Showing papers on "Nusselt number published in 1978"

Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation

Abstract: Thermal convection in a fluid contained between two rigid walls with different mean temperatures is considered when either spatially periodic temperatures are prescribed at the walls or surface corrugations exist. The amplitudes of the spatial non-uniformities are assumed to be small, and the wavelength is set equal to the critical wavelength for the onset of Rayleigh-Benard convection. For values of the mean Rayleigh number below the classical critical value, the mean Nusselt number and the mean flow are found as functions of Rayleigh number, Prandtl number, and modulation amplitude. For values of the Rayleigh number close to the classical critical value, the effects of the non-uniformities are greatly amplified, and the amplitude of convection is then governed by a cubic equation. This equation yields three supercritical states, but only the state linked to a subcritical state is found to be stable.

Three-dimensional natural convection motion in a confined porous medium

Abstract: Weakly nonlinear analysis is used to calculate the possible two‐ and three‐dimensional convection patterns in a rectangular parallelepiped of saturated porous media when the horizontal dimensions are integral multiples of the vertical dimension. A two‐term expansion for the Nusselt number is found for values of the Rayleigh number close to the critical values. It is shown that the two‐dimensional roll configurations transfer heat more effectively than does the three‐dimensional pattern of motion when the Rayleigh number is just above the critical value.

Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference

Abstract: Natural convection in a porous medium filling a slender horizontal space with an end-to-end temperature difference is studied analytically. The end-to-end temperature difference gives rise to a horizontal counterflow pattern augmenting the heat transfer rate through the porous medium. Two basic geometries are considered: horizontal layer confined between 2 adiabatic and impermeable parallel plates, and horizontal cylinder surrounded by an adiabatic and impermeable cylindrical surface. Nusselt number relations are derived in terms of the Rayleigh number and the cavity aspect ratio. The end-wall permeability is shown to affect the heat transfer rate through the medium. (12 refs.)

Natural Convection in a Square Enclosure by a Finite-Element, Penalty Function Method Using Primitive Fluid Variables

Abstract: Numerical solutions for the problem of laminar natural convection in a square enclosure using the penalty function, finite-element method are presented. Solutions are obtained for values of the Rayleigh number up to 107 using primitive fluid variables, and the efficacy of the method is demonstrated through a qualitative and quantitative evaluation of the results. The simplicity and general applicability of the method are shown especially in the context of extensions to three-dimensional geometries and irregular computational grids.

Further thoughts on convective heat transport in a variable-viscosity fluid

Abstract: In a previous paper (Booker 1976) we found experimentally that the convective heat transport in a fluid with temperature-dependent viscosity decreased significantly as the ratio of the viscosities at the top and bottom boundaries increased. In this note, we show that this decrease in heat transport can be entirely accounted for by an increase in the critical Rayleigh number with variable viscosity.

Free convective heat transfer with density inversion in a confined rectangular vessel

Abstract: An experimental and analytical investigation pertaining to the effect of density inversion on steady free convective heat transfer of water in a confined rectangular vessel in which different temperatures are imposed on the opposing vertical walls is carried out. Water, as a testing fluid, has its maximum density at 4‡C. Temperature of the cold wall is maintained at 0‡C, while that of the hot wall is varied from 1‡C to 12‡ C. Photographs and analytical descriptions of the flow patterns, temperature distributions and average Nusselt number are presented. Moreover, the effect of dimensions of a rectangular vessel on the average Nusselt number is investigated. From the present investigation, it can be demonstrated both experimentally and analytically that the density inversion of water have an influential effect on the free convection heat transfer in the prescribed water layer, moreover, the average Nusselt number is a peculiar function of temperature difference between the cold and the hot walls, unlike the previous results for common fluids without density inversion.

Shock wave ignition of magnesium powders

Abstract: The paper is concerned with magnesium powder ignition caused by the interaction of powder with incident shock wave-induced flows. Experimentally observed ignition delays are correlated with predicted times for particle melting and the onset of thermal erosion, and a good agreement is found between experiment and theory. Ignition delays were measured as functions of particle screening, cloud concentration, incident shock strength, initial pressure, and oxygen concentration (diluted with nitrogen). An expression for the Nusselt number in the Reynolds number range 0-10,000 and the Mach number range 0-6 is proposed. The expression, when applied to predict particle behavior, provides results in agreement with experimental data for M/Re less than 0.5.

