The large-scale structure of compressible convection

When a horizontal layer of fluid is heated from below and cooled from above with the mean temperature and physical parameters of the fluid constant, the two-dimensional roll is known to be the stable solution near the critical Rayleigh number. In this study, with the mean temperature changing steadily at a rate η, the Rayleigh number and the velocity and temperature fields governed by the Boussinesq equations are expanded in two parameters: η, and the amplitude ε. Hexagons are shown to be the stable solution near the critical Rayleigh number. The direction of the motion depends upon the sign of η. A finite amplitude instability is possible with an associated hysteresis in the heat flux as the critical Rayleigh number is approached from below or from above.

This paper uses Cluster data during the period from 2001 to 2010 to study the polytropic processes of magnetosheath ions. Utilizing the method of homogeneous magnetohydrodynamic (MHD) Bernoulli integral (MBI), we first identify streamflow tubes, then use the constant of polytropic relation to guarantee that the streamflow tube experiences an unchanged polytropic process, and finally determine the polytropic index of ions in these streamflow tubes. The statistical results show that the magnetosheath is a complicated system in which the polytropic index of ions ranges from −2 to 3. The polytropic index distribution of ions is dependent on the electromagnetic energy flux perpendicular to the streamline. The median polytropic index of ions in the magnetosheath is 0.960, 0.965, and 0.974 for perpendicular electromagnetic energy ratio δE × B < 5%, δE × B < 3%, and δE × B < 1%, respectively. There are two basic polytropic processes in the magnetosheath: the dominant isothermal process and the isobaric process. When there is no exchange of electromagnetic energy between neighboring streamflow tubes, the magnetosheath ions are isothermal. However, when the perpendicular electromagnetic energy ratio increases, the isobaric polytropic process starts to emerge. The magnetosheath ion flows are highly localized because most streamflow tubes experiencing same polytropic processes last less than 60 s. Thus, the polytropic index of magnetosheath ion flows is highly variable.

On the differential effect of temperature on the Nusselt-Rayleigh relationship in free convection

The natural convection heat transfer from horizontal circular cylinder placed in a square enclosure is investigated numerically. The study deals with the effect of magnetic field on the flow and heat transfer characteristics. The investigation employs different Hartman numbers (0, 50, 100, 200), different Rayleigh numbers (103, 104, and 105) with constant enclosure width to cylinder diameter ratios W/D = 2.5. The study included the solving of the governing equations in the form of the vorticity-stream function to be fitted with coordinate system. The algebraic grid generation is used to generate initial transformation. The elliptic grid generation is used to fit with physical domain between the heated horizontal cylinder and the enclosure into a computational domain. The resulting equations are solved using finite difference method that based on the finite volume. The research studied the influence of the variation the Hartman number on the local and average Nusselt numbers, flow patterns and temperature distributions with different Rayleigh numbers. The effect of Hartman numbers on the flow patterns and temperature distributions will be displayed using streamlines and isotherms. The results show that the conduction heat transfer is the dominant mode for low Rayleigh numbers. The convection heat transfer is the dominant mode of the heat transfer for high Rayleigh number in absence of the magnetic effect. The convection heat transfer convert to conduction mode at high Rayleigh numbers due to the effect of the magnetic field in the fluid. Also, the results show that the behavior of the local Nusselt numbers for Ha = 0 are unique and differ from those of other higher Hartman numbers for all Rayleigh numbers.

Prandtl number dependence of laminar natural convection heat transfer in a horizontal cylindrical enclosure with an inner coaxial triangular cylinder

Buoyancy driven flow in a parallelogrammic enclosure with an obstructive block and magnetic field

In this paper, the flow and free convection heat transfer of a multi-walled carbon nanotube/water nanofluid in a triangular cavity with a solar heater is studied using the lattice Boltzmann method. The side walls of the cavity are cold and the bottom wall is partially heated by a solar heater, which have a non-uniform temperature distribution. It is assumed that the heating energy is provided by an absorber that is directly exposed to sunlight. Because of the limited variations of density, the Boussinesq approximation is used, which causes the coupling of hydrodynamic and thermal fields. For velocity and temperature distribution functions, a lattice Boltzmann model with two dimensions and nine directions is adopted. The effect of parameters, such as the Rayleigh number, the volume fraction of nanoparticles, and the position of solar heater, on the flow and heat fields is studied. The results show that, for all Rayleigh numbers studied, the Nusselt number increases as nanoparticles volume fraction increases. The addition of 4% nanoparticles causes the average Nusselt number to increase about 11% at low (Ra = 103) and moderate (Ra = 104) Rayleigh numbers and 217% at the high Rayleigh number (Ra = 105). Furthermore, it is shown that for a fixed Rayleigh number, heat transfer can be optimized by adjusting solar heater’s position. This study can provide a useful insight for utilizing solar heaters with non-uniform temperature distribution in triangular cavities.

