Slender Enclosure Research Articles

Chemical Reaction and Internal Heating Effects on the Double Diffusive Convection in Porous Membrane Enclosures Soaked with Maxwell Fluid.

In this paper, the joint impact of the interior heating and chemical reaction on the double diffusive convective flow in porous membrane enclosures soaked by a non-Newtonian Maxwell fluid is investigated applying linear and nonlinear stability techniques. The porous enclosures are square, slender and rectangular. Using the linear stability analysis, the expression for the critical thermal Rayleigh–Darcy number, above which the convective movement occurs, is derived analytically in terms of associated physical parameters. A nonlinear stability examination reliant on the Fourier double series is executed to calculate the convective heat and mass transports of the arrangement. It is observed that the pattern of convective activity is oscillatory only in the occurrence of a relaxation parameter and the threshold value of the relaxation parameter for the occurrence of the oscillatory pattern depends on the other physical parameters. The onset of convective instability accelerates with the increasing chemical reacting parameter, the interior heating parameter, the solute Rayleigh–Darcy number, the Lewis number, the Vadasz number, and the relaxation parameter, while it delays with the heat capacity ratio. The convective heat and mass transfers increase with the solute Rayleigh–Darcy number, the Vadasz number, the relaxation parameter, and the aspect ratio (for rectangular enclosure), while it decreases with the heat capacity ratio and the aspect ratio (for slender enclosure). Additionally, the convective heat transfer enhances with the interior heating parameter, while the convective mass transfer enhances with the chemical reacting parameter and the Lewis number. The effects of Vadasz number, heat capacity ratio, and relaxation parameter are witnessed only on the oscillatory pattern of convection and unsteady convective heat and mass transfers. Further, some existing literature results are compared with the current findings.

Smoothed Particle Hydrodynamics Modeling of Natural Convection Around a Heated Horizontal Cylinder: A Comparison With Experiments

AbstractAn experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers (1.18≤Ra≤242). Both the experiments and the SPH calculations were performed for positive (0.1≤ΔT≤10 K) and negative (−10≤ΔT≤−0.1 K) temperature differences between the source and the surrounding fluid. In all cases, a pair of steady, counter-rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for ΔT>0 and a vertically descending flow just below the source for ΔT<0. The maximum flow velocities always occur within the ascending/descending plumes. The SPH predictions are found to match the experimental observations acceptably well with root-mean-square errors (RMSE) in the velocity profiles of the order of ∼10−5 m s−1. The fact that the SPH method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach.

A thermal non-equilibrium approach on thermo-solutal natural convection due to the lateral flux of heat and solute on enclosure walls: Multi-solutions and oscillations

In this paper, we address the influence of the thermal non-equilibrium state on double-diffusive convection in a porous enclosure, subject to constant heat and solute fluxes at the vertical walls, while other walls of the enclosure are adiabatic. For this, Darcy model has been adopted. The governing equations are solved numerically by the ADI method and analytically by using parallel flow assumption valid for the slender enclosure. A comparative study has been made in between buoyancy aiding flow(i.e., buoyancy ratio, N>0) and buoyancy opposed flow(i.e., buoyancy ratio, N<0). It was found that same as LTE (local thermal equilibrium) state particular oscillations and multiple solutions have also been observed on considering local thermal non-equilibrium (LTNE) state between the fluid and solid phase, for a certain range of interphase heat transfer coefficient (H) and conductivity ratio of fluid and solid (γ), when both buoyancy forces are opposite in nature (buoyancy ratio, N<0). The range of the interval for buoyancy ratio, INM, (in which multiple solutions exists) increases on increasing the value of H as well as γ, while the range of the interval for buoyancy ratio, INO, (in which oscillation exits) vary in a subtle way. In general, same as LTE state, here also INO is found to be a subset of INM for most of the values of H as well as γ considered in this study. Apart from this, in case of buoyancy aiding flow, the enhancement of aspect ratio (A) enhances the heat transfer rate for both the phases, up to a threshold value A0 of A, beyond that threshold value the impact of the same is negligible, while Sh acts in other way.

Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides: The Opposing Case

An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.

