Particle Shape and Aspect Ratio Effect of Al2O3–Water Nanofluid on Natural Convective Heat Transfer Enhancement in Differentially Heated Square Enclosures

The present numerical investigation, based on the finite volume method, deals with the characterization of flow and thermal fields inside differentially heated square enclosures filled with Al₂O₃–water nanofluid. The study focuses on the effect of shapes and aspect ratios of nanoparticles (NPs), depicted by Rayleigh number (Ra), solid volume fraction (?), and enclosure on both flow and heat transfer enhancement. Streamlines, isotherms contours, and velocity profiles as well as the average Nusselt number are considered. Results found show that the heat transfer rate increases with Rayleigh number as well as with nanofluid volume fraction. For the six different examined cases of NPs’ aspect ratios, nanofluid with oblate spheroids NPs (d_p = 0.13) was found to engender a significant enhancement in the overall heat transfer. In addition, heat transfer rate was more pronounced at great values of aspect ratios of NPs for prolate spheroids. Results also showed that heat transfer enhancement decreases as the Rayleigh number increases independently of the considered enclosure, shapes, and aspect ratios of NPs.     

Natural convection in a vertical porous cavity filled with a non‐newtonian binary fluid

Numerical and analytical study of natural convection in a vertical porous cavity filled with a non‐Newtonian binary fluid is presented. The density variation is taken into account by the Boussinesq approximation. A power‐law model is used to characterize the non‐Newtonian fluid behavior. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. Both double‐diffusive convection (a = 0) and Soret‐induced convection (a = 1) are considered. Scale analysis is presented for the two extreme cases of heat‐driven and solute‐driven natural convection. For convection in a thin vertical layer (A ? 1), a semianalytical solution for the stream function, temperature, and solute fields, Nusselt and Sherwood numbers are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. Numerical results of the full governing equations show the effects of the governing parameters, namely the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, φ, the power‐law index, n, and the integer number a. A good agreement between the analytical predictions and the numerical simulations is obtained. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1704–1716, 2012     

Free Heat and Mass Transfer in a Porous Enclosure with Side Vents

Free heat and mass transfer during drying in a porous enclosure with free vents has been investigated numerically. Enclosed moist air interacts with the surrounding air through freely vented ports situated on both sides perpendicular to the heated wall. Air, heat, and moisture transport structures are visualized respectively by streamlines, heat lines, and mass lines. Effects of thermal Rayleigh number, Darcy number, vent location, and enclosure inclination on the convective heat/moisture transfer rate and volume flow rate across this enclosure are discussed. For each case, partially enclosed fluid flow undergoes different phases, increasing with buoyancy ratio; that is, heat transfer–driven flow, heat- and moisture-aided flow, and moisture transfer–dominated flow. Numerical results demonstrate that the convective heat and moisture transport patterns and transport rates greatly depend on thermal Rayleigh number, properties of porous medium, and enclosure inclination. Practices for enhancing heat and moisture transfer have been suggested for drying processes.     

A bifurcation study of convective heat transfer in a hele-shaw cell

Steady-state multiplicity characteristics of convective heat transfer within a Hele-Shaw cell are investigated. The Navier-Stokes equations and the energy equation are averaged across the narrow gap, d, of the cell. The resulting two-dimensional, stationary equations depend on the following parameters: (i) the length to height aspect ratio γ, (ii) the tilt anle ? (iii) the Prandtl number Pr, (iv) an inertia parameter ξ = d²/ 12a², and (v) the Grashof number. Gr = Q_gβga⁵/kv². Here a is the height of the cell and Q, is the heat generation rate per unit volume. The complete structure of symmetric and asymmetric stationary solutions are traced using recent algorithms from bifurcation theory. In the double limit of ξ → 0 and Gr → ∞ such that Ra = 4GrPrξ remains finite (where Ra is the Rayleigh number for the Darcy model) the Hele-Shaw model reduces to that of the Darcy model.     

