Showing papers on "Nusselt number published in 1972"

Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles

Abstract: Previously obtained experimental heat transfer data have been collected and are illustrated along with minor variations of the standard correlations. Analysis of data for heat transfer in randomly packed beds and compact (void fraction less than 0.65) staggered tube bundles indicates that the Nusselt number for a wide range of packing materials and tube arrangements is given by provided NRe ≥ 50. The correlations presented in this paper are not necessarily the most accurate available; however, they have wide application, are easy to use, and are quite satisfactory for most design calculations.

Thermal convection in a horizontal fluid layer with uniform volumetric energy sources

Abstract: Energy transport at Rayleigh numbers up to 675 times the critical (linear stability theory) value is measured in a layer of dilute electrolyte bounded horizontally by two rigid planes of constant and equal temperature; Joule heating by an alternating current passing horizontally through the layer provides the volumetric energy source. Horizontally averaged temperature profiles are determined optically. Mean temperature distributions are asymmetric at elevated Rayleigh numbers, the energy transport at the upper boundary being more than twice that at the lower boundary. Three regimes of flow are identified and discrete transitions in the energy transport appear to exist when the flow is turbulent. Extrapolation of the data to the conduction value of the Nusselt number yields a critical Rayleigh number which is within + 10·7% of linear theory values. No subcritical convection is observed when finite amplitude disturbances are introduced into the fluid at a Rayleigh number between the critical values predicted by the linear stability theory and energy theory respectively.

On steady convection in a porous medium

Abstract: For convection in a porous medium the dependence of the Nusselt number on the Rayleigh number is examined to sixth order using an expansion for the Rayleigh number proposed by Kuo (1961). The results show very good agreement with experiment. Additionally, the abrupt change which is observed in the heat transport at a supercritical Rayleigh number may be explained by a breakdown of Darcy's law.

Hydrodynamic stability and natural convection in Ostwald-de Waele and Ellis fluids: The development of a numerical solution

Abstract: An algorithm was developed for the finite-difference computation of hydrodynamic stability and natural convection in non-Newtonian fluids heated from below. Test calculations were carried out for fluids whose viscosity characteristics are described by the Ostwald-de Waele (power-law) and Ellis models and for roll-cells with both rigid and dragless vertical boundaries. The effects of time-step and grid-size were tested thoroughly. The results were found to be independent of the assumed initial state. The computed values of the Nusselt number and the critical Rayleigh number for Newtonian fluids agree well with prior experimental results. The computations for the Ostwald-de Waele model indicate that the approximate solution of Tien, Tsuei, and Sun may underestimate the critical Rayleigh Number.

Bounds for heat transport in a porous layer

Abstract: Strongly nonlinear heat transport across a porous layer is studied using Howard's (1963) variational method. The analysis explores a bifurcation property of Busse's (1969) multi-a solution of this variational problem and complements the 1972 study of Busse & Joseph by further restricting the fields which are allowed to compete for the maximum heat transported a t a given temperature difference. The restriction arises, as in the case of infinite Prandtl number convection studied by Chan (1971), from letting a parameter tend to infinity from the outset; here, however, the parameter which is assumed infinitely large (the Prandtl-Darcy number) is actually seldom smaller than O(107).The theoretical bounding heat-transport curve is computed numerically. The maximizing Nusselt number (Nu) curve is given a t first by a functional of the single-a solution; then this solution bifurcates and the Nusselt number functional is maximized for an interval of Rayleigh numbers (R) by the two-a solution. The agreement between the numerical analysis and recent experiments is striking. The theoretical heat-transport curve is found to be continuously differentiable but has piecewise discontinuous second derivatives.The results of an asymptotic (R → ∞) analysis following Chan (1971) are in qualitative agreement with the results of numerical analysis and give the asymptotic law Nu = 0.016R. This law is consistent with the result of the porous version of the well-known dimensional argument leading to the one-third power law for regular convection. The asymptotic results, however, do not appear to be in good quantitabive agreement with the numerical results.

Instantaneous Heat Transfer to the Cylinder Wall in Reciprocating Compressors

Abstract: This study first reviews, discusses, and compares existing correlations for heat transfer in reciprocating compressors and engines. Then after a discussion of the significance of obtaining accurate instantaneous heat transfer data, the authors describe an experimental investigation of the instantaneous heat transfer rates to the cylinder wall of a reciprocating refrigerating compressor. Finally, this report presents an expression which correlates the time averaged data within 20%. INTRODUCTION Previous attempts at describing and predicting the heat transfer occurring in reciprocating engines and compressors have in some cases been moderately successful and in others completely unsuccessfuly. Most of the reported investigations have attempted to predict the instantaneous heat transfer from measured average heat transfer rates [1 through 5]. More recent investigations, however, have been concentrating on the problems of measurement and correlation of instantaneous heat transfer rates [6 through lOJ. All these investigations were carried out on internal combustion engines and, to the authors' knowledge, there has been no previous measurement of instantaneous "\eat transfer rates in reciprocating compressors. Thus, this investigation was undertaken with the hope of providing additional insight into the fundamentals of heat transfer processes in reciprocating machinery. The present investigation, which is part of a more extensive research program [11], begins with a review and discussion of the presently available heat transfer correlations. A comparison of these correlations exposes their basic characteristics and differences and is followed by a prediction of the maximum errors introduced when the estimation of compressor efficiencies is b~sed upon a poor knowledge of the 521 instantaneous heat transfer rates. Finally, experimental methods and results are presented together with a correlation of the data obtained. REVIEW OF AVAILABLE HEAT TRANSFER CORRELATIONS The available correlations on cylinder heat transfer have all been developed for internal combustion engines and they can be divided into two main groups according to the choice of variables. Representative for the first group are the correlations by Nusselt [1], Eichelberg [2], and Pflaum [3]. In this group the heat-transfer coefficient chosen is of the following form: h(t) = f[V ,P (t), T (t)] p g g ( 1) where t denotes the instantaneous value of a quantity. Representative of the second group are Woschni [6], Annand [4], Sitkei [5] and LeFeuvre [7]. This group utilizes correlations of the type Nu(t) = f[Re(t), gas properties J. (2) All the correlations in these two groups include constants that have to be determined experimentally and are, therefore, empirical in the first group and semi-empirical in the second. The correlations are given below. First group: Nusselt: h(t)=.0278(1+.38 V )[P (t) 2T (t)]l/3 p g g Eichelberg: h(t)=.0565 V l/3 [P (t)T (t)]l/2 p g g ( 3)

Heat transfer in a channel with a porous wall for turbine cooling application

Abstract: A method of cooling turbine blades internally by continuous injection through an interior baffle is analyzed. The analytical model consists of a two-dimensional channel formed by a solid wall (blade surface) and a porous plate (injection source). Based on incompressible- and laminar-flow assumptions, the velocity and the temperature fields are determined. The Nusselt numbers for a power-law surface-temperature variation are obtained and expressed in terms of the Prandtl and the Reynolds numbers. A related problem of cooling the turbine disk is also solved.

Finite-amplitude thermal convection within a self-gravitating fluid sphere.

Abstract: Finite-difference calculations have been carried out to determine the structure of finite-amplitude thermal convection within a self-gravitating fluid sphere with uniform heat release. For a fixed-surface boundary condition, single-cell convection breaks up into double-cell convection at a Rayleigh number of 30,000, at a Rayleigh number of 500,000 four-cell convection is observed. With a free-surface boundary condition only single cell convection is obtained up to a Rayleigh number of 5,000,000.

Direct contact heat transfer between immiscible fluid layers in laminar flow

Abstract: The problem of heat transfer (and, by analogy, mass transfer) between immiscible fluids in laminar parallel flow is analyzed as a conjugated boundary value problem. Exact solutions are developed in terms of known functions by solving for the temperature fields in the two phases separately for constant boundary conditions, then generalizing the results to obtain