A thermal non-equilibrium approach for 2D natural convection due to lateral heat flux: Square as well as slender enclosure

This paper reports the influence of local thermal non-equilibrium state between solid porous matrix and saturated fluid on natural convection in enclosure. The two dimensional steady flow is induced by constant heat flux on side walls of the enclosure, when both horizontal walls are insulated. The governing equations are solved numerically by ADI method and analytically by using parallel flow assumption valid for slender enclosure. A comparative study has been made between convection in square cavity and the same in slender enclosure. Numerical experiments indicate that in comparison with square cavity, where a sharp decrease of local heat transfer rate for fluid (Nuf) takes place up to a certain small value of interface heat transfer coefficient (H), in slender enclosure a smooth decrease of Nuf has been observed in the entire range of H when conductivity ratio (γ) is very small. However, for relatively high values of γ (e.g., γ=10), Nuf is almost independent of H in both geometries. For a given γ, when the value of H is relatively very high, up to a certain value of Ra the difference between both solid as well as fluid temperature rates is negligible. Corresponding temperature contours of two phases becomes almost identical in magnitude as well as patterns point of view, which indicates that equilibrium state between two phases is achieved. Finally, in equilibrium state maximum heat transfer rate used to take place at a certain value (Ao) of aspect ratio, lying in between 1 and 1.5, and is almost independent of all equilibrium parameters. In case of non-equilibrium state, Ao acts as an increasing function of γ.

Constructal dendritic configuration for the radiation heating of a solid stream

Here we show that the configuration of a slender enclosure can be optimized such that the radiation heating of a stream of solid is performed with minimal fuel consumption at the global level. The solid moves longitudinally at constant rate through the enclosure. The enclosure is heated by gas burners distributed arbitrarily, in a manner that is to be determined. The total contact area for heat transfer between the hot enclosure and the cold solid is fixed. We find that minimal global fuel consumption is achieved when the longitudinal distribution of heaters is nonuniform, with more heaters near the exit than the entrance. The reduction in fuel consumption relative to when the heaters are distributed uniformly is of order 10%. Tapering the plan view (the floor) of the heating area yields an additional reduction in overall fuel consumption. The best shape is when the floor area is a slender triangle on which the cold solid enters by crossing the base. These architectural features recommend the proposal to organize the flow of the solid as a dendritic design, which enters as several branches, and exits as a single hot stream of prescribed temperature. The thermodynamics of heating is presented in modern terms in the Sec. VII (exergy destruction, entropy generation). The contribution is that to optimize “thermodynamically” is the same as reducing the consumption of fuel.

Constructal architecture for heating a stream by convection

In this paper we consider the fundamental problem of how to heat a stream to a specified exit temperature such that the overall fuel consumption is minimal. As illustration, we consider metal slabs that move at constant speed through a very slender enclosure with fixed total volume and arbitrary (nonuniform) distribution of cross-sectional area (heat transfer contact area). The heating is provided by a large number of heaters, which are distributed arbitrarily along the enclosure. The combustion gases flow in the x direction, which is oriented against the direction of the metal stream. The heat transfer is by convection. We show that minimal heat consumption is achieved when the heaters and the heat transfer contact area are distributed nonuniformly. The density of heaters per unit length must decrease as x −0.8 toward the entrance of the metal stream, and the heat transfer contact area must increase in proportion with x. These features suggest that the metal must move not as a single stream but as a tree-shaped flow. The metal enters in several parallel streams, which serve as tributaries to larger streams, leading to a single stream that exits at the specified temperature.

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

We conducted a large eddy simulation (LES) of a locally applied electromagnetic control of turbulent thermal convection of an electrically conductive fluid (electrolyte solution) inside of a slender enclosure. Generic configurations, consisting of two or three magnets of opposite polarities located below the lower wall, and two oppositely charged electrodes along the side walls, are considered. The neutral situation (pure thermal convection) is selected to be in turbulent regime at Ra = 107, Pr = 7. A magnetically extended Smagorinsky type model for the subgrid turbulent stresses and a simple-gradient diffusion model for the subgrid turbulent heat fluxes are used. Different intensities of applied DC current through electrodes are imposed. The effects of the resulting Lorentz force on flow, turbulence reorganisation and wall-heat transfer are analysed. It is demonstrated that significant flow and turbulence structure reorganisation takes place in the proximity of the lower horizontal wall and in the central parts of the enclosure—even for weak DC current of I = 1 A. Significant turbulence increase, generated by the elevated electromagnetic mixing, produced significant enhancements of the wall-heat transfer—up to 70% for the 2-magnet configuration.

