central gas stream coming from the top. The operating conditions consider the variation of the gas mass flow rate at Reynolds and Weber numbers in the order of 10<sup>4</sup>-10<sup>5</sup>. Phase Doppler anemometry (PDA) measurements at four radial, four axial, and two perpendicular azimuthal positions are combined with a patternator device to obtain droplet size, axial velocity, and mass flux distributions. An approach for evaluating the overall spray asymmetry based on the mass flux distributions is proposed, which enabled the detection of slight asymmetries throughout the azimuthal direction, where especially differences in droplet sizes and velocities measured between the two azimuthal positions are observed. Higher Sauter mean diameters (SMDs) and lower velocities in regions of the spray with higher liquid mass flux are observed when compared to the azimuthal position perpendicular to it. In general, the liquid is considerably faster in the spray center than at the boundaries, where the fluctuating component of the velocity is higher due to the interaction of small droplets with the surrounding air. Overall, an increase in the gas flow rate reduces the droplet sizes and increases the velocity across the spray.

Variations of Tween Surfactant and Propylene Glycol Cosurfactant in Topical Microemulsion Formulation on The Penetration of Ibuprofen

Ibuprofen is a derivative of propionic acid, a class of non-steroidal anti-inflammatory drugs (NSAIDs). Ibuprofen has side effects on the gastrointestinal tract. So that topical use can be a solution to reduce the side effects of oral use because of the release of topical drugs through the stratum corneum which makes it selective in certain places. The preparation chosen was a topical microemulsion because it is more thermodynamically stable and has no effect on the gastrointestinal tract. This study aims to determine the effect of the ratio of surfactant concentrations of various ratios of tween 20:tween 80 and cosurfactant propylene glycol to the penetration rate of ibuprofen across the membrane and to determine the physical characteristics of topical microemulsions. Selection of tween surfactant and propylene glycol cosurfactant because it has high physical stability. This research is an experimental study, namely by making four formulations with various ratios of surfactant and cosurfactant with a difference of 2.5% in each formulation of topical ibuprofen microemulsion with a concentration of 5% ibuprofen using variations of surfactant tween 20 and tween 80, cosurfactant propylene glycol with black cumin oil phase. Evaluation of the preparation by organoleptic test, pH test of the preparation, examination of the type of emulsion, particle size measurement, microemulsion release test in vitro using the Franz diffusion method. The results show that the concentration ratio of surfactant tween 20:tween 80 and cosurfactant propylene glycol can affect particle size, pH and penetration velocity (flux) in Franz diffusion. The results of the study showed that in F1 using surfactant tween 20:tween 80 with a concentration of 71.6% (6:4) had the smallest particle size of 11.5 nm and the largest flux value was 128.45 g.cm-2.H- 1. In conclusion, variations in surfactant and cosurfactant concentrations can affect the pH of the preparation, particle size, penetration speed (flux). The results obtained that the cumulative percent and penetration speed of all formulas had significant differences (p<0.05).

Assessment of riverine plastic flux in Pulot River and its tributary in Sofronio Española, Palawan, Philippines

The Philippines is the world’s third major contributor to global marine plastic pollution and the biggest polluter of riverine plastics into the sea. Several rivers in Philippines including those in Palawan, the country’s Last Frontier, are assumed to be the main pathways of land-based plastic waste into the ocean. However, variations, model estimations and plastic litter’s composition among rivers remains uncertain due to lack of field data. In this regard, the quantity, temporal variations and composition of plastic flux were studied in Pulot River and its tributary in Sofronio Española, Palawan. This aims to collect field data on floating macroplastics and its composition, as well as to determine the effect of flow velocity to plastic flux. Plastic flux was measured at three different locations along Pulot River, two hourly measurements during two different time of the day was made. The results showed significant difference on the amount of plastic flux during the morning and afternoon measurements. On the other hand, plastic flux during the weekends and weekdays measurements showed no significant difference. Instantaneous plastic flux and flow velocity showed significant positive correlation at all locations for all periods of measurements except the Pulot River Bridge during morning. Predominant plastic types are food packaging, plastic bottles, and toiletries. Multilayers and mixed plastics under the “Other” category were the most abundant plastic polymer classified. These results provide new insights on variations and prevalence of plastic flux in Pulot River which may benefit future long-term monitoring efforts and plastics pollution mitigation strategies.

Computational Fluid Dynamic Analysis of Thermal Characteristics on the PLCC Package: Influence of velocity and heat flux

Computational Fluid Dynamic Analysis of Thermal Characteristics on the PLCC Package: Influence of velocity and heat flux

Artificial intelligence-based approach for cluster identification in a CFB riser

Cluster evolution dominates the gas–solid interaction and heat and mass transfer in risers, but cluster identification is still a challenge. Based on the unsupervised artificial intelligence approach, a two-step K-means cluster identification method is proposed to distinguish the clusters in a riser. With the consideration of the instantaneous particle motion and position information, it is able to capture the phenomenon of particles attaching and detaching a cluster. The estimated solid fraction threshold is located in the region where the slope of the solid fraction is the smallest, and approximately makes the numbers of particles detaching and attaching the clusters equal. The solid fraction threshold is about 0.204. It is found that the particles penetrating a cluster are in a more violent turbulent movement. Larger gas velocity and solid flux result in stronger interactions between clusters. The proposed method provides a new way to identify the cluster.

