Constant Fluid Properties Research Articles

Buoyancy in developed laminar curved tube flows

The influence of buoyancy on fully developed laminar flow in curved tubes of circular cross-section is studied numerically. Steady flow for a constant property fluid, in terms of the Boussinesq approximation, is assumed. The thermal boundary conditions are specified as axially uniform heat flux and peripherally uniform wall temperature. The problem is solved using coarse, unequally spaced grids. The solutions cover a wide range of Prandtl, Dean and Grashof numbers and include the curvature ratio as an explicit parameter. The results are compared with results from the literature and reveal considerable differences. The buoyancy acts to increase the average Nusselt number, change the local Nusselt number distribution around the periphery, and rotate the orientation of the secondary flow.

A Generalized Steady-State Reynolds Equation for Non-Newtonian Fluids, With Application to Journal Bearings

The purpose of this paper is to derive lubrication equations suitable for constant-property fluids exhibiting inelastic non-Newtonian characteristics. The analysis results in a slightly modified form of Reynolds equation. Fluid characteristics show up in this equation through an equivalent power-law. Data are presented for journal bearing performance over a range of L/D’s and rheological exponents.

Numerical evaluation of thermal diffusion column coefficients

Numerical methods were developed for evaluating the coefficients which appear in the theory of the thermal diffusion column. An associated computer code (program COLCO) was developed to calculate coefficients based on tables of physical properties or (for gases) on physical properties calculated from the kinetic theory of gases. The program was used to calculate thermogravitation velocity profiles for a planar column filled with a fluid of constant properties. The results agreed well with those calculated from the simple algebraic expressions which can be derived for that case. Coefficients calculated by the program were also found to be in good agreement with published tables of reduced coefficients (shape factors) for a dilute Lennard-Jones gas.

Numerical computation of buoyancy-induced recirculation in curved square duct laminar flow

The influence of buoyant effects on developing heat transfer in strongly curved duct flows has been studied numerically for the special case of steady state, incompressible laminar flow of a constant physical property fluid to which the Boussinesq approximation applies. The two cases of: (a) buoyant forces aligned with, and (b) opposed to the main flow direction were investigated. The presence of several streamwise recirculation zones necessitates the solution of fully elliptic transport equations. It is found that when buoyant forces are aligned with the main flow direction in curved duct flow geometries they can significantly enhance the rate of heat transfer, especially at the inner-radius wall. By contradistinction, when buoyant forces and the main flow are opposed, three additional elongated recirculation zones which appear at the inner-radius wall are the cause for reduced heat transfer to the flow in a curved duct.

EFFECTS OF VARIABLE PROPERTIES AND INTERNAL HEAT GENERATION ON NATURAL CONVECTION AT A HEATED VERTICAL PLATE IN AIR

Numerical results are presented for the transient and steady-state velocity field, temperature field, and heat transfer characteristics. These results were obtained by solving the partial differential equations describing the conservation of mass, momentum, and energy by an explicit finite-difference method in time-dependent form. Two cases were studied, namely the variable fluid property (VFP) case and the constant fluid property (CFP) case. Values of the velocity components u, v (absolute) and the temperature 8 in the VFP case are larger away from the plate and smaller near the plate than those in the CFP case. Further, the velocity and temperature fields are more prominent in the presence of heat sources than in their absence. Numerical results indicate that the wall heat transfer coefficient in the VFP case is about 30% higher than in the CFP case. This warrants further analyses of the effect of variable fluid properties on the flow and heat transfer characteristics. Another useful result is that the ...

Incompressible magnetohydrodynamic flow with heat transfer between inclined walls

Self-similar flows of viscous, incompressible, electrically conducting fluids and of heat in a diffuser with an azimuthal magnetic field and plane walls (at constant temperature) are analyzed by analytical and numerical methods. Velocity distributions for pure outflows and temperature distributions are presented for various invariance parameters I1=ϑ0R1/2, I2= (H2−4)/R, and Prandtl numbers 𝒫 where ϑ0 is the duct angle, R is the Reynolds number, and H is the Hartmann number. In the approximation of constant fluid properties, the onset of flow separation is independent of the heat transfer, and separation is inhibited for I2⩾2/3 if R ≫ 1. The theory is applicable to proper incompressible fluids such as liquid metals (small Prandtl numbers), in which self-similar velocity and temperature fields can be realized.

Approximate Methods for Calculating Heated Water Laminar Boundary-Layer Properties

The integral method of Thwaites, for computing the primary parameters of laminar boundary layers with constant fluid properties, is extended to heated boundary layers in water, taking into account variable fluid properties. Universal parameters are correlated from numerical solutions of heated water wedge flows for use with the integral method. The method shows good accuracy in a test with the Howarth retarded flow. The Lighthill high Prandtl number approximation is extended to permit computation of the Nusselt number for boundary layers with variable fluid properties. Nusselt numbers computed for the Howarth flow are close to the exact numerical solutions, except near separation.

