Effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls

We examined the effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non‐dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20319     

Effects of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls

This paper describes the effect of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls numerically and experimentally. In the numerical analysis, fluid flow and temperature distributions for Ri=1.61, Pr=6.99, Re=100 and aspect ratio, Ar=0.2–10, were obtained by solving dimensionless governing equations using the SIMPLE procedure. The QUICK scheme was applied to the convective term of these equations. In the experimental analysis, the flow behavior for A_r=0.5–2 was visualized by the dye‐injection method. Numerical results showed that the swirl flow was generated along the flow direction, and its pitch length was influenced by A_r. The pitch length was the shortest when A_r=0.5–1, and this tendency was the same in numerical results and experimental results. The heat transfer behavior was also discussed corresponding to the flow, and the heat transfer ratio was highest at A_r=1 in 0.2 ≤ A_r ≤ 10. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20391     

Heat transfer augmentation in developing flow through a ribbed square duct

An experimental study is conducted to investigate the heat transfer augmentation in developing turbulent flowthrough a ribbed square duct.The duct is made of 16mm thick bakelite sheet.The bottom surface of the ribbedwall having rib pitch to height ratio of 10 is heated by passing a c current to the heater placed under it.Theuniform heating is controlled using a digital temperature controller and a variac.The results of ribbed duct arecompared with the results of a smooth duct under the same experimental conditions.It is observed that the heattransfer augmentation in ribbed duct is better than that of the smooth duct.At Re=5.0×10~4,the meantemperature of air flowing through the ribbed duct increases by 2.45 percent over the smooth duct,whereas in theribbed duct Nusselt number increases by 15.14 percent than that of the smooth duct with a 6 percent increase inpressure drop.     

Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity

Conjugate effect of joule heating and magnetic force, acting normal to the left vertical wall of an obstructed lid-driven cavity saturated with an electrically conducting fluid have been investigated numerically. The cavity is heated from the right vertical wall isothermally. Temperature of the left vertical wall, which has constant flow speed, is lower than that of the right vertical wall. Horizontal walls of the cavity are adiabatic. The physical problem is represented mathematically by sets of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. To see the effects of the presence of an obstacle on magnetohydrodenamic mixed convection in the cavity, we considered the cases of with and without obstacle for different values of Ri varying in the range 0.0 to 5.0. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the magnetic parameter, Ha and Joule heating parameter J. The results showed that the obstacle has significant effects on the flow field at the pure mixed convection region and on the thermal field at the pure forced convection region. It is also found that the parameters Ha and J have notable effect on flow fields; temperature distributions and heat transfer in the cavity. Numerical values of average Nusselt number for different values of the aforementioned parameters have been presented in tabular form.     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

Enhancement of convection heat-transfer in a rectangular duct

Characteristics of wall-to-air heat transfer for a fully developed forced convection have been studied in a large rectangular packed duct with 160 cm heated length, 40 cm width, and for low bed equivalent diameter to particle diameter ratio. The separation distance between the top and bottom walls is 10 cm. A uniform heat flux is supplied at the top wall, while the bottom wall is insulated. Raschig rings in two and spherical packing in three sizes have been used in the air flow passage to investigate the enhancement of heat transfer due to packing. Temperature profiles for the steady and unsteady states have been measured. In modeling, the Ergun equation and energy equations are solved to calculate the temperature profile for the steady-state only. It has been found that the introduction of the packing into the air flow passage increases the wall-to-fluid heat transfer approximately three times compared with that of empty bed. This finding can enhance the rational use of energy from solar air heaters, chemical reactors, electronic cooling and many other engineering applications.     

Fully developed mixed convection and flow reversal in a vertical rectangular duct with uniform wall heat flux

Combined forced and free flow in a vertical rectangular duct is investigated for laminar and fully developed regime. The velocity field, the temperature field, the friction factor and the Nusselt number are evaluated analytically by employing finite Fourier transforms. The thermal boundary condition considered is an axially uniform wall heat flux and a peripherally uniform wall temperature, i.e. an H1 boundary condition. The necessary and sufficient condition for the onset of flow reversal is determined either in the case of upward flow in a cooled duct or in the case of downward flow in a heated duct. The special case of free convection, i.e. the case of a purely buoyancy-driven flow, is discussed. The occurrence of effects of pre-heating or pre-cooling in the fluid is analysed. It is pointed out that although these effects occur in rectangular ducts, they are not present either in circular ducts or in parallel-plate channels.     

