Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium

In this article nonsimilarity solution for mixed convection from a horizontal surface in a saturated porous medium was obtained for the case of variable surface heat flux. The entire mixed convection regime, ranging from pure forced convection to pure free convection, is considered by introducing a single nonsimilarity parameter. Heat transfer results are predicted by employing four different flow models, namely, Darcy's law, the Ergun model, and the Brinkman-Forchheimer-extended Darcy model with constant and variable porosity. The variable porosity effect is approximated by an exponential function. Effects of transverse thermal dispersion are taken into consideration in the energy equation, along with variable stagnant thermal conductivities. The formulation of the present problem shows that the flow and heat transfer characteristics depend on five parameters, that is, the power in the variation of surface heat flux, the nonsimilarity mixed-convection parameter, the inertia effect parameter, the boundary effect parameter, and the ratio of thermal conductivity of the fluid phase to that of the solid phase. Numerical results for the local Nusselt number variations, based on the various flow models, are presented for the entire mixed convection regime. The impacts␣of different governing parameters on the heat transfer results are thoroughly investigated. Received on 7 August 1997     

Microconvection in a vertical layer

In the case of very weak gravity the classical Oberbeck-Boussinesq approximation is not valid for describing thermal gravitational convection. This was pointed out in [1] where a new model was proposed under the assumption that the fluid is isothermal and incompressible. In this model the velocity vector is no longer solenoidal. Below, on the basis of this model we analyze the convective motion in a vertical layer, on the rigid boundaries of which a heat flux that depends on time only is prescribed. It is found that the nonsolenoidal character of the velocity does not lead to considerable restructuring of the steady-state convection. At the same time, the patterns of the unsteady, in particular, periodic convective flow calculated within the framework of the classical and the new models differ significantly.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 76–84, September–October, 1994.     

Untersuchung von Schwingungen einer Zweiphasenströmung durch Druckabfall und Dichtewellen mit Hilfe finiter Differenzen

The previous experimental analysis has indicated the existence to two major modes of oscillations, i.e., Density-Wave (high frequency) and Pressure-Drop (low frequency) Oscillations in single channel, electrically heated, forced convection upflow systems. In this work the stability of such a system is investigated theoretically and the results are compared with experimental findings obtained by the authors. The Homogeneous Phase Equilibrium model is used to describe the two-phase flow characteristics. The friction between the pipe wall and the expanding fluid is modeled using the Moody friction factor assuming an effective two-phase viscosity. Gravitational forces are included and heat transfer into the fluid is assumed to be the function of the wall temperature, fluid temperature and heat transfer coefficient which is also assumed to be a function of the flow rate. Though simple, this model is found to be very satisfactory in simulating both modes of oscillations with acceptable accuracy. The physical nature of each mode is different and distinct, therefore, separate solution methods are developed for each case. The Steady-State Flow Characteristics are obtained for various heat inputs and inlet temperatures by solving the conservation equations together with the equation of state by using an Implicit Finite- Difference technique. In the analysis of low frequency oscillations it is assumed that the quasi-steady state conditions prevail in the heater. The system equations obtained with this assumption are solved under constant exit pressure and constant container pressure boundary conditions using the finite-difference technique. Two methods of approach are adapted in solving the non-linear hyperbolic equations which describe the system at low mass flow rates where the density-wave type oscillations are observed. They are the Explicit Integral Momentum method (EIM) and the Explicit Finite-Difference method (EFD). A comparison of the results with experiments and other mathematical models is discussed.     

Study of heat transport by stationary magneto-convection in a Newtonian liquid under temperature or gravity modulation using Ginzburg–Landau model

The present paper deals with a weak non-linear stability problem of magneto-convection in an electrically conducting Newtonian fluid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT) or gravity modulation (ITGM). In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. Using Ginzburg–Landau equation, the effect of modulations on heat transport is analyzed. Effect of various parameters on the heat transport is also discussed.     

An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the Ginzburg–Landau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically.     

