Showing papers on "Combined forced and natural convection published in 1986"

On dual solutions occurring in mixed convection in a porous medium

Abstract: The dual solutions to an equation, which arose previously in mixed convection in a porous medium, occuring for the parameter α in the range 0 < α < α0 are considered. It is shown that the lower branch of solutions terminates at α=0 with an essential singularity. It is also shown that both branches of solutions bifurcate out of the single solution at α=0 with an amplitude proportional to (α0-α)1/2. Then, by considering a simple time-dependent problem, it is shown that the upper branch of solutions is stable and the lower branch unstable, with the change in temporal stability at α=α0 being equivalent to the bifurcation at that point.

Engineering Heat Transfer

Abstract: Fundamental Concepts Mechanisms of Heat Transfer Dimensions and Units Fourier's Law of Heat Conduction Thermal Conductivity Convection Heat Transfer Convection Heat-Transfer Coefficient Radiation Heat Transfer Emissivity and Other Radiative Properties Combined Heat-Transfer Mechanisms Steady-State Conduction in One Dimension One-Dimensional Conduction Equation Plane Geometry Systems Polar Cylindrical Geometry Systems Spherical Geometry Systems Thermal Contact Resistance Heat Transfer from Extended Surfaces Steady-State Conduction in Multiple Dimensions General Conduction Equation Analytical Method of Solution Graphical Method of Solution Conduction Shape Factor Solution by Numerical Methods (Finite Differences) Numerical Method of Solution for Two-Dimensional Problems Methods of Solving Simultaneous Equations Unsteady-State Heat Conduction Systems with Negligible Internal Resistance Systems with Finite Internal and Surface Resistances Solutions to Multidimensional Geometry Systems Approximate Methods of Solution to Transient-Conduction Problems Introduction to Convection Fluid Properties Characteristics of Fluid Flow Equations of Fluid Mechanics Thermal-Energy Equation Applications to Laminar Flows Applications to Turbulent Flows Natural-Convection Problem Dimensional Analysis Convection Heat Transfer in a Closed Conduit Heat Transfer to and from Laminar Flow in Circular Conduit Heat Transfer to and from Turbulent Flow in Circular Conduit Heat-Transfer Correlations for Flow in Noncircular Ducts Convection Heat Transfer in Flows Past Immersed Bodies Boundary-Layer Flow Turbulent Flow over Flat Plate Flow Past Various Two-Dimensional Bodies Flow Past a Bank of Tubes Flow Past a Sphere Natural-Convection Systems Natural Convection on a Vertical Surface: Laminar Flow Natural Convection on a Vertical Surface: Transition and Turbulence Natural Convection on an Inclined Flat Plate Natural Convection on a Horizontal Flat Surface Natural Convection on Cylinders Natural Convection around Spheres and Blocks Natural Convection about an Array of Fins Combined Forced- and Natural-Convection Systems Heat Exchangers Double-Pipe Heat Exchangers Shell-and-Tube Heat Exchangers Effectiveness-Number of Transfer Units Method of Analysis Crossflow Heat Exchangers Efficiency of a Heat Exchanger Condensation and Vaporization Heat Transfer Condensation Heat Transfer Boiling Heat Transfer Introduction to Radiation Heat Transfer Electromagnetic Radiation Spectrum Emission and Absorption at the Surface of an Opaque Solid Radiation Intensity Irradiation and Radiosity Radiation Laws Characteristics of Real Surfaces Radiation Heat Transfer between Surfaces View Factor Methods for Evaluating View Factors Radiation Heat Transfer within Enclosure of Black Surfaces Radiation Heat Transfer within an Enclosure of Diff use-Gray Surfaces Bibliography and Selected References Appendices Index

Turbulent thermal convection in wide horizontal fluid layers

Abstract: Turbulence in thermal convection is investigated for flows in which the production of turbulence energy is due solely to buoyancy, and the statistics of the flow are homogeneous in horizontal planes. New experimental results for high Rayleigh number unsteady turbulent convection in a horizontal layer heated from below and insulated from above are presented and compared to turbulent Rayleigh convection, convection in the planetary boundary layer, and laboratory penetrative convection. Mean temperature fields are correlated in terms of wall layer scales and convection scales. Joint statistics of turbulent temperature and horizontal velocity and vertical velocity through fourth order are presented for the core region of the convection layer.