Finite element analysis of natural convection in a triangular enclosure: Effects of various thermal boundary conditions

The phenomena of natural convection in a right-angled triangular enclosure is studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier-Stokes and energy balance equations. The detailed study is carried out in two cases depending on various thermal boundary conditions:

(a)

Vertical wall is uniformly or linearly heated while inclined wall is cold isothermal.

(b)

Inclined wall is uniformly or linearly heated while vertical wall is cold isothermal.

In all the cases horizontal bottom wall is adiabatic and the aspect ratio of the lengths of base and height is considered to be one. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Rayleigh number Ra(10³?Ra?10⁵) and Prandtl number Pr(0.07?Pr?1000) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It has been found that at low Rayleigh numbers (Ra?10⁴), the isotherms are almost parallel near the bottom portion of the triangular enclosure while at Ra=10⁵, the isotherms are more distorted. This is because the heat transfer is primarily due to conduction for lower values of Rayleigh number. As Rayleigh number increases, there is a change from conduction dominant region to convection dominant region, and the critical Rayleigh number corresponding to on-set of convection is obtained. It has been shown that the average Nusselt number for vertical wall is times that of the inclined wall as the bottom wall is adiabatic and that verifies the thermal equilibrium of the system for all case studies.     

Analysis of heat recovery and thermal transport within entrapped fluid based on heatline approach

The wide applications of indirect heating and cooling processes have opened scope for various researchers to explore in-depth analysis and applications of systems involving heat exchange processes. This paper targets the analysis and visualization of heat transfer in entrapped triangular cavities within adjacent square tubes forming a system of practical application especially in pollution control with hot fluid flowing through the stack and entrapped cold fluid confined within the triangular cavities. Also, efficient heat recovery has been examined for the entrapped fluid in the system. The parameters for this study are the Prandtl number (Pr), Rayleigh number (Ra) and Nusselt number (Nu). Complete details of heating patterns in both triangular cavities have been analyzed with heatline approach for visualization of heat flow. At low Rayleigh number, it is found that the heatlines are smooth and perfectly normal to the isotherms indicating the dominance of conduction for both the triangles. But as Ra increases, flow slowly becomes convection dominant. Multiple secondary circulations within the upper triangle are formed for fluids with low Pr, whereas this is absent in higher Pr fluids. Multiple circulation cells for smaller Pr also correspond to multiple cells of heatlines which illustrate less thermal energy transport from hot wall. On the other hand, the dense heatlines at bottom wall display enhanced heat transport for larger Pr. But interestingly for lower triangle there is hardly any variation of patterns with the increase in Prandtl number in the system. Analysis is concluded with the average Nusselt number plots. It is found that fluid with higher Pr may be recommended for upper triangle, but fluid with all ranges of Pr may be used for lower triangle.     

Natural convection and flow simulation in differentially heated isosceles triangular enclosures filled with porous medium

A finite element analysis is performed to investigate the effects of uniform and non-uniform heating of bottom wall on natural convection flows within isosceles triangular enclosures filled with porous medium. The detailed analysis is carried out in two cases depending on various thermal boundary conditions:

(I)

two inclined walls are maintained at constant cold temperature while the bottom wall is uniformly heated;

(II)

two inclined walls are maintained at constant cold temperature while the bottom wall is non-uniformly heated.

The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Darcy number, Da (10^-5?Da?10^-3), Rayleigh number, Ra (10³?Ra?10⁶) and Prandtl number, Pr (0.026?Pr?1000) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It is observed that at small Darcy numbers, the heat transfer is primarily due to conduction irrespective of Pr. As the Darcy number increases, there is a change from conduction dominant regime to convection dominant regime. Flow circulations are also found to be strong functions of Pr at large Da (Da=10^-3) and multiple circulation cells occur at small Pr with Ra=10⁶. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case, but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. As average Nusselt number is same on both the inclined walls, the average Nusselt number for bottom wall is times that of the inclined wall which is well matched in two cases considered for verifying the thermal equilibrium of the system. The correlations are proposed for average Nusselt number as functions of Ra for various Darcy and Prandtl numbers.     