Reduce-Order Modeling and Higher Order Numerical Solutions for Unsteady Flow and Heat Transfer in Boundary Layer with Internal Heating

We obtain similarity transformations to reduce a system of partial differential equations representing the unsteady fluid flow and heat transfer in a boundary layer with heat generation/absorption using Lie symmetry algebra. There exist seven Lie symmetries for this system of differential equations having three independent and three dependent variables. We use these Lie symmetries for the reduced-order modeling of the flow equations by constructing invariants corresponding to linear combinations of these Lie point symmetries. This procedure reduces one independent variable of the concerned fluid flow model when applied once. Double reductions are achieved by employing invariants twice that lead to ordinary differential equations with one independent and two dependent variables. Similarity transformations are constructed using these two sets of derived invariants corresponding to linear combinations of the Lie point symmetries. These similarity transformations have not been obtained earlier for this flow model. Moreover, the corresponding reduced systems of ordinary differential equations are different from those which exist in the literature for fluid flow and heat transfer that we have been dealing with. We obtain multiple similarity transformations which lead us to new classes of systems of ordinary differential equations. Accurate numerical solutions of these systems are obtained using the combination of an adaptive fourth-order Runge–Kutta method and shooting procedure. Effects of variation of unsteadiness parameter, Prandtl number and heat generation/absorption on fluid velocity, skin friction, surface temperature and heat flux are studied and presented with the help of tables and figures.

Flow Boiling of R450A, R515B, and R1234ze(E) Inside a 7.0 mm OD Microfin Tube: Experimental Comparison and Analysis of Boiling Mechanisms

A comparative analysis of the flow boiling characteristics of R450A, R515B, and R1234ze(E) inside a 7.0 mm OD microfin tube was performed. The mass velocity was explored from low values, starting from 50 kg m−2 s−1, up to 400 kg m−2 s−1, and the heat flux was tested in the range of 10–50 kW m−2, keeping a constant saturation temperature of 30 °C at the inlet of the test section. R515B and R1234ze(E) showed similar values of the heat transfer coefficient and frictional pressure gradient under all the investigated working conditions. R450A showed lower values of the heat transfer coefficient, especially at low heat flux and high mass velocity, compared to R515B and R1234ze(E), but the gap of the heat transfer performance between the three fluids reduced at high heat flux. The frictional pressure drops of R450A were generally lower than those of R515B and R1234ze(E). In the end, some correlations for the evaluation of both the heat transfer coefficient and the pressure drop were selected, and the estimated values were compared against the experimental counterpart. Furthermore, the effects of nucleate boiling and of convective boiling, as well as of the temperature glide for R450A, were analyzed and estimated.

Thermo‐Hydro‐Chemical Simulation of Mid‐Ocean Ridge Hydrothermal Systems: Static 2D Models and Effects of Paleo‐Seawater Chemistry

AbstractDecades of research have resulted in characterization of the ocean floor manifestations of mid‐ocean ridge (MOR) hydrothermal systems, yet numerical models accounting for the connections between heat transfer, hydrology and geochemistry have been slow to develop. The Thermo‐hydro‐chemical code ToughReact can be used to describe the coupled effects of fluid flow, heat transfer, and fluid‐rock chemical interactions that occur in MOR systems. We describe the results of 2‐dimensional simulations of steady state flow in fractured diabase with mineral‐fluid chemical reactions. Basal heating and specified permeability yield maximum temperature of 400°C. Total fluid flux and high fracture flow velocities are in accord with observations. Fluid chemistry, mineralogical changes and 87Sr/86Sr ratios can be compared to observations to assess and calibrate models. Simulated high temperature fracture fluids have Mg and SO4 near zero, elevated Ca and 87Sr/86Sr of about 0.7040. Total alteration is 10%–50% for simple models of spreading. Anhydrite forms mainly near the base of the upwelling zone and results in substantial local fracture porosity reduction. A calibrated model is used to predict how Sr isotopes and other features of altered oceanic crust would be different in the Cretaceous (95 Ma) early Proterozoic (1,800 Ma) and Archean (3,800 Ma), when seawater may have had high Ca and Sr concentrations, lower pH, higher temperature, and lower Na, Mg, and SO4. The simulations are offered as a start on what ultimately may require a longer‐term community effort to better understand the role of MOR thermo‐hydro‐chemical systems in Earth evolution.