Convective transport of nanoparticles in multi-layer fluid flow

Technologically, multi-layer fluid models are important in understanding fluid-fluid or fluid-nanoparticle interactions and their effects on flow and heat transfer characteristics. However, to the best of the authors’ knowledge, little attention has been paid to the study of three-layer fluid models with nanofluids. Therefore, a three-layer fluid flow model with nanofluids is formulated in this paper. The governing coupled nonlinear differential equations of the problem are non-dimensionalized by using appropriate fundamental quantities. The resulting multi-point boundary value problem is solved numerically by quasi-linearization and Richardson’s extrapolation with modified boundary conditions. The effects of the model parameters on the flow and heat transfer are obtained and analyzed. The results show that an increase in the nanoparticle concentration in the base fluid can modify the fluid-velocity at the interface of the two fluids and reduce the shear not only at the surface of the clear fluid but also at the interface between them. That is, nanofluids play a vital role in modifying the flow phenomena. Therefore, one can use nanofluids to obtain the desired qualities for the multi-fluid flow and heat transfer characteristics.     

Double tube heat exchanger with novel enhancement: part I—flow development length and adiabatic friction factor

The study is conducted to evaluate the flow characteristics in a double tube heat exchanger using two new and versatile enhancement configurations. The novelty is that they are usable in single phase forced convection, evaporation and condensation. Correlations are proposed for flow development length and friction factor for use in predicting fluid pumping power in thermal equipment as well as in subsequent heat transfer characterization of the surface.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.     

Effect of trigonometric sine,square and triangular wave-type time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and Newtonian nanoliquids

The influence of trigonometric sine, square and triangular wave-types of time-periodic gravity-aligned oscillations on Rayleigh–Bénard convection in Newtonian liquids and in Newtonian nanoliquids is studied in the paper using the generalized Buongiorno two-phase model. The five-mode Lorenz model is derived under the assumptions of Boussinesq approximation, small-scale convective motion and some slip mechanisms. Using the method of multiscales, the Lorenz model is transformed to a Ginzburg–Landau equation the solution of which helps in quantifying the heat transport through the Nusselt number. Enhancement of heat transport in Newtonian liquids due to the presence of nanoparticles/nanotubes is clearly explained. The study reveals that all the three wave types of gravity modulation delay the onset of convection and thereby to a diminishment of heat transport. It is also found that in the case of trigonometric sine type of gravity modulation heat transport is intermediate to that of the cases of triangular and square types. The paper is the first such work that attempts to theoretically explain the effect of three different wave-types of gravity modulation on onset of convection and heat transport in the presence/absence of nanoparticles/nanotubes. Comparing the heat transport by the single-phase and by the generalized two-phase models, the conclusion is that the single-phase model under-predicts heat transport in nanoliquids irrespective of the type of gravity modulation being effected on the system. The results of the present study reiterate the findings of related experimental and numerical studies.

     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999     

界面张力梯度驱动对流向湍流转捩的研究

作为空间自然对流热质输运的基本形式,界面张力梯度驱动对流是流动和传热强耦合的复杂非线性过程,也是一个多控制参数耦合作用的过程,表现出丰富的流动时空特征.界面张力梯度驱动对流是微重力流体物理的重要研究内容和学科前沿,同时在空间燃料输运过程和空间能源或热管利用等空间流体管理问题中均有重要应用.本文综述了界面张力梯度驱动对流...     

Conjugate heat transfer in square enclosures

Building elements represented by square vertical enclosures encircled with finite walls or with centered solid body, could maintain the equivalent fluid volumes through the volume ratio scale. Present work aims to investigate the fluid flow and heat transfer in these two building elements. Complete two-dimensional numerical simulation of the conjugate heat conduction and natural convection occurring in both enclosures is carried out. An analytical expression for the minimum size of the inserted body at which the body begins to suppress the natural convection flow is proposed and validated by the numerical results. The fluid flow and heat transfer characteristics are analyzed through the streamlines, heatlines, and total heat transfer rates across both enclosures. Results reveal that heat transfer rates across both enclosures are complex functions of the volume ratio scale, Rayleigh number, and the relative thermal conductivity.     