Onset of solutal convection in liquid phase epitaxy system

The onset of convective instability in the liquid phase epitaxy system is analyzed with linear stability theory. New stability equations are derived under the propagation theory, and the dimensionless critical time τ _c to mark the onset of the buoyancy-driven convection is obtained numerically. It is here found that the critical Rayleigh number Ra _c is 8000, below which the flow is unconditionally stable. For Ra>Ra _c the dimensionless critical time τ _c to mark the onset of a fastest growing instability is presented as a function of the Rayleigh number and the Schmidt number. Available numerical simulation results and theoretical predictions show that the manifest convection occurs starting from a certain time τ _o (> τ _c ). It seems that during τ _c ≤τ≤τ _o secondary motion is relatively very weak. This article is dedicated to Professor Chang Kyun Choi for celebrating his retirement from the School of Chemical and Biological Engineering, Seoul National University.     

含相变颗粒流体的Rayleigh-Benard对流热启动

引　言含固液相变颗粒的乳胶液流体是一种混合物质的复杂流体,这种流体在化工、空调等工业领域有较好的应用潜力,近年来对它的研究比较活跃[1～3] .人们把在一定温度范围内的潜热变化归结为表观比热容或有效比热容.在相变温度范围内,由于热物性的剧烈变化,对流换热的机理研究也就显得十分必要.而Rayleigh Bnard对流问题是一个经典的复杂物理现象,它是指上下分别有固体冷却和加热面的自然对流问题.在重力场内,对水平放置的流体层,这种传热方式没有自然对流存在的充分条件,只有超过一定的临界状态时自然对流才会发生.由于这一问题也涉及到…     

Effect of non‐isothermal condition on heterogeneous flow through biofilter media by lattice Boltzmann simulation

BACKGROUND: Biofiltration technology has received much attention due to its effectiveness, low cost and environment friendly properties. It is used to remove odors caused chiefly by hydrogen sulfide (H2S) via biological treatments. RESULTS: In this study, numerical simulations using the thermal lattice Boltzmann method are implemented to investigate the effect of non‐isothermal conditions on heterogeneous flow through three biofilter models that are partly filled with porous media. The generalized Navier–Stokes model based on the Brinkman‐Forchheimer–extended Darcy model is used to make several assumptions. CONCLUSIONS: The numerical results indicate that the Rayleigh number has significant influence on the removal efficiencies of biofilters. There also exist critical Rayleigh numbers for biofilters under non‐isothermal conditions. If the Rayleigh number is less than the critical value, the flow heterogeneity will reduce with increasing Rayleigh number; otherwise, the flow heterogeneity will enhance with increasing Rayleigh number. Moreover, it was found that the performances of biofilters can be improved by designing non‐isothermal conditions between the porous media layers, i.e. by adjusting the Rayleigh number to optimize the detention time of waste air. © 2012 Society of Chemical Industry     

Numerical simulation of natural convection in a square enclosure filled with nanofluid using the two-phase Lattice Boltzmann method

Considering interaction forces (gravity and buoyancy force, drag force, interaction potential force, and Brownian force) between nanoparticles and a base fluid, a two-phase Lattice Boltzmann model for natural convection of nanofluid is developed in this work. It is applied to investigate the natural convection in a square enclosure (the left wall is kept at a high constant temperature (T_H), and the top wall is kept at a low constant temperature (T_C)) filled with Al₂O₃/H₂O nanofluid. This model is validated by comparing numerical results with published results, and a satisfactory agreement is shown between them. The effects of different nanoparticle fractions and Rayleigh numbers on natural convection heat transfer of nanofluid are investigated. It is found that the average Nusselt number of the enclosure increases with increasing nanoparticle volume fraction and increases more rapidly at a high Rayleigh number. Also, the effects of forces on nanoparticle volume fraction distribution in the square enclosure are studied in this paper. It is found that the driving force of the temperature difference has the biggest effect on nanoparticle volume fraction distribution. In addition, the effects of interaction forces on flow and heat transfer are investigated. It is found that Brownian force, interaction potential force, and gravity-buoyancy force have positive effects on the enhancement of natural convective heat transfer, while drag force has a negative effect.     