Meteorological and geological controls on dust devil activity: Initial results from a field study at Smith Creek Valley, Nevada, USA

We present initial results of an investigation into meteorological and geological controls on the formation of dust devils (i.e., dust-filled vortices formed in the daytime dry convective boundary layer). During a 2-week field campaign in June 2019 at Smith Creek Valley (SCV), Nevada, USA, we conducted automated time-lapse stereo imaging of dust devils (DDs), while monitoring local meteorological conditions with a broad suite of instruments. Counts of imaged dust devils from two near-cloudless days were compared with a standard suite of atmospheric measurements from a weather tower, eddy correlation flux measurements, and ceilometer backscatter returns. DDs forming in moderate winds (5–8.5 m/s) were more likely to be relatively wide and disorganized, with qualitatively low dust opacity, whereas those forming in weaker winds were more likely to be coherent, dusty, well-formed conical or cylindrical structures. The daily maximum DD counts at SCV occurred shortly after their onset in late morning (11:00–12:00 local time), coinciding with a surge in CBL growth that was likely delayed by the thermal properties of the playa. This late morning peak contrasts with previous studies conducted elsewhere that typically observed peak DD counts in the afternoon. As observed in previous field studies, DDs formed in highly convective conditions, when the heat flux (H) and friction velocity (u∗) were elevated and the convective ratio w∗/u∗ exceeded ∼ 4 (i.e., -h/L exceeded ∼ 25). However, values of>4w∗/u∗ also occurred in mid-morning, prior to DD formation and CBL growth, suggesting that this metric is not the sole condition required for DD generation. Aside from the late morning maxima, DD counts fluctuated considerably throughout the afternoon at timescales of 0.5–2 h–correlating poorly with fluctuations in H and u∗, and not at all with either w∗/u∗ or the Monin-Obukhov length (L). Several factors, such as local variations in surface thermal properties and meteorology, may be responsible for these short-term fluctuations.

Performance analysis of micro-fin tubes compared to smooth tubes as a heat transfer enhancement technique for flow condensation

• Entropy generation of R134a flow condensation inside micro-fin and straight tubes is studied and compared. • Geometrical parameters impact on entropy generation is investigated. • Flow conditions impact on entropy generation is analyzed. • Favorable geometrical and flow conditions at which the micro-fin tube has superior performance are identified. Heat transfer enhancement techniques are accompanied by pressure drop amplification, detrimentally affecting their performance; entropy generation analysis is an effective approach to assess heat transfer enhancement along with resulting pressure drop. Current study investigates and compares the performance of micro-fin (as a passive enhancement technique) and smooth tubes during flow condensation (for R134a refrigerant) through conducting entropy generation analysis. First, the impact of geometrical and operating variables on pressure losses and heat transfer contributions to entropy generation and total generated entropy inside both types of tubes is examined. Then, the conditions at which the application of micro-fin tubes in lieu of smooth ones is justifiable and of superior performance are identified utilizing entropy generation number. The simulation results indicate that entropy generation enhances in the micro-fin tubes as tube diameter, mass velocity, vapor quality, and wall heat flux rise, and saturation temperature declines. The same is observed in the smooth tube except for the mass velocity; an increase in this parameter leads to a decreasing-increasing trend in entropy generation. Moreover, the entropy generation number results indicate that applying micro-fin tubes rather than smooth ones is justifiable, i.e., has better performance, at lower mass velocities and vapor qualities, but higher saturation temperatures and wall heat fluxes.

Enhancement of the cooling by mixed convection of a CPU using a rotating heat sink: Numerical study

The technological progress made in recent years has driven electronic apparatus to become not only more efficient and work faster but also considerably smaller in weight and size. Furthermore, the power densities of these devices have known an impressive increase. However, the challenge for the electronic industry is the lifetime device improvement by controlling the adequate removal of their excess heat. The use of more efficient cooling systems is, therefore, crucial in order to ensure durable device functionality. In this work, computational simulation was carried out to study the enhancement cooling process mixed convection of an electronic component (CPU mounted in a motherboard) using a new design of a heat exchanger by combining the heat sink (the finned surface) and the fan in a single component, this allows more heat to be moved faster and with less energy than a conventional cooler. Three radial heat sinks (HS18, HS24 and HS36) are considered depending on circumferential fin numbers ( n = 18, 24 and 36). The effect of Reynolds number, heat flux and rotational velocity is investigated, and the optimum comprehensive performance was determined. The results reveal the cooling performance turns out to be better for heat sink with n = 36. The rotational velocity operates a significant effect on the temperature field only for values below than 900 rpm. We also found that the improvement in the Nusselt number and its percentage enhancement is intensified with increased rotational velocity and decreased with heat flux. A bigger Ω and ReΩ meant a more obvious heat transfer enhancement (NuΩ/Nu0) in the case of smaller Q, but (NuΩ/Nu0) decreased with increasing Q.

A mixed virtual element method for Biot's consolidation model.

In this paper, we shall present a weak virtual element method for the standard three field poroelasticity problem on polytopal meshes. The flux velocity and pressure are approximated by the low order virtual element and the piecewise constant, while the elastic displacement is discretized by the virtual element with some tangential polynomials on element boundaries. A fully discrete scheme is then given by choosing the backward Euler for the time discretization. With some assumptions on the exact solutions, we prove that the convergence order is of order 1 with respect to the meshsize and the time step, and the hidden constants are independent of the parameters of the problems. Some numerical experiments are given to verify the results.