Heat transfer enhancement for laminar flow of ethylene glycol through a square duct fitted with increasing and decreasing orders of twisted tape

The isothermal friction factor and heat transfer enhancement through a square duct fitted with increasing and decreasing order of twist ratio sets have been studied under nearly uniform wall temperature conditions. The ethylene glycol flows under laminar flow (Re = 30–1200) through a square duct and hot water flows through an annular channel formed between a square duct and circular tube, in a counter current fashion. The hot water at a very high flow rate is circulated though the annular channel to ensure a nearly uniform wall temperature condition. There is not much change in the magnitude of the heat transfer coefficient enhancement with the increasing twist ratio and with the decreasing twist ratio set, as the intensity of the swirl generated at the inlet or at the outlet in the order of increasing twist ratio or decreasing twist ratio, is the same in both the cases. Performance evaluation analysis on constant pumping power was made and a maximum performance ratio was obtained for each twist insert corresponding to a Reynolds number of 680. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20410     

水平矩形管中气固两相流的PDA实验研究

应用三维颗粒动态分析仪(3D-PDA)对方形水平管道内的气固两相流进行了测试。实验采用的颗粒为玻璃微珠,对不同工况下的水平方向(主流方向)的平均速度和湍流强度进行了讨论。发现在垂直截面上的速度分布呈上部高而下部低的分布特点,且随平均风速、颗粒体积分数和粒径的增大这种不均匀分布有加剧的趋势。湍流强度中心位置较低,而靠近壁面的位置较高,尤其是底部湍流强度更大一些。在大部分位置颗粒相的速度滞后于气相,在边壁附近特别是底部壁面附近颗粒速度较气相速度稍大。颗粒体积分数沿垂直方向上分布较均匀,越靠近壁面颗粒体积分数越高,在管道的底部和垂直壁面的交角附近颗粒体积分数最高。     

Fluid flow and heat transfer of mixed convection adjacent to vertical heated plates placed in uniform horizontal flow of air

Experiments have been carried out for mixed convective flows of air adjacent to the vertical heated plates in uniform horizontal forced flows to investigate relationships between the flow and the heat transfer. The experiments cover the ranges of the Reynolds and modified Rayleigh numbers: Re_L = 160 to 2300 and Ra_L^* = 4.3 × 10⁵ to 2.0 × 10⁸. The flow fields over the plates are visualized with particles and smoke. The results show that a stagnation point moves downward away from the center of the plate when the surface heat flux is beyond a critical value. The condition where the stagnation point begins to move is expressed with non‐dimensional parameters as: Gr_L^*/Re_L^2.5 = 0.15. Profiles of measured local heat transfer coefficients are smooth even at the stagnation points in all the cases examined. When buoyancy effect is sufficiently weak, the coefficients agree well with those of the wedge flow. With increasing the surface heat flux, the coefficients are augmented to approach asymptotically the boundary layer solution of natural convection along a vertical heated plate. Finally, forced, mixed, and natural convection regimes are classified by the non‐dimensional parameter (Gr_L^*/Re_L^2.5). © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20256     

Heat transfer enhancement for combined convection flow of nanofluids in a vertical rectangular duct considering radiation effects

In this paper, combined convective heat transfer and nanofluids flow characteristics in a vertical rectangular duct are numerically investigated. This investigation covers Rayleigh numbers in the range of 2 × 10⁶ ≤ Ra ≤ 2 × 10⁷ and Reynolds numbers in the range of 200 ≤ Re ≤ 1000. Pure water and five different types of nanofluids such as Ag, Au, CuO, diamond, and SiO₂ with a volume fraction range of 0.5% ≤ φ ≤ 3% are used. The three‐dimensional steady, laminar flow, and heat transfer governing equations are solved using finite volume method (FVM). The effects of Rayleigh number, Reynolds number, nanofluids type, nanoparticle volume fraction of nano‐ fluids, and effect of radiation on the thermal and flow fields are examined. It is found that the heat transfer is enhanced using nanofluids by 47% when compared with water. The Nusselt number increases as the Reynolds number and Rayleigh number increase and aspect ratio decreases. A SiO₂ nanofluid has the highest Nusselt number and highest wall shear stress while the Au nanofluid has the lowest Nusselt number and lowest wall shear stress. The results also revealed that the wall shear stress increases as Reynolds number increases, aspect ratio decreases, and nanoparticle volume fraction increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20354     