Thermal instability of plane poiseuille flow in the thermal entrance region

The onset of thermal convection in plane Poiseuille flow is investigated theoretically. New stability equations are derived by using the propagation theory considering the variations of disturbance amplitudes in the main flow direction. In the thermal entrance region an analytical procedure to predict the critical conditions for extremely small Prandtl-number fluids is described, based on the local similarity. For x_c≤0.01 the critical Rayleigh numbers are well represented in the whole domain of the Prandtl number by Ra_c = 200(1 + 0.123Pr^-1)Ra _C =200(1+0.123Pr⁻¹)x _C ⁻¹ under the conventional boundary layer theory. It is of much interest that the time-independent, three dimensional disturbances become more stable with a decrease in the Prandil number.     

EFFECTS OF SURFACE TENSION ON LAMINAR FILMWISE CONDENSATION ON A HORIZONTAL PLATE IN A POROUS MEDIUM WITH SUCTION AT THE WALL

The problem of two-dimensional, steady-state film condensation on an isothermal finite-size horizontal plate embedded in a porous medium is studied for the case in which the plate faces upward into a region of dry saturated vapor. Due to surface tension effects, a two-phase zone is formed between the liquid film on the horizontal plate and the vapor zone. The effects of surface tension are shown to reduce the thickness of the liquid film and hence to increase the heat transfer performance of the horizontal plate. Furthermore, the results show that the dimensionless heat transfer coefficient depends on the Darcy number Da, the Jacob number Ja, the effective Rayleigh number Ra_e, the effective Prandtl number Pr_e, the wall suction parameter Sw, and the surface tension parameter Bo_c. When the surface tension effects are neglected and there is no suction at the wall, a closed-form correlation for the Nusselt number can be established.     

Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two‐dimensional non‐Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear‐coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non‐dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction. © 2011 Canadian Society for Chemical Engineering     

Experimental Investigation of Convective Heat Transfer Between Silicon-Melt and Solidification Front

Convective heat transfer between silicon melt and solidification front during Bridgman-type solidification process in a ceramic crucible has been investigated by means of heat balance analysis of the crucible during the process. The effect of aspect ratio on the Rayleigh and Nusselt numbers has been investigated. For a large crucible size (with inner diameter of about 0.50-m), the dependence correlates well with the empiric formula Nu?=?0.303 Ra^0.279. For a small crucible size (with inner diameter of about 0.20-m), the dependence correlates well with the empiric formula Nu?=?0.181 Ra^0.285. The experimental data obtained were compared with the available literature experimental and numerical simulation data.

     

Onset of buoyancy-driven convection in the horizontal fluid layer heated from below with time-dependent manner

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with time-dependent manner is analyzed by using propagation theory. Here the dimensionless critical time Τ_c to mark the onset of convective instability is presented as a function of the Rayleigh number Ra_Ø and the Prandtl number Pr. The present stability analysis predicts that Τ_c decreases with increasing Pr for a given Ra_Ø. The present predictions compare reasonably well with existing experimental results. It is found that in deep-pool systems the deviation of temperature profiles from conduction state occurs starting from a certain time Τ?(2～4) Τ_c .     

