Natural Convection in a Porous Cavity with Sinusoidal Heating on Both Sidewalls

A numerical study has been performed on buoyancy-induced convection in a square porous cavity. The vertical sidewalls of the cavity are maintained with sinusoidal temperature distribution. The finite volume method is used to numerically solve the nondimensional governing equations. The Brinkman Forchheimer extended Darcy model is used in the present study. The results are analyzed over a range of the amplitude ratio, phase deviation, porosity, and Grashof and Darcy numbers. It is found that the heat transfer rate is increased when increasing the amplitude ratio, porosity, and Darcy number. The nonuniform heating on both sidewalls provides higher heat transfer rate than the nonuniform heating of one wall.     

Magnetoconvection in a Square Enclosure with Sinusoidal Temperature Distributions on Both Side Walls

A computational study of convective flow and heat transfer in a cavity in the presence of uniform magnetic field is carried out. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. The governing equations are solved by the finite volume method. The results are discussed for different combinations of phase deviation, amplitude ratio, and Hartmann and Rayleigh numbers. It is observed that the heat transfer rate is increased with amplitude ratio. The heat transfer rate is increased first and then decreased on increasing the phase deviation. It is also found that the heat transfer rate is decreased with an increasing Hartmann number.     

Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls

Mixed convection in a square cavity of sinusoidal boundary temperatures at the sidewalls in the presence of magnetic field is investigated numerically. The horizontal walls of the cavity are adiabatic. The governing equations are solved by finite-volume method. The results are obtained for various combinations of amplitude ratio, phase deviation, Richardson number, and Hartmann number. The heat transfer rate increases with the phase deviation up to ? = π/2 and then it decreases for further increase in the phase deviation. The heat transfer rate increases on increasing the amplitude ratio. The flow behavior and heat transfer rate inside the cavity are strongly affected by the presence of the magnetic field.     

Comparison of Mixed Convection in a Square Cavity with an Oscillating versus a Constant Velocity Wall

This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.     

Experimental and numerical investigation of the melting process and heat transfer characteristics of multiple phase change materials

The melting and heat transfer characteristics of multiple phase change materials (PCMs) are investigated both experimentally and numerically. Multiple PCMs, which consist of three PCMs with different melting points, are filled into a rectangle-shaped cavity to serve as heat storage unit. One side of the cavity is set as heating wall. The melting rate of multiple PCMs was recorded experimentally and compared with that of single PCM for different heating temperatures. A two-dimensional mathematical model to describe the phase change heat transfer was developed and verified experimentally. The properties of multiple PCMs, including the effect of the melting point difference (combined type), thermal conductivity, and latent heat, on the heat transfer performance of the PCM were analyzed numerically. The results show that, the melting time decreases before it increases, with an increasing melting point difference for the multiple PCMs. In addition, the melting point decreases with increasing distance from the heating wall. Most of these types of multiple PCMs melt faster than the single PCM, and the multiple PCMs, with the melting point arranged as 322 K/313 K/304 K, has the shortest melting time in this study. The melting rate of the multiple PCMs, 322 K/313 K/304 K, accelerates faster than for the single PCM as the thermal conductivity, latent heat, and heating wall temperature increase. Finally, generalized results are obtained using a dimensionless analysis for both single and multiple PCMs.     

Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure

In this paper, numerical simulations of laminar, steady, two-dimensional natural convection flows in a square enclosure with discrete heat sources on the left and bottom walls are presented using a finite-volume method. Two different orientated wall boundary conditions are designed to investigate the natural convection features. The computational results are expressed in the form of streamlines and isothermal lines for Rayleigh numbers ranging from 10² to 10⁷ in the cavity. In the course of study, a combination of third-order and exponential interpolating profile based on the convective boundedness criterion is proposed and tested against the partially heated cavity flow up to the highest Rayleigh number 10⁷. The effects of thermal strength and heating length on the hydrodynamic and thermal fields inside the enclosure are also presented. Numerical results indicate that the average Nusselt number increases as Rayleigh number increases for both cases. Moreover, it is seen that the effect of the heat transfer rate due to the heating strength on the left wall is different from the one on the bottom. For the heater size effect, it is observed that by increasing the length of heat source segment, the heat transfer rate is gradually increased for both cases.     