Non-Darcy double-diffusive natural convection in axisymmetric fluid saturated porous cavities

Double-diffusive natural convection in a fluid saturated porous medium has been investigated using the finite element method. A generalised porous medium model is used to study both Darcy and non-Darcy flow regimes in an axisymmetric cavity. Results indicate that the Darcy number should be a separate parameter to understand flow characteristics in non-Darcy regime. The influence of porosity on heat and mass transfer is significant and the transport rates may differ by 25% or more, at higher Darcy and Rayleigh numbers. When compared with the Darcy and other specialised models of Brinkman and Forchheimer, the present generalised model predicts the least heat and mass transfer rates. It is also observed that an increase in radius ratio leads to higher Nusselt and Sherwood numbers along the inner wall.     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Convection of a heat-generating fluid in a rotating horizontal cylinder

Thermal convection of a fluid in a horizontal cylinder rotating about its own axis with uniformly volume-distributed internal heat sources is experimentally investigated. The enclosure boundary temperature was kept constant. The threshold of the excitation of convective flows and their structure are studied as functions of the heat-release intensity and the rotation velocity. The experiments are performed with water and water-glycerin solutions. It is shown that rapidly rotating fluid is in a stable quasiequilibrium state, namely, the temperature distribution is axisymmetric and has a maximum at the center of the enclosure. It is found that with decrease in the rotation velocity a convective flow arises thresholdwise, in the form of vortex cells periodically arranged along the axis. The thermal convection in the rotating enclosure is shown to be determined by the effects of two different mechanisms. One of these is due to the centrifugal force of inertia and plays the stabilizing role, while the other, thermovibrational mechanism is connected with nonisothermal fluid oscillations under the action of gravity in the enclosure-fitted reference frame and is responsible for the occurrence of mean thermal convection. The boundaries of the convection generation are plotted in the plane of the governing dimensionless parameters and the heat transfer in the supercritical region is studied.     

Three-dimensional mixed convection squeezing flow

The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations (ODEs) by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.     

Thermal stratification studies in a side heated water pool for advanced heavy water reactor applications

Strong heat source at the isolation condenser wall of an Advanced Heavy Water Reactor, results in natural convection in gravity driven water pool, which leads to a thermally stratified pool. Governing equations simulating fluid flow and heat distribution are solved numerically by a general purpose Computational Fluid Dynamics solver developed at Indian Institute of Technology, Kanpur. Incompressible finite volume method with non-staggered grid arrangement is used in this exercise. This algorithm is fully implicit and semi-coupled. Turbulent natural convection in a boundary layer for high Rayleigh numbers is analyzed by the Lam–Bremhorst k − ε turbulence model. Analysis of unsteady laminar natural convection in a side-heated water cavity is also done for different values of Rayleigh number. Results show a warm fluid layer floating on the top of gradually colder layer (along the vertical direction) that indicates the presence of thermal stratification phenomenon. This fact necessitates additional safety features in such a system so that the detrimental effect such as stratification is minimized.     

Investigation of turbulence effects on forced convection in a composite porous/fluid duct: Constant wall flux and constant wall temperature cases

Forced convection heat transfer in composite porous/fluid domains is of great practical and theoretical significance. However, research in this area traditionally addressed only the laminar flow case in both homogeneous fluid and porous regions of the domain. This paper investigates the interaction between turbulent flow in the center of a circular tube filled with a homogeneous fluid and laminar flow in the porous layer adjacent to the tube wall. A two-layer algebraic turbulence model suggested by Cebeci and Smith is utilized for the flow in the central region of the tube. The effects of turbulence in the central region on velocity and temperature distributions as well as on the Nusselt number are analyzed.     

Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Dynamical responses of non-isothermal flow between two independently rotating disks with time-dependent wall conditions

The present work develops a theoretical model of rotational convection and uses it to investigate the dynamical responses of the flow and heat transfer between two disks rotating at different rates under the influences of time-dependent disturbances. The unsteady non-isothermal flow model is formulated by extending a recently developed steady-state similarity model of axi-symmetric rotational convection. In the new model all the rotation-induced buoyancy forces are considered. Using one disk as reference, effects of the time-dependent changes in wall temperature or rotating rate of the other disk on the flow and heat transfer are explored. Various rotational modes with asymptotic or fluctuating change in boundary condition of temperature or disk rotation are studied. The present time-dependent model for this non-isothermal rotating flow is numerically solved by a finite-difference method. By using the present results, the complicated flow and heat transfer mechanisms with thermal-flow coupling in the class of time-dependent rotational convection are manifested.