Natural convection in a heat generating fluid bounded by two horizontal concentric cylinders

Convective flow and heat transfer of a Boussinesq fluid contained between two horizontal concentric cylinders is investigated under the effects of two driving mechanisms – an externally-imposed temperature gradient across the annulus, and a uniform internal heat generation. Numerical results for flow field and temperature distribution are obtained in terms of four dimensionless parameters, namely the radius ratio, R, the Prandtl number, Pr, the Rayleigh number, Ra*, and the ratio, S, between the characteristic temperature induced by internal heating and the applied temperature difference between the boundaries. Depending on the value of S, the flow pattern is made up of either one or two vortices in each half cavity, and heat is transferred into or out of the cavity through the hot wall. In particular, for a certain value of the applied temperature difference, the hot wall apparently acts as a thermally-insulated boundary, the internal heat is completely lost through the cold wall, and the fluid undergoes a transition from a bicellular to a unicellular flow regime.     

Power‐Law Fluid Flow Over a Sphere: Average Shear Rate and Drag Coefficient

Based on the consideration of the rate of mechanical energy dissipation, an expression for the average shear rate for a sphere falling in a power‐law fluid in the creeping flow regime has been deduced. The average shear rate in a power‐law fluid (n<1) appears to be higher than that in an equivalent Newtonian fluid. This in turn has been combined with the numerical predictions of drag coefficient (up to Reynolds number of 100) of a sphere to develop a generalized drag correlation for power‐law liquids encompassing both n > 1 and n < 1 which appears to apply up to much higher values of the Reynolds number. The available experimental data have been used to demonstrate the reliability and accuracy of the new correlation for shearthinning liquids. Also, in the limit of n = 1, this expression reproduces the standard drag curve with a very high accuracy.     

Fully developed mixed convection of a binary fluid in a vertical porous channel

This paper reports an analytical and numerical study of mixed convection heat and mass transfer of a binary fluid in a vertical parallel plate channel filled with a porous medium. The thermal conditions applied on the walls of the system are uniform heat fluxes. Both the cases of double‐diffusion and Soret‐induced convection are considered. The governing equations for the porous medium rely on Darcy's model. The governing parameters for the problem are the Rayleigh number, Ra, Peclet number, Pe, Lewis number, Le, buoyancy ratio, φ, aspect ratio of the channel $A = L'/H'$ and the constant a (a = 0 for double diffusive convection and a = 1 for Soret induced convection). The resulting problem, in the limit of fully developed mixed convection, is solved analytically in closed form. A numerical solution of the full governing equations is demonstrated to be in good agreement with the analytical model. The temperature and velocity fields and the Nusselt and Sherwood numbers are obtained in terms of the governing parameters. The possible existence of reversed flows in the channel is discussed. © 2011 Canadian Society for Chemical Engineering     

Insight into C35 terpene Biosyntheses by Nonpathogenic Mycobacterium Species: Functional Analyses of Three Z‐Prenyltransferases and Identification of Dehydroheptaprenylcyclines

Nonpathogenic Mycobacterium species produce rare cyclic C₃₅ terpenes that are biosynthesized by cyclization of Z‐type C₃₅ polyprenyl diphosphate. To provide deeper insight into the biosynthesis of C₃₅ terpenes, we carried out functional analyses of three Z‐prenyltransferase homologues in M. vanbaalenii identified by genomic analysis. Mvan_3822, a novel bifunctional Z‐prenyltransferase, biosynthesizes C₃₅‐heptaprenyl diphosphate as a main product from (E,E)‐farnesyl diphosphate (E,E‐FPP) and (E,E,E)‐geranylgeranyl diphosphate (E,E,E‐GGPP), but produces a C₅₀‐decaprenyl diphosphate from geranyl diphosphate. Mvan_1705 is a novel Z,E,E‐GGPP synthase. In addition, novel cyclic C₃₅ terpenes, (14E)‐ and (14Z)‐dehydroheptaprenylcycline, were identified as minor metabolites in nonpathogenic Mycobacterium cells. C₃₅ terpenes could be biosynthesized by two routes, in which E and Z geometric isomers of heptaprenyl diphosphate are produced from E,E‐FPP and E,E,E‐GGPP, and the prenylreductase responsible for the biosynthesis of C₃₅ terpenes could reduce both E and Z prenyl residues.