The problem of thermal convection is studied in a horizontal layer of fluid with an internal heat source which is restricted to vary linearly with the vertical variable. Square and hexagonal cells are found to be the only possible stable convection cells. Finite amplitude instability can occur for a range of the amplitude of convection. The presence of internal heating is found to be able to affect strongly the cell's size, the critical Rayleigh number, the heat transported by convection, the stability of the convective motion and the internal motion of the hexagonal cells.

In this paper a numerical investigation is performed to study the effects of different nanofluids on convective heat transfer enhancement in a partitioned square cavity subject to different shapes of nanoparticle using water-SiO2 nanofluid. This study has been carried out to analyze the effects of SiO2 nanoparticle, its volumetric fraction between 2 and 4%, and nanoparticle shape (i.e. blades, platelets, cylindrical, bricks, and spherical), on the fluid flow and heat transfer characteristics. The overall continuity, momentum, and energy equations are solved by using the finite-volume method and the SIMPLE algorithm. The influence of related parameters such as Rayleigh number (Ra=105 to 107) and height of partition (h=0.1, 0.3, 0.5H) are studied. Based on the results, independent of nanoparticle shape, the streamlines and isotherms are extremely affected by Rayleigh number and height of partition. For a fixed amount of the partition height, average Nusselt number increases as the Rayleigh number rises.

Unsteady conjugate heat transfer characteristics in hexagonal cavity equipped with a multi-blade dynamic modulator

Study of Fe3O4-water nanofluid with convective heat transfer in the presence of magnetic source

Enhancement of the natural and forced convection heat transfer has been the subject of numerous academic and industrial studies. Air blenders, mechanical agitators, and static mixers have been developed to increase the forced convection heat transfer rate in compressible and incompressible flows. Stationary inserts can be efficiently employed as heat transfer enhancement device in the natural convection systems with compressible flow. Generally, a stationary heat transfer enhancement insert consists of a number of equal motionless units, placed on the inside of a pipe or channel in order to control flowing fluid streams. These devices have low maintenance and operating costs, low space requirements and no moving parts. A range of designs exists for a wide range of specific applications. The shape of the elements determines the character of the fluid motion and thus determines thermal effectiveness of the insert. There are several key parameters that may be considered in the design procedure of a heat transfer enhancement insert, which lead to significant differences in the performance of various designs. An ideal insert for natural conventional heat transfer of compressible flow applications provides a higher rate of heat transfer and a thermally homogenous fluid with minimized pressure drop and required space. To choose an insert for a given application or in order to design a new insert, besides experimentation, it is possible to use computational fluid dynamics (CFD) tools to study insert performance. This paper presents the outcomes of the numerical studies by the authors on an industrial stationary heat transfer enhancement insert and illustrates how a heat transfer enhancement insert can improve the heat transfer in a buoyancy driven compressible flow. The numerical predictions were validated using experimental data. Using different measuring tools, the global performance of the insert and the impact of the geometrical parameters are studied in order to choose the most effective design for a given application.

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.

Numerical investigations are performed into the natural convection heat transfer characteristics within a wavy-wall enclosure filled with Cu-water nanofluid. In the paper, the bottom wall of the enclosure has a wavy geometry and is maintained at a constant high temperature, while the top wall is straight and is maintained at a constant low temperature. The left and right walls of the enclosure are both straight and insulated. In performing the simulation, the Boussinesq approximation is used to model the governing equations. The study examines the effect of the nanoparticle volume fraction, the Rayleigh number, the wave amplitude, and the wavelength on the heat transfer characteristics. It is shown that the heat transfer performance can be enhanced as the volume fraction of nanoparticles increases. It is also shown that for a given Rayleigh number, the heat transfer effect can be optimized via an appropriate changing of the geometry conditions.

The development of modern technology in microelectronics and power engineering requires the creation of efficient cooling systems. This is made possible by the use of special fin technology inside the cavity or special heat transfer Ethylene glycol-copper nanofluids to intensify the heat removal from the heat-generating elements. A numerical study of the natural convection of stationary laminar heat transfers in a closed rectangular cavity with a local source of internal volumetric heat generation. For different Rayleigh numbers and different volume fractions of nanoparticles. The system of equations governing the problem was solved numerically by the fluent computer code based on the method of finite volumes. Based on the Boussinesq approximation. Interior and exterior surfaces are maintained at a constant temperature. The study is carried out for Rayleigh numbers ranging from 104 to 106. The effects of different Rayleigh numbers and volume fractions of nanoparticles on natural convection have been studied. The results are presented as isotherms, isocurrents, and local and mean Nusselt numbers. The aim of this study is to see the influence of the thermal Rayleigh number and the volume fraction of the nanoparticles on the rate of heat transfer.