Application of flux-corrected transport (FCT) to high Rayleigh number natural convection in a porous medium

Abstract: A numerical technique designed to solve a wide class of convectively dominated flow problems is applied to natural convective flow in a porous medium at large Rayleigh number. The technique is a finite difference method based on flux-corrected transport (FCT) and possesses four desirable numerical properties: stability, accuracy, monotonicity, and conservation. Steady natural convection is investigated for Rayleigh numbers as large as 10,000. An efficient methodology for obtaining steady state solutions is illustrated. A simulation is performed for transient thermal convection at a Rayleigh number of 2500. Transient natural convection involving both heat and mass transfer is illustrated for a Rayleigh number of 2500, Lewis number of 2, and buoyancy ratio of 0.1. All simulations are performed in a square cavity with heated vertical side walls. 17 refs.

Correlations for laminar mixed convection flows on vertical, inclined, and horizontal flat plates

Abstract: Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.

Laminar Mixed Convection in a Symmetrically or Asymmetrically Heated Vertical Channel

Abstract: A numerical investigation is made of laminar mixed convection of air in a vertical channel. The thermal boundary conditions considered are symmetric heating, where both plates are heated, and asymmetric heating, where one plate is heated and the other is adiabatic. Results are obtained for Rayleigh numbers of 10 3 , 10 5 , and 10 6 and Gr/Re 2 values of 0.1, 1, 3, and 5. The temperatures are observed to increase with increasing Gr/Re 2 and decreasing Rayleigh number. The velocity profile peaks near the hot plates and exhibits a concavity, which, in the symmetric heating case, occurs around the centerline. With increasing Gr/Re 2 the velocity near the hot wall increases while the velocity near the centerline decreases. The Nusselt number attains its maximum value near the inlet of the channel and increases with decreasing Gr/Re 2 values.

Numerical simulation of double‐diffusive Marangoni convection

Abstract: Marangoni convection is important in a variety of physical systems and occurs as a result of surface tension gradients at a liquid free surface. In general, liquid surface tension varies with temperature and species concentration in a binary fluid. If the temperature and concentration distributions make opposing contributions to the overall surface tension gradient at a free surface, convective motion, as well as heat and mass transfer within the system, is shown to depend on double‐diffusive effects. This situation is analogous to double‐diffusive natural convection, in that convection may occur, even though the overall surface tension difference along the free surface suggests stagnant fluid conditions.

Proceedings of the eighth international heat transfer conference

Abstract: This book presents the papers given at a conference on heat transfer. Topics considered at the conference included numerical techniques and modeling, measurement techniques, conduction and thermal insulation, thermal radiation, combustion, internal forced convection, external forced convection, jets, wakes, film cooling, natural and mixed convection, natural convection in confined spaces, vapor condensation, freezing, melting, evaporation, interfacial phenomena, pool boiling, flow boiling, two-phase flow, nuclear reactor heat transfer, particulates and porous materials, heat exchangers, heat transfer augmentation, and special applications.

Mixed convection in horizontal porous layers heated from below.

Abstract: Numerical studies are reported for steady, mixed convection in two-dimensional horizontal porous layer with localized heating from below. The interaction mechanism between the forced flow and the buoyant effects is examined for wide ranges of Rayleigh number Ra* and Peclet number Pe*. The external flow significantly perturbs the buoyancy-induced temperature and flow fields when Pe* is increased beyond unity. For a fixed Peclet number, an increase in Rayleigh number produces multicellular recirculating flows in a domain close to the heat source. This enhances heat transfer by free convection. However, for a fixed Ra*, an increase in forced flow or Peclet number does not necessarily increase the heat transfer rate. Hence, there exists a critical Peclet number as a function of Ra* for which the overall Nusselt number is minimum. The heat transfer is, generally, dominated by the buoyant flows for Pe* < 1 whereas the contribution of free convection is small for Pe* 10 when Ra* {le} 10.

Laminar forced convection of power-law non-Newtonian fluids inside ducts

Abstract: Thermal entrance region heat transfer for laminar forced convection of power-law fluids inside a circular tube and parallel plate channel for uniform wall temperature is solved exactly, and as many eigenvalues and eigenfunctions as needed for the solution are determined automatically and with high accuracy by using the recently advanced Sign-Count method. Results are presented for the local and average Nusselt number over a wide range of the Graetz number in both graphical and tabular forms. The present benchmark results are utilized to critically examine the accuracy of the approximate Leveque solution.

