On the thermal field of a wall plume (The response to artificial disturbances)

Experimental investigations were carried out on the characteristics of the thermal field of a wall plume ascending from a horizontal line heat source embedded on the low part of a vertical wall surface. For the stability analysis of the present wall plume field, a vibrating copper wire was set horizontally near the line heat source in the field and the wall plume field was disturbed by the vibrating wire. Some two-dimensional sinusoidal thermal disturbances were introduced into the wall plume field and the growth or diminution of the amplitude of temperature fluctuations by the artificial disturbance were measured in the wall plume field with a thermal probe. The response characteristics of the wall plume field to the disturbance frequency were also examined. As a result, it was ascertained that the frequency response of a wall plume field could be predicted by linear stability analysis. © 1999 Scripta Technica, Heat Trans Asian Res, 28(7): 559–572, 1999     

Investigation of a large top wall temperature on the natural convection plume along a heated vertical wall in a square cavity

The characteristics of the laminar natural convection in an air-filled square cavity heated and cooled on the side walls was studied for cases where the temperature of the top wall was significantly larger than the heated vertical wall. Experiments were performed for a horizontal Grashof number of 1.3 × 10⁸, and non-dimensional top wall temperatures from 1.4 to 2.3. The results show that the plume formed on the heated vertical wall separated from this wall before reaching the top wall. As a result, three different regions were observed in the cavity: a stratified core region, a buoyant plume region, and a highly stratified region above the plume after it had separated from the vertical wall. The highly stratified region above the plume became larger and more stable with an increase of the top wall temperature, stabilizing the motion of the plume across the cavity. The similarity solutions developed by Kulkarni et al. [A.K. Kulkarni, H.R. Jacobs, J.J. Hwang, Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium, Int. J. Heat Mass Transfer 30 (1987) 691–698] to characterize the natural convection heat transfer along an isothermal single vertical plate did not agree with the results for the current measurements; however, the non-similarity model of Chen and Eichhorn [C.C. Chen, R. Eichhorn, Natural convection from a vertical surface to thermally stratified fluid, J. Heat Transfer 98 (1976) 446–451] was in good agreement over most of the wall. There were some discrepancies in the temperature distributions and the heat transfer characteristics, especially at y/H ? 0.8 due to the separated flow in this region.     

Impingement heat transfer of a single thermal plume on the upper wall

We present numerical calculations of the generation, growth and impingement of a thermal plume in a two-dimensional buoyancy induced flow. Numerical values are obtained for the aspect ratios H/W=1/4, 3/8, 1/2, the Grashof numbers Gr=10⁴, 10⁵, and the Prandtl number Pr=170. Impingement heat transfer on the upper wall is evaluated at various times. Numerical results show that before a thermal plume impinges on the upper heated wall, the thermal conduction layer, which is the stable stratification, near the upper wall becomes thinner and the local heat transfer peaks. The local Nusselt number approaches the steady condition after the impingement of a thermal plume. Additionally, under certain conditions the stream function takes a symmetrical form of two ellipses.     

Natural-Convection Heat Transfer in Channels With Isoflux Convex Surfaces

Numerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 10⁴) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.     

Chaotic Oscillations of Forced Convection in Tightly Coiled Ducts

The present work is on the stability of forced convection in a tightly coiled square duct of curvature ratio 0.5 in high Dean number region. Dynamic responses of multiple flows to finite random disturbances are examined by direct transient computation. It is found that physical realizable, fully developed flows evolve to chaotic oscillations at high values of Dean number. The power spectrum of these oscillating flows is constructed by empirical mode decomposition and Hilbert spectral analysis for the characteristics of chaotic oscillations. With increase of the Dean number, the temporal scale of chaotic oscillation becomes wider; high-frequency flows appear, and the energy contained in the bursts becomes stronger.     

Laser schlieren measurement of vertical flow past a heated horizontal circular cylinder

Flow past a heated horizontal circular cylinder in the vertically upward direction has been experimentally studied using a monochrome schlieren technique. Both free convection ((Gr)^1/3Re)=0 and mixed convection ((Gr)^1/3Re)=1011, 1055, 1095 and 1133 cases have been studied. The Reynolds number based on the cylinder diameter is set at 102 for the mixed convection, and four heating levels have been utilized with Grashof numbers of Gr=975, 1105, 1240 and 1370. The temperature distribution of the plume, the Strouhal number and the schlieren images have been reported. The vortex shedding frequency decreases with increasing Grashof number and a complete suppression of vortex shedding takes place at Grashof number of 1370. The wake is seen to become visibly narrow during the suppression of vortex shedding. The nondimensional temperature profile inside the plume is a strong function of Grashof number for free convection in comparison to that of mixed convection.     