Numerical Studies on Natural Convection in a Trapezoidal Enclosure With Discrete Heating

Abstract

A steady state laminar natural convection flow in a trapezoidal enclosure with discretely heated bottom wall, adiabatic top wall, and constant temperature cold inclined walls is performed. The finite volume based commercial code “ANSYS-FLUENT” is used to investigate the influence of discrete heating on natural convection flows in a trapezoidal cavity. The numerical solution of the problem covers various Rayleigh numbers ranging from 10³ to 10⁶, non-dimensional heating length ranging from 0.2 to 0.8 and Prandtl number is 0.7. The performance of the present numerical approach is represented in the form of streamfunction, temperature profile and Nusselt number. Heat transfer increases with increase of Rayleigh numbers at the corners of the cavity for same heating length from center of the bottom wall. However, the heat transfer rate is less and almost constant for the Rayleigh numbers considered. It is found that the average Nusselt number monotonically increases with increase of Rayleigh number and length of heat source. The variation of local and average Nusselt numbers is more significant for larger length of heating than smaller one. The heat transfer correlations useful for practical design problems have been predicted.     

Lattice Boltzmann simulation of mixed convection heat transfer in a corrugated wall cavity utilizing water‐based nanofluids

In the present study, the effects of Cu and CuO nanoparticles' presence on mixed convection heat transfer in a lid‐driven cavity with a corrugated wall are investigated using the lattice Boltzmann method. The boundary fitting method with second‐order accuracy at both velocity and temperature fields is used to simulate the curved boundaries in the LBM. The problem is investigated for different Richardson numbers (0.1–10), volume fractions of nanoparticles (0–0.05), curve amplitudes (0.05–0.25), and phase shifts of corrugated wall (0–270) when the Reynolds number is equal to 25. The volume fraction of added nanoparticles to the water‐based fluid is less than 0.05 to make dilute suspensions. Results show that adding nanoparticles enhances the rate of heat transfer. It is found that nanoparticles have significant effects on both fluid flow and heat transfer of the mixed convection, especially for low Richardson numbers. A comparison between Cu and CuO nanoparticles shows the Cu nanoparticles have a better effect on heat transfer enhancement for all tested conditions. The results also represent the effective role of a corrugated wall on the rate of nanofluid heat transfer. It is observed that increasing the wavy wall's amplitude leads to a decrease of the average Nusselt numberfor a high Richardson number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21024     

Laminar heat transfer in an asymmetrically heated rectangular duct

This paper presents a numerical study concerning the effects of non-uniform heating on the heat transfer of a thermally undeveloped gas flow in a horizontal rectangular duct; a vertical side wall is uniformly heated, and the other walls are insulated. As an initial step of the study, the duct flow is assumed to be laminar, and buoyancy effects are considered. The heat transfer rate and drag increase with the secondary flow due to buoyancy; the effects of the buoyancy force on the heat transfer and friction coefficient of the thermally undeveloped region are found to depend only upon modified Grashof numbers of the duct entrance.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Varying Heating Effect on Mixed Convection of Nanofluids in a Vented Horizontal Cavity with Injection or Suction

The problem of mixed convection heat transfer inside a horizontal vented enclosure through the lower and upper parts, respectively, of its left and right vertical walls is studied numerically using Al₂O₃-water nanofluid as working fluid. The bottom wall is subjected to a linearly varying (increasing or decreasing) heating temperature profiles, while the other boundaries are considered thermally insulated. The fresh fluid is admitted from the bottom part of the left vertical wall by injection or by the suction imposed on the opening of the right vertical wall. Based on numerical predictions, the conjugate effect of the Reynolds number and the nanoparticle concentration on fluid flow and heat transfer characteristics is studied. The obtained results demonstrate clearly the positive role of the nanoparticles addition on the improvement of the heat transfer rate and the mean temperature within the cavity. In addition, the flow structure and the temperature distribution inside the cavity are seen to be very sensitive to the variations of the Reynolds number, the imposed external flow mode, and the heating type. Results presented show that, in general, the decreasing heating mode is more favorable to the heat transfer in comparison with the case of the increasing heating mode. The cooling efficiency is found to be more pronounced by the injection/suction mode by applying the increasing/decreasing heating type.     

Convective transport in rectangular cavities partially heated at the bottom and cooled at one side

Laminar natural convection heat transfer inside air-filled, rectangular enclosures partially heated from below and cooled at one side is studied numerically. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of the mass, momentum, and energy transfer governing equations. Simulations are performed for a complete range of heater size, for Rayleigh numbers based on the height of the cavity ranging from 10~3to 10~6, and for height-to-width aspect ratios of the cavity spanning from 0.25 to 4. It is found that the heat transfer rate increases with increasing the heater size and the Rayleigh number, while it decreases with increasing the aspect ratio of the cavity. Dimensionless heat transfer correlations are also proposed.     