Heat transfer enhancement of free convection from a heated horizontal plate

A device was developed to enhance heat transfer from heated horizontal plates. The device consists of six straight gutters with slits at the center for the introduction of air. Heat transfer coefficients were measured for several device heights above the heated surface. A height of about 10 mm was found to give rise to the highest heat transfer coefficients. In this case heat transfer rates were 1.2 to 1.4 times larger than those for smooth plates. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 26 (1): 30–38, 1997     

Internal gravity wave resonance of thermal convection fields in a square cavity with heat‐flux vibration

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat‐flux vibration were numerically investigated. As the angular velocity ω is changed, the thermal convection field at Pr = 0.71,Ra = 10⁶ is found to be classified into 5 regions. In particular, the field has the local maximum relative amplitude of midplane Nusselt's number at ω_c = 350, which corresponds to the angular velocity of internal gravity wave ω_r estimated by a theoretical equation proposed by Thorpe. This shows that the local enhancement is induced by internal gravity wave resonance. Such correspondence is observed for Ra ≥ 10⁵,Ra ≥ 10⁶ for Pr = 0.71, 7.1, respectively. For these ranges of Ra we propose a correlation equation, a function of Pr and Gr only, to estimate the resonant angular velocity. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 309–322, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20122     

Time-periodic laminar mixed convection in an inclined channel

The steady-periodic regime of laminar mixed convection in an inclined channel is studied analytically, with the following boundary conditions: the temperature of one channel wall is stationary, while the temperature of the other wall is a sinusoidal function of time. Analytical expressions of the velocity field, of the temperature field, of the pressure drop, of the friction factors, as well as of the Nusselt number at any plane parallel to the walls are determined. It is found that, for every value of the Prandtl number greater than 0.277, there exists a resonance frequency which maximizes the amplitude of the friction factor oscillations at the unsteady-temperature wall. Moreover, for any plane which lies between the midplane of the channel and the unsteady-temperature wall, every value of the Prandtl number yields a resonance frequency which maximizes the amplitude of the Nusselt number oscillations.     

Convective heat transfer to water near the critical region in a horizontal square duct

Numerical analysis has been carried out to investigate forced convective heat transfer to water near the critical region in a horizontal square duct. Near the critical point convective heat transfer in the duct is strongly coupled with large variation of thermophysical properties such as density and specific heat. Buoyancy force parameter has also severe variation with fluid temperature and pressure in the duct. There is flow acceleration along the horizontal duct resulted from fluid density decrease due to the heat transfer from the wall. Local heat transfer coefficient has large variation along the inner surface of the duct section and it depends on pressure. Nusselt number on the center of the bottom surface also has a peak where bulk fluid temperature is higher than the pseudocritical temperature and the peak decreases with the increase of pressure. Flow characteristics of velocity, temperature, and local heat transfer coefficient with water properties are presented and analyzed. Nusselt number distributions are also compared with other correlations for various pressures in the duct.     

Forced turbulent heat convection in a square duct with non-uniform wall temperature