Experiments on centrifugally driven thermal convection in a rotating cylinder

Abstract: Heat-transfer measurements have been carried out in a right circular cylinder of fluid which is heated from above and rotated steadily about its vertical axis. Convection is produced relative to solid-body rotation through the coupling of the centrifugal acceleration and density variations in the fluid. Two silicone oils having kinematic viscosities of 350 cS and 0·65 cS were used in the experiments. In the former case viscous forces are important throughout the cylinder whereas in the latter case Ekman layers form and the Coriolis acceleration controls the interior flow. With the 350 cS oil the Nusselt number for heat transfer from the top to the bottom of the cylinder is a function of Gr ω and r 0 , where Gr ω is a Grashof number defined by employing the centrifugal acceleration evaluated at the outer edge of the cylinder in place of the gravitational acceleration, and r 0 is the cylinder aspect ratio. The behaviour is quite different for the 0·65 cS oil. Ekman layers form on the horizontal surfaces and heat is convected by Ekman suction. The Nusselt number is given by \[ Nu = 4.16\beta^{0.822}\epsilon^{-0.499}r_0^{0.173},\quad Ac\leqslant 0.025,\quad\sigma\beta\epsilon^{-\frac{1}{2}} > 0.7, \] where β is the thermal Rossby number, e is the Ekman number, σ is the Prandtl number, and Ac is the ratio of gravitational to centrifugal accelerations. This is consistent with previous theories which indicate that the system should depend on the parameters σβe −½ and r 0 in the limit as e and β approach zero.

Correlations of thermodynamic effects for developed cavitation

Abstract: The net positive suction head (NPSH) requirements for a pump are determined by the combined effects of cavitation, fluid properties, pump geometry, and pump operating point. An important part of this determination is the temperature depression (Delta T). Correlations are presented of the temperature depression for various degrees of developed cavitation on venturis and ogives. These correlations, based on a semi-empirical entrainment theory, express Delta T in terms of the dimensionless numbers of Nusselt, Reynolds, Froude, Weber, and Peclet, and dimensionless cavity length (L/D). The Delta T data were obtained in Freon 114, hydrogen and nitrogen for the venturis and in Freon 113 and water for the ogives.

Free Convection across Inclined Air Layers with One Surface V-Corrugated

Abstract: Experimental measurements are presented for free convective heat transfer across incline air layers, heated from below, and bounded by one V-corrugated plate and one flat plate. The measurements covered three values for the ratio, A, (average plate spacing to V-height), namely, A=1,2.5 and 4. It also covered angles of inclination with respect to the horizontal, theta, of 0,30,45 and 60 deg, and a range in Rayleigh number of 10

Heat transfer from a row of jets impinging on concave semi-cylindrical surface

Abstract: Heat transfer from impinging jets has been analyzed. Based on similarities of the boundary conditions of the related flow fields, analogies between heat transfer from impinging jets at the stagnation point and in the wall jet region have been shown for several flow geometries. Calculation of heat transfer in the stagnation region and in the wall jet region, based on available theory and the parameters, obtained from direct measurements, have been carried out, for the single, round, impinging jets. It has been shown that heat transfer from a row of round jets impinging on flat and concave surfaces can be comprehensively described through analysis of impinging jets of simpler geometries. Finally, experimental results for the local and average heat transfer effects are presented and discussed. Comparisons are made with theory and results of other investigators, with fairly satisfactory agreement.

Thermal design of a heat exchanger for heating or cooling blood.

Abstract: Experimental data, and their correlation with predictions from theory, are presented for the thermal design of a countercurrent heat exchanger for heating or cooling blood. The thermal design considers the influence on the Nusselt number of blood and the heat exchanger effectiveness of variables such as the blood flow rate, tube diameter and length, and the thermal properties of blood. The data presented are compared with data from the literature and with predictions from theory. Insofar as the design of a blood heat exchanger is concerned, flowing blood can be considered a single-phase fluid. Some applications of the thermal design analysis, the production and control of blood hyperthermia or hypothermia are discussed.

Correlation Equations for Turbulent Thermal Convection in a Horizontal Fluid Layer Heated Internally and from Below

Abstract: High Rayleigh number thermal convection in a horizontal fluid layer with uniform volumetric energy sources and a constant rate of bottom heating is studied analytically by a simple boundary layer approach. Heat transfer characteristics of the layer are defined in terms of local boundary-layer variables. Correlation equations are derived for the upper and the lower surface Nusselt numbers as functions of two independent Rayleigh numbers, based respectively on the surface to surface temperature difference and the volumetric heating rate. Variation of the turbulent core temperature, which so far has not been determined successfully by existing analytical methods, is obtained. This is found to depend on a single dimensionless parameter which measures the relative rates of internal and external heating. Results of this study are presented with available experimental data.