Buoyant heat transport in fluids across tilted square cavities discretely heated at one side

Laminar natural convection heat transfer inside fluid-filled, tilted square cavities cooled at one side and partially heated at the opposite side, is studied numerically. A computational code based on the SIMPLE-C algorithm is used for the solution of the system of mass, momentum, and energy transfer equations. Simulations are performed for a complete range of heater sizes and locations, Rayleigh numbers based on the side of the cavity from 10³ to 10⁷, Prandtl numbers from 0.7 to 700, and tilting angles of the enclosure from ?75° to +75°, where negative angles correspond to configurations with the heater facing downwards. It is found that the heat transfer rate increases with increasing the Rayleigh and Prandtl numbers, and the size of the heater. In addition, for negative inclinations of the enclosure the amount of heat exchanged decreases with increasing the tilting angle, while for positive inclinations the heat transfer rate either increases or decreases according as the heater is located toward the top or the bottom of the cavity. Finally, as far as the heater location is specifically concerned, the heat transfer performance has a peak for intermediate positions, the higher are the Rayleigh and Prandtl numbers, as well as the tilting angle for positive inclinations, the closer to the bottom of the cavity is the optimum heater location for maximum heat removal.     

Magnetoconvection in a square cavity with partially active vertical walls: Time periodic boundary condition

Magnetoconvection of an electrically conducting fluid in a square cavity with partially thermally active sidewalls is investigated numerically. Temperature of one of the thermally active regions of the side walls is periodic in time while the opposite wall is isothermal. The horizontal walls and the remaining parts of the side walls are thermally inactive. Nine different combinations of the relative positions of the active zones are considered. The governing equations are discretized by the control volume method with QUICK scheme and solved numerically by SIMPLE algorithm for the pressure–velocity coupling together with under relaxation technique. The tests were carried out for various values of amplitude, period, Grashof number, Hartmann number and Prandtl number. The heat transfer characteristics are presented in the form of streamlines, isotherms and velocity profiles both for transient and steady state. It is observed that the flow and the heat transfer rate in the cavity are affected by the sinusoidal temperature profile and by the magnetic field at lower values of Grashof number. The rate of heat transfer oscillates for increasing periods but it is maximum for Ω = 3 and it is found to be an increasing function of amplitude but decreases for higher values of Hartmann number. The heat transfer rate is maximum for the middle–middle thermally active locations while it is poor for the top heating and bottom cooling active locations. The average Nusselt number decreases with an increase of Hartmann number and increases with increase of Prandtl number and Grashof number.     

Optimal Natural Convection Heat Transfer Improvement by Combining Periodic Heating Temperature,Cavity Inclination,and Nanofluid

Natural convection within a square inclined cavity filled with Al₂O₃–water nanofluid is investigated numerically. The temperature of the cooled surface is maintained constant, while that of the opposite surface (heating temperature) is varied sinusoidally in time. The remaining walls are considered adiabatic. The parameters governing the problem are the amplitude and the period of the variable temperature, the Rayleigh number, the inclination of the cavity, and the solid volume fraction. A substantial enhancement of heat transfer is obtained by combining the beneficial effects of the variable heating temperature (via its period and amplitude), the inclination of the cavity, and the nanoparticles fraction. In comparison with the constant heating conditions, it is found that both the variable heating temperature and the inclination of the cavity may lead to drastic changes in the flow structure and the corresponding heat transfer. The resonance phenomenon, observed for critical periods of the exciting temperature, is amplified by adding Al₂O₃ nanoparticles to the base fluid.     

采用不等径结构自激振荡流热管实现强化传热

针对不等径结构回路型自激振荡流热管,利用电加热板作为热源,通过改变加热板的输入功率以及加热板的位置,对其壁温和热传输特性进行了实验研究,并与等径结构回路型自激振荡流热管在相同的工质及充液率,相同的热管长度及倾角,以及相同的电加热热板位置等条件下的传热特性进行了对比分析.结果表明:不等径结构自激振荡流热管在中、低负荷情况下,可以起到明显的强化传热作用;而当不等径位置在热管的最下面、热源位置在变径区域的下部时强化传热效果最佳.     