THERMOGRAVITATIONAL SEPARATION IN A VERTICAL ANNULAR POROUS LAYER

We report an analytical and numerical study of the separation of the components of a binary mixture in a vertical circular porous annulus. Uniform fluxes of heat are applied on the vertical walls of the enclosure, In the formulation of the problem, use is made of the Darcy model while the density variation is taken into account by the Boussinesq approximation. The problem is solved analytically on the basis of the parallel flow, valid in the limit of a slender enclosure. Results are obtained in terms of the optimum separation conditions as a function of Rayleigh and Lewis numbers, separation parameter and the curvature parameter

Stability analysis of thermosolutal convection in a vertical packed porous enclosure

A linear stability theory is performed to investigate the stability of the quiescent state and fully developed thermosolutal convection within a vertical porous enclosure subject to horizontal opposing gradients of temperature and solute. The fluid motion is modeled using the unsteady form of Darcy’s law coupled with energy and species conservation equations. The effect of different thermal and solutal boundary conditions is considered. The linearized governing equations are solved numerically using a finite element method. The thresholds for oscillatory and stationary convection are determined as functions of the governing parameters. It is concluded that the porosity and the acceleration parameter of the porous medium have a strong effect on the onset of overstability for a confined enclosure and on the wave number for an infinite enclosure. The stability analysis of fully developed flows within a slender enclosure reveals that an increase in the porosity and the acceleration parameter of the porous media delays the appearance of oscillatory finite amplitude flows. A nonlinear numerical solution is also computed by solving the full governing equations using a finite element method. Within the overstable regime, nonlinear traveling waves exist within slender enclosures, subject to Dirichlet thermal and solutal boundary conditions.

Low-Prandtl number natural convection in volumetrically heated rectangular enclosures: II. Square cavity, AR=1

Following a previous study for a slender enclosure ( AR=4), direct numerical two-dimensional simulations were conducted for the free convective flow of a low-Prandtl number fluid ( Pr=0.0321) with internal heat generation in a square cavity having adiabatic top and bottom walls and isothermal side walls. The Grashof number, Gr, based on conductive maximum temperature and cavity width, ranged from 10 5 to 10 9. For Gr up to ∼10 7, the flow was steady and exhibited left–right symmetry. For Gr≈3×10 7, the spatial symmetry was broken and asymmetric steady-state flow patterns were obtained. For Gr≈5×10 7, the asymmetric flow became time-periodic. Finally, for Gr≥10 8, chaotic flow was predicted; the time-averaged velocity and temperature fields were still markedly asymmetric at Gr=10 8, but reattained bilateral symmetry at higher Gr (10 9), when developed two-dimensional turbulence was observed. For Grashof numbers above ∼10 6, the friction coefficient averaged along the vertical walls scaled roughly with Gr −1/3 (as in the AR=4 cavity), while the Nusselt number (overall/conductive heat transfer) increased roughly as Gr 1/7, i.e. slightly less markedly than in the slender cavity.

Thermal aspects of a vertical annular enclosure divided into a fluid region and a porous region

A numerical study was performed to analyze the natural convection fluid flow and heat transfer in a vertical annular enclosure that is partially filled with a vertical annular layer of a porous medium. The vertical boundaries of the slender enclosure were isothermal whereas the horizontal boundaries were adiabatic. The interface between the two regions was impermeable, impeding the fluid to flow from one region to the other. The flow in the porous annular layer was modeled utilizing the generalized Brinkman extended Darcy equation. A finite-volume based scheme was employed in conjunction with a coordinate transformation to numerically solve the set of conservation equations in two regions. The effects of the governing parameters (geometrical, hydrodynamical and thermal) on fluid flow and heat transfer were established. Furthermore, it was found that heat transfer suppression across the annular fluid/porous region could be minimized by filling it partially with a porous medium. Results obtained in this study are directly applicable to the analysis and design of insulation systems, such as storage tanks and vertical pipes.

Natural Convection in a Vertical Enclosure Filled With Water Near 4°C

The natural circulation of near-4°C water in a vertical cavity heated from the side was studied experimentally in a 0.74-m-tall enclosure. The results of a scale analysis were used in order to correlate the overall wall-to-wall heat transfer rate measured experimentally in the Rayleigh number range 108–1011. An analytical similarity solution was obtained for the slender enclosure limit. In that limit the flow pattern is one of incomplete vertical penetration, with stagnant maximum-density water filling the lower end of the vertical enclosure.