Unsteady natural convection heat transfer from a heated horizontal circular cylinder to its air-filled coaxial triangular enclosure

Unsteady natural convection heat transfer in a horizontal annular region bounded by a heated inner circular cylinder and a coaxial outer triangular cylinder is numerically studied for a wide range of Grashof numbers, aspect ratios, and inclination angles of the triangular enclosure. Different phases are identified during the course of flow development through the evolutions of the average Nusselt number over the inner circular wall. Snapshots of streamlines and isotherms for two typical cases are presented to exhibit identification among these phases. The flow development time and time-averaged Nusselt number over the inner circular wall are predicted and scaled with Grashof number. Additionally, the onset and evolution of pitchfork bifurcation are quantitatively investigated.     

Vortex instability of natural convection flow on inclined surfaces

The linear stability of laminar natural convection flow adjacent to a heated, inclined, upwardfacing plate is investigated for disturbances having the form of longitudinal vortices. The stability problem is formulated with account being taken of the fact that the basic flow and temperature fields depend on the streamwise coordinate. One of the demonstrated consequences of retaining the transverse velocity of the basic flow is the so-called bottling effect, wherein the disturbance vorticity and temperature are contained within the respective boundary layers of the basic flow. The calculated neutral stability curves exhibit an altogether different character depending upon whether the streamwise dependence of the basic flow and temperature fields is taken into account or suppressed; the magnitude of the critical Grashof numbers from the two models differs by several orders of magnitude. The results also show that the greater the inclination of the plate from the vertical, the more susceptible is the flow to the vortex-type instability.The relationship of the analytical results to available experimental information is discussed.     

Magnetoconvection in an enclosure with partially active vertical walls

Magnetoconvection of an electrically conducting fluid in a square cavity with partially thermally active vertical walls is investigated numerically. The active part of the left side wall is at a higher temperature than the active part of the right side wall. The top, bottom and the inactive 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 underrelaxation technique. The results are obtained for Grashof numbers between 10⁴ and 10⁶, Hartmann numbers between 0 and 100 and Prandtl numbers 0.054–2.05. The heat transfer characteristics are presented in the form of streamlines and isotherms. The heat transfer rate is maximum for the middle–middle thermally active locations while it is poor for the top–bottom thermally active locations. The average Nusselt number decreases with an increase of Hartmann number and increases with an increase of Grashof number. For sufficiently large magnetic field Ha = 100 the convective mode of heat transfer is converted into conductive mode in the low region of Grashof number than in the high region.     

Simulation of Laminar Axisymmetric Buoyant Plumes: A Case Study of the Anatomy of Similarity Solutions

This article is concerned with the numerical simulation of the laminar buoyant plume created by a heated sphere situated in an otherwise quiescent environment. The limit of vanishing sphere diameter corresponds to the point source of heat, for which extensive results have been obtained in the literature. The dual objectives of this work are the attainment of an exact characterization of the buoyant plume, and the diagnosis of an existing similarity solution for the limiting problem of the point source. These objectives were fulfilled by means of a numerically exact solution of the equations representing mass, momentum, and energy conservation. The solutions were carried out over a range of the radius-based Grashof number extending from 50 to 5 × 10⁶ for a Prandtl number of 0.7, which corresponds to air. The velocities in the plume were found to increase with elevation above the sphere but approach a fully developed state characterized by congruent (similar) velocity profiles at sufficiently high elevations. The temperature profiles, while attaining a self-similar shape at high elevations, actually decay with increasing elevation. The approach to both the fully developed state for the velocity and the self-similar state for the temperature occurs more rapidly at low Grashof numbers. In general, it was found that the existing similarity solutions become viable only at very large elevations above the source of buoyancy.     

Simultaneous heat and mass transfer on oscillatory free convection boundary layer flow

The problem of simultaneous heat and mass transfer in two-dimensional free convection from a semi-infinite vertical flat plate is investigated. An integral method is used to find a solution for zero wall velocity and for a mass transfer velocity at the wall with small-amplitude oscillatory wall temperature. Low- and high-frequency solutions are developed separately and are discussed graphically with the effects of the parameters Gr (the Grashof number for heat transfer), Gc (the Grashof number for mass transfer) and Sc (the Schmidt number) for Pr = 0–71 representing aid at 20°C.     

Mixed convection from an isolated spherical particle

A numerical study on mixed convection around a hot spherical particle moving vertically downwards in a still fluid medium has been made. The flow field is considered to be axisymmetric for the range of Reynolds number (based on the diameter and the settling velocity of the particle) considered. A third-order accurate upwind scheme is employed to compute the flow field and the temperature distribution. The form of the wake and the thermal field is analyzed for several values of Grashof number and the Reynolds number. The influence of buoyancy on drag and the rate of heat transfer are studied. At moderate Reynolds number, recirculating eddy develops in the downstream of the sphere. With the rise of surface temperature this eddy collapses and the fluid adjacent to the heated surface develops into a buoyant plume above the sphere. The increase in surface temperature of the sphere delays the flow separation. Our results show that the drag force and the rate of heat transfer strongly depend on Grashof number for the moderate values of Reynolds number. The conjugate heat transfer from the moving sphere is also addressed in the present paper. We have compared our computed solution with several empirical and asymptotic expressions available in the literature and found them in good agreement.     