Visualization of Heat Transport during Natural Convection in a Tilted Square Cavity: Effect of Isothermal and Nonisothermal Heating

Bejan's heatlines approach has been introduced to visualize heat flow during natural convection within a tilted square cavity inclined at an angle of ? = 30°. The enclosure is bounded by hot wall AB (case 1: isothermal heating and case 2: nonisothermal heating), isothermally cooled walls DA and BC in the presence of adiabatic wall CD. The results are presented in terms of streamlines, isotherms, heatlines, and local and average Nusselt numbers. The nonisothermal heating case produces the greater heat transfer rate at the center of the wall AB compared to that of the isothermal heating case, whereas the average Nusselt number shows an overall lower heat transfer rate for the nonisothermal heating case.     

Experimental Investigation of Heat Storage and Heat Transfer Rates during Melting of Nano-Enhanced Phase Change Materials (NePCM) in a Differentially-Heated Rectangular Cavity

In this work, an experimental study of melting heat transfer of nano-enhanced phase change materials(NePCM) in a differentially-heated rectangular cavity was performed. Two height-to-width aspect ratios of the cavity, i.e., 0.9 and 1.5, were investigated. The model Ne PCM samples were prepared by dispersing graphene nanoplatelets(GNP) into 1-tetradecanol, having a nominal melting point of 37℃, at loadings up to 3 wt.%. The viscosity was found to have a more than 10-fold increase at the highest loading of GNP. During the melting experiments, the wall superheat at the heating boundary was set to be 10℃ or 30℃. It was shown that with increasing the loading of GNP, both the heat storage and heat transfer rates during melting decelerate to some extent, at all geometrical and thermal configurations. This suggested that the use of NePCM in such cavity may not be able to enhance the heat storage rate due to the dramatic growth in viscosity, which deteriorates significantly natural convective heat transfer during melting to overweigh the enhanced heat conduction by only a decent increase in thermal conductivity. This also suggested that the numerically predicted melting accelerations and heat transfer enhancements, as a result of the increased thermal conductivity, in the literature are likely overestimated because the negative effects due to viscosity growth are underestimated.     

加热方向对方腔内相变石蜡储热性能影响研究

为探究方腔内相变石蜡的储热性能,基于等效热容法和Boussinesq假设,建立相变石蜡融化储热计算模型,并针对加热方向及约束形式等因素对相变石蜡的储热性能的影响进行研究,并开展相变石蜡融化试验,验证计算模型的正确性。结果表明：相变石蜡融化储热过程是由热传导和自然对流传热综合决定的,其中自然对流传热在相变石蜡融化储热过程中起着极为显著的促进作用;不同加热方向下,相变石蜡表现出截然不同的融化储热效率,其中顶、底、侧边单独加热下的自然对流传热效应依次使储热效率提升了0.01,27.9和13.1倍,即底部热源的储热效率最高;在四面加热下,固相因无约束而下沉至底部,并抑制底部热壁面的自然对流传热效应,此时顶、底、侧热壁面的储热贡献率分别为17.3%,37.3%和22.7%;当固相运动被预埋热电偶等因素限制时,将形成钟型融化前缘,该形态包含了各热壁面单独加热下的融化储热特征,此时顶、底、侧热壁面的储热贡献率分别为19.2%,29.8%和25.5%。     

A numerical investigation of the effect of sinusoidal temperature on mixed convection flow in a cavity filled with a nanofluid with moving vertical walls

The aim of this study is to investigate numerically the effect of sinusoidal temperature on mixed convection flow in a cavity filled with nanofluid and moving vertical walls by using a new temperature function, where thermal heating takes the form of the sinusoidal temperature; and could be found in various natural processes and industries such as solar energy, and cooling of electronic components. The heating is concentrated in the center and then distributed to both ends at different values of Rayleigh numbers, Reynolds numbers, and volumetric fractions of nanoparticles ranging from 1.47 × 10³ to 1.47 × 10⁶, 1 to 100, and 0 to 0.1, respectively. The impact of nanoparticle size on thermal characteristics and hydrodynamics was considered and evaluated. From the results, the volume fraction concentration of nanoparticles affects the flow shape and thermal performance in the case of a constant Reynolds number. Moreover, the effect of nanoparticles decreases with the increase of the Reynolds number. Besides this, with increasing the volume percentage of nanoparticles, the rate of heat transmission increases. It is worth noting that the presence of nanoparticles results in height convective heat transfer coefficient. On the other hand, the thickness of thermal boundary layers decreases with increasing Rayleigh number. The current investigation found that the (sinusoidal) temperature change significantly affects heat transfer.