Natural Convection in a Confined Region between Two Horizontal Ducts for Variable Fluid Properties

Two dimensional steady state laminar natural convection and the effect of localized heating at various pressures and temperatures on flow patterns in a rectangular channel is studied numerically. The governing equations for conservation of mass, momentum, energy and equation of state for the problem are solved by using an explicit finite difference scheme. All properties of the fluid, helium, are considered to be temperature dependent. The numerical results obtained with variable fluid properties differ remarkably from those with constant fluid properties. Flow patterns at the Rayleigh number greater than 1100 (pressure 50 mm Hg) are found to be almost similar to those previously reported.

Laminar heat transfer in a rectangular channel for the temperature boundary condition of the third kind

To investigate the influence of the temperature boundary condition of the third kind on the laminar forced convection heat transfer in the thermal entrance region of a rectangular channel, the energy equation is solved by applying the Galerkin-Kantorowich method of variational calculus. Uniform and fully developed velocity profiles are considered. Constant fluid properties are assumed. The heat conduction in flow direction is neglected. It is concluded that there can be a significant influence of Biot number on local Nusselt number. Representative results are tabulated for different aspect ratios.

The effect of buoyancy on flow and heat transfer for a gas passing down a vertical pipe at low turbulent reynolds numbers

For the analysis of low-flow situations in the core of the High-Temperature Gas-Cooled reactor it is necessary to have a knowledge of the variation of pressure drop and heat transfer with flow and buoyancy influence. Nitrogen at 4 bar has been used to simulate the high pressure helium in the reactor and an experiment performed for downward flow in a heated vertical pipe. The measurements show that for the range of flow and buoyancy influence parameters investigated, (2000 < Re < 10000 and Gr < 10 6), friction factors are reduced by up to 20% compared with a correlation for isothermal flows and heat transfer is increased by up to 40% compared with a correlation for constant fluid properties. Agreement with the limited amount of previous data is quite satisfactory. The changes in heat transfer and friction factor with buoyancy influence can be attributed to distortion of the normally linear, radial shear stress profile. Simple equations have been determined to correlate the present results but extrapolation to conditions of higher flow and buoyancy influence, where the interaction of forced and free convection may be different, is not advised.

Heat transfer in laminar entrance region of a flat channel for the temperature boundary condition of the third kind

To explore the influence of the developing flow in a flat channel on the laminar forced convection heat transfer, the non-linear momentum and the linear energy equation are solved successively by employing the Galerkin-Kantorowich method of variational calculus. Assuming constant fluid properties, negligible axial diffusion and temperature boundary condition of the third kind, semi analytic solution for velocity and temperature is derived. The local Nusselt numbers are tabulated for various values of Biot and Prandtl number.

A Numerical Analysis of Heat Transfer to Fluids Near the Thermodynamic Critical Point Including the Thermal Entrance Region

A two-dimensional numerical method has been developed to predict heat transfer to near critical fluids in turbulent flow through circular tubes. The analysis is applicable to the thermal entry region as well as fully developed flows. Agreement with experimental data for water at 31.0 MN/m2 is quite good. A correlation in the form of the heat flux parameter of Goldmann was found to be satisfactory for water at that pressure. Results are presented in graphical form which apply to a wide range of heat fluxes, mass velocities, and tube diameters. Preliminary results in the entrance region show that film coefficients remain well above the corresponding fully developed values for a larger distance downstream than would be the case with a constant property fluid. This effect becomes more pronounced as the heat flux is increased.

Laminar flow natural convection from the open vertical cylinder with uniform heat flux at the wall

A solution is obtained for fully developed flow of a constant-property fluid, with the lowest temperature equal to the fluid bulk temperature. This is satisfactory only for low values of Rayleigh number, up to about 20, that is, for relatively long cylinders. A second solution has in addition a thermal entry region, for application to shorter cylinders, to the point where the entry region fills the cylinder. This solution has not yet been made mathematically exact. Nusselt numbers up to the terminal point, at Rayleigh number of about 16000, are identical with those for the finite difference result of Dyer {6}.