In the present work, the numerical simulation to calculate the problem of the turbulent convection with non-uniform wall temperature in a square cross-section duct was adopted. To solve this problem some assumptions for the flow, such as: the condition of fully developed turbulence and incompressible flow have been assumed. The methodology of the dimensionless energy equation was used to calculate the fluid temperature field in the square cross-section in function of the non-uniform wall temperatures prescribed. Numerical simulations were done using two different turbulent models to resolve the momentum equations and two more models to resolve the energy equation. The models of turbulence k-ε Nonlinear Eddy Viscosity Model (NLEVM) and the Reynolds Stress Model (RSM) were used to determine the turbulent intensities as well as the profiles of axial and secondary mean velocities. The turbulence model RSM was simulated using a commercial software. The thermal field was determined from other two models: Simple Eddy Diffusivity (SED), based in the hypothesis of the constant turbulent Prandtl number; and Generalized Gradient Diffusion Hypothesis (GGDH). In this last model, as the turbulent heat transfer depends on the shear tensions, the anisotropy is considered. These two last equation models of the energy equation of the fluid have been implemented in FORTRAN, a code of programming. The performances of the models were evaluated by validating them based in the experimental and numerical results published in the literature. Two important parameters of great interest in engineering are presented: the friction factor and the Nusselt number. The results of this investigation allow the evaluation of the behavior of the turbulent flow and convective heat fluxes for different square cross-sectional sections throughout the direction of the main flow, which is mainly influenced by the temperature distribution in the wall.     

Mixed convection within a porous heat generating horizontal annulus

A numerical investigation of mixed convection in a horizontal annulus filled with a uniform fluid-saturated porous medium in the presence of internal heat generation is carried out. The inner cylinder is heated while the outer cylinder is cooled. The forced flow is induced by the cold outer cylinder rotating at a constant angular velocity. The flow field is modeled using a generalized form of the momentum equation that accounts for the presence of porous medium viscous, Darcian and inertial effects. Discretization of the governing equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previous works are performed and the results show excellent agreement. The effects of pertinent parameters such as the internal Rayleigh number, the Darcy number, the annulus gap, and the Richardson number on the flow and heat transfer characteristics are considered in the present study. The obtained results depict that the Richardson number plays a significant role on the heat transfer characterization within the annulus. The present results show that an increase in Reynolds number has a significant effect on the flow patterns within the annulus with respect to two-eddy, one-eddy and no-eddy flows. Categorization of the flow regimes according to the number of eddies is established on the Ra-Re plane for various Rayleigh numbers.     

Thermal convection for a thermo-dependent yield stress fluid in an axisymmetric horizontal duct

This paper deals with the combined forced and free convection heat transfer of a yield stress fluid in a horizontal duct heated uniformly with a constant heat flux density. It is assumed that (i) the rheological behavior of the fluid can be described by the Herschel–Bulkley model and that the consistency K* varies with temperature T*, as K* = a exp(−bT*); (ii) the variation of the fluid density ρ, with temperature, , is considered important only in the buoyancy term and (iii) the Péclet number is sufficiently large so that it is possible to resort to an asymptotic solution. The aim of this study is to quantify the effect of the rheological properties on the magnitude of the secondary flows induced by the thermo-dependency of K* and ρ. Expressions for local Nusselt number and wall shear stress are given. Finally, to be consistent with the variation along the duct of the axial velocity in the central zone around the axis, due to the thermo-dependency of K* or ρ, the pseudo-plug zone and pseudo-yield surface notions are introduced. Some characteristics of the stresses distribution within the pseudo-plug zone are discussed.     

Flow visualization of natural convection in a vertical channel with asymmetric heating

A dynamical study of the flow in an asymmetrically heated vertical plane channel has been conducted experimentally. Experiments were carried out in water for three aspect ratios and for a range of modified Rayleigh numbers corresponding to the boundary layer flow regime. The flow dynamics were characterized by means of visualization techniques based on laser tomography using discrete and continuous tracers. Flow visualizations were carried out in the plane of symmetry of the channel along its entire height. The investigations focused more specifically on the influence of the aspect ratio and the modified Rayleigh number on the flow structure both in steady-state regime and during the transitional phase occurring just after the start of the heating. An upward boundary layer flow is found near the heated wall, accompanied by a reverse flow developing on the opposite side from the top open-end of the channel. In steady state, the reverse flow takes the form of an elongated eight-shaped structure with two main recirculation cells. The length of the upper cell of the eight-shape structure decreases with increasing aspect ratio. For a fixed aspect ratio, the increase in modified Rayleigh number results in a decrease in the penetration of the reverse flow. During the transient the flow structure is shown to evolve from a single cell to a final eight-shaped structure.