An unsteady flow structure on a heated rotating disk under mixed convection

A flow field under mixed convection on a heated rotating disk has been measured using an ultrasonic velocity profiler (UVP). The measured velocity field is a spatio‐temporal one as a function of radial coordinates and time. The objective of this paper is to clarify the vortex structure caused by the instability between buoyancy and centrifugal force. The vortex appears under typical conditions of Reynolds numbers and Grashof numbers and it moves toward the outside of the disk. This behavior can be classified into two patterns. The size of the vortex structure decreases with an increasing Reynolds number and increases with the Grashof number. The traveling velocity of the vortex increases with the Grashof number. Moreover, it decreases with an increasing Reynolds number in spite of increasing centrifugal force. According to these results, the region dominated by natural, forced, and mixed convection is classified in the relationship between Reynolds and Grashof numbers. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(6): 407–418, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20074     

On the stability of natural convection of a radiating fluid in a vertical slot

Linear stability theory is applied to examine the effects of radiation on the natural convection of a fluid contained in a vertical slot. The formulation of the radiation terms is based on the modified P-1 approximation and a tau spectral method with Chebyshev polynomials as trial functions is used to solve the basic state equations and the eigenvalue problem which specify the states of neutral stability. The influence of the radiation parameters on the variations of the critical Grashof number with the stratification parameter is investigated. Critical curves for the stationary and travelling modes are shown.     

Mixed convective flow of two immiscible viscous fluids in a vertical wavy channel with traveling thermal waves

The problem of fully developed laminar mixed convection flow in a vertical wavy channel filled with two immiscible viscous fluids is studied analytically. Non‐linear equations governing the motion have been solved by linearization technique, wherein the flow is assumed to be in two parts; a mean part and a perturbed part. Exact solutions are obtained for the mean part and a perturbed part is solved using long wave approximation. Separate solutions are matched at the interface using suitable matching conditions. Numerical results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters such as Grashof number, viscosity ratio, width ratio, and conductivity ratio. The effect of these parameters on the physical characteristics such as Nusselt number and skin friction at the walls is studied. It is found that Grashof number, viscosity ratio, width ratio, and conductivity ratio enhance the velocity parallel to the flow direction. Reversal effect is observed on the velocity which is perpendicular to the flow direction. The Nusselt number remains invariant on Grashof number. As the width ratio decreases, the Nusselt number decreases at the right wall and increases at the left wall and reversal effect is observed for variations of conductivity ratio. The skin friction increases at the left wavy wall and decreases at the right wavy wall as the Grashof number increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20379     

Oscillatory natural convection of water-glycerin mixture in a tall rectangular cavity: Transition to the chaos

This paper presents results of a numerical investigation involving bifurcation sequence leading to chaos in natural convection inside a vertically tall rectangular cavity having an aspect ratio equal to 15 and a Prandtl number equal to 125, corresponding to water-glycerin mixture. The flow is characterized by a vertical stratification of the temperature field for Grashof numbers greater than or equal to 200 that is outside the conduction regime and it is stationary monocellular up to a critical value Gr_c = 2800 where a periodic oscillatory regime appears. As Grashof number is increased, a transition from a steady periodic bicellular flow to an oscillatory multicellular flow, with 2 main central cells and 2 secondary cells, occurs. The regime remains periodic until Gr = 3100 where there is a first appearance of the chaotic regime which extends over a narrow interval of the Grashof number delimited by Gr = 3200.     

Natural convection heat transfer in a partially opened cavity filled with porous media

This paper examines the steady natural convection in a partially opened enclosure filled with porous media using the Brinkman–Forchheimer model. Whilst the part of the left vertical wall of the cavity is heated, the other walls are adiabatic or thermally insulated Based upon numerical predictions, the effects of pertinent parameters such as Grashof number, Darcy number, porosity, length of the heated wall and the location center of the opened cavity are examined. It is found that as the Grashof number increases, due to strengthening buoyancy driven flows, the local Nusselt number from partially heated vertical wall, at a given position on this wall increases. This, in turn, increases the temperature of the heated wall. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Buoyant Darcy flow driven by a horizontal temperature gradient: A linear stability analysis

The linear stability of a fluid saturated porous layer bounded by two parallel impermeable plane walls is investigated. The lower wall is subject to a uniform heat flux, while the upper wall is subject to a linearly varying temperature in a horizontal direction. Two parameters govern the onset of convection in the porous layer: the vertical Darcy–Rayleigh number, and the horizontal Darcy–Rayleigh number. The objective of this study is to obtain the onset conditions for the instability of the basic parallel flow in the layer. The governing balance equations are written in a dimensionless form and solved on assuming oblique roll disturbances, arbitrarily oriented in the horizontal plane. Mathematically, this leads to a system of two ordinary differential equations to be solved as an eigenvalue problem. The solution, carried out numerically, provides the neutral stability condition. The numerical solution is performed by employing a procedure based on the sixth-order Runge–Kutta method and on the shooting method for satisfying the boundary conditions at the upper boundary wall.