Type Curves for Analysis of Afterflow-Dominated Gas-Well Buildup Data

A set of type curves is described that permits estimation of near-wellbore damage or stimulation from the afterflow-dominated portion of a pressure buildup test in a gas well. The result is portion of a pressure buildup test in a gas well. The result is an improved estimate of damage or stimulation relative to that obtained with constant fluid-property analyses of afterflow-distorted data. Introduction The conventional semilog plot of pressure buildup data is commonly used to determine formation permeability and, by means of the skin factor and flow efficiency, the degree of near-wellbore damage or stimulation. However, when these data are distorted by afterflow, other methods of analysis are required to extract useful information. One such method involves the use of type curves. Several sets of type curves are available, all of which work well when applied to oil wells and, in many cases, to gas wells. However, all were derived assuming constant fluid properties. For gas wells, this may result in inaccurate values of permeability and flow efficiency, particularly at low pressures when the gas compressibility is large. This paper presents an extension to gas wells of the "McKinley method" of type-curve analysis for afterflow-dominated data by including the effects of changing gas properties with pressure. While many approximations are involved, it will be demonstrated that, for gas wells, the new curves offer an improvement over McKinley's constant fluid-property curves. There is a penalty to be paid for this improved accuracy, however - the new types curves are more difficult to use than McKinley's. Therefore, they should be used only when (1) pressures beyond the afterflow region are not available for conventional semilog analysis, and (2) improved accuracy is desired relative to what would be obtained using the McKinley (or any constant fluid property) type curves to analyze gas-well buildup data. property) type curves to analyze gas-well buildup data. For rough estimates of damage or stimulation in gas wells, the easier-to-use McKinley curves will be shown to be adequate. With these new curves, it should be possible to obtain from afterflow-distorted gas-well buildup data a reliable value for near-wellbore permeability, and improved estimates of formation permeability and flow efficiency. This information is valuable in selecting workover and stimulation candidates, as well as in evaluating the effectiveness of workovers, stimulation treatments, and well completions. Development of the Type Curves Parameters Governing Afterflow Parameters Governing Afterflow When a flowing well is shut in at the surface, there will be a period of time during which appreciable flow into the wellbore will continue. This "afterflow" or "afterproduction" is a result of the wellbore storage capacity, which may be written F = 5.615 cw V,.............................(1) where cw = wellbore fluid compressibility, psi V = wellbore volume, bbl. The constant 5.615 converts F to cu ft/psi. JPT P. 915

Simultaneous development of the laminar velocity and temperature fields in a circular duct for the temperature boundary condition of the third kind

To analyze the influence of the developing flow in a circular duct on the laminar forced convection heat transfer, the non-linear momentum and linear energy equation are solved successively by employing the Galerkin-Kantorowich method of variational calculus. Assuming constant fluid properties, negligible axial diffusion and temperature boundary condition of the third kind, a closed form solution for velocity and a semi analytic solution for temperature are derived. It is concluded that there can be a considerable difference, depending upon Biot number and Prandtl number, between the local Nusselt number considering the radial convection and that neglecting it.

A convenient correlation for heat transfer to constant and variable property fluids in turbulent pipe flow

A recent equation for calculating heat-transfer coefficients to constant property fluids in pipes is modified to correlate variable property data. The correlating equation is of convenient form, applies to both liquids and gases, correlates constant property results within 10 per cent for 0·1 < Pr < 10 4 with 10 4 < Re < 10 6 , and correlates variable property data within 20 per cent for 0·7 < Pr < 75 with 10 000 < Re < 506 000. The equation is compared with the Sieder-Tate equation for liquids and the two equations of Petukhov for gases and liquids. Equations for heat transfer to variable property liquid metals are suggested.

Transient Evaporation and Combustion of a Fuel Droplet Near Its Critical Temperature

Abstract Recently obtained exact solutions for the transport-controlled lifetime of an isolated sphere of arbitrary density and “solubility” in a quiescent, constant-property fluid are exploited to predict the corresponding behavior of a fuel droplet evaporating (with or without vapor phase combustion) into a surrounding dense gas. Emphasis is placed on (i) systematic errors associated with the familiar quasi-steady (QS) approximation when applied to the vaporization of droplets which are not much denser than their surroundings, (ii) the chamber pressure-droplet temperature conditions under which the droplet will be driven to a subcritical (wet-bulb) temperature, or to its thermodynamic critical temperature, and (iii) the effects of gas/liquid solubility on the predicted lifetime of a fuel droplet. Illustrative calculations are included for the case of a kerosene-like (x-dodecane) droplet evaporating into compression-heated air, as encountered in diesel engine cylinders.

On the existence of solution of the Greenspan-Carrier equation

We are concerned with the flow of a viscous incompressible electrically conducting fluid of constant properties past a semi-infinite rigid plate. The governing boundary layer equations were derived by Greenspan and Carrier [2] in 1959. Numerical solutions of these equations subject to different boundary conditions have been considered by Stewartson and Wilson [5], Wilson [8], and recently by Bramley [1].

A Numerical Study of Laminar Free Convective Heat Transfer from Vertical Cones

A numerical study of free convective flow over vertical cones is described. The study is based on the use of the constant fluid properties boundary layer equations. Solutions have been obtained for...

Convection in the mantle: A laboratory model with temperature-dependent viscosity

Some exploratory laboratory experiments are described, using a working fluid (glycerine) whose viscosity depends strongly on temperature. Surface cooling produces a thin, viscous sheet which is driven away from regions of upward convection, and then plunges down steeply into the less viscous interior, maintaining its identity as it does so. When there are gradients of composition as well as temperature, convective motions can also be produced above the plunging sheets by a “double-diffusive” mechanism. The behaviour is quite unlike that observed previously in a fluid of constant properties, but it closely resembles some features of recent plate model of the Earth's mantle.