Mixed-convection flows within a horizontal concentric annulus with a heated rotating inner cylinder

Abstract: Numerical analysis is performed for two-dimensional mixed convection in the annulus between horizontal concentric cylinders with a heated rotating inner cylinder. The ratio of the annulus gap width to the inner cylinder radius is held fixed at 1.6. The Grashof number range is taken from 1.39 × 10 2 to 1.39 × 10 5 and the rotational parameter σ ( = Gr/Re 2 ) varies from ∞ ( pure natural convection) to 1. The flow and temperature fields and heat transfer characteristics are presented over this parameter range where effects of both buoyancy and centrifugal force due to rotation are significant. A relatively novel formulation of the Navier-Stokes equations is employed in the present study. A vorticity transport equation, two Poisson equations for the velocity components, and the energy equation are solved by a finite-difference scheme. A direct method is used to solve simultaneously for the dependent variables along a grid line via a block tridiagonal matrix algorithm. The formulation is found to be stable ov...

An experimental investigation of convection in a rotating sphere subject to time varying thermal boundary conditions.

Abstract: A series of experiments has been undertaken to investigate the onset of convection in a rapidly rotating fluid filled sphere. The boundary is subjected to a time varying temperature allowing the simulation of radial temperature profiles associated with internal heating. The system is similar to that treated theoretically by Roberts (1968), Busse (1970) and Soward (1977). It is found that Busse's modification of Roberts' linear analysis, taking into account velocity perturbations which are antisymmetric about the equatorial plane, provides a good estimate of the temperature gradient required to initiate convection. As observed in the experiments of Carrigan and Busse (1983) and predicted by linear theory, convection appears in the form of rolls or columns, aligned parallel to the rotation axis. As in earlier experiments, observed azimuthal wavenumbers are consistently smaller than predicted which we postulate to be a consequence of nonlinear effects. Owing to the presence of a centrifugally driven...

The onset of time‐dependent convection in spherical shells as a clue to chaotic convection in the Earth's mantle

Abstract: This work presents a detailed numerical study of the dynamical behavior of convection in a spherical shell, as applied to mantle convection. From both two-dimensional (120 radial and 360 tangential points) and three-dimensional (60 radial levels and spherical harmonics up to order and degree L = 33, m = 33), it is shown that for a spherical shell (with inner-to-outer radii ratio eta = 0.62) convection becomes time-dependent, with l = 2 dominating, at a Rayleigh number of about 31 times supercritical for a constant-viscosity, base-heated configuration. This secondary instability is characterized by oscillatory time dependence, with higher frequencies involved, at slightly higher Rayleigh numbers. In illustrating the onset of time dependence, the analysis is extended to show that the onset of weak turbulence in spherical-shell convection takes place at about 60 times the critical Rayleigh number via a quasi-periodic mode.

Steady State Forced Convection Heat Transfer in He II

Abstract: A study of forced convection heat transfer in superfluid helium (He II) is initiated to better understand the physical behavior of this process and to compare it with the more familiar He II heat transfer mechanism of internal convection. An experimental assembly is designed to achieve fluid flow by a motor-driven hydraulic pump which utilizes two stainless steel bellows. Each bellows is connected to one end of a copper tube, 3 mm in diameter and 2 m long. The system allows measurements of one dimensional heat and mass transfer where the measured quantities include: temperature profile and pressure drop. The variable quantities are the helium bath temperature, flow velocity and heat input. The helium bath is held at 1.8 K and under saturation pressure. The flow tube is heated at the middle and the flow velocity is varied up to 97 cm/s. The helium pressure is monitored at both ends of the tube and a friction factor is estimated for He II. Temperature measurements are made at seven evenly spaced locations along the tube. The experimental temperature profile is compared with a numerical solution of an analytical model developed for the problem under study.

The Role of Transient Convection in the Melting and Solidification in Arc Weldpools

Abstract: A mathematical formulation has been developed to describe the transient growth and collapse of axisymmetric weldpools in spot welding operations. In the statement of the problem allowance is made for both conductive and convective heat transfer. In describing convection, the driving forces included buoyancy, electromagnetic forces, and surface tension forces. In most cases it was found that convection played a major role in affecting the weldpool shape, and that this convection was often dominated by surface tension forces. The model also allowed us to represent the transient collapse of weldpools upon the cessation of the heat and current supply. It was found that the melt velocity was reduced as the weldpool shrank. Most of the solidification took place from a circulating weldpool. By calculating both the growth rate and the relevant temperature gradients, it was possible to estimate the dendrite arm spacing which was found to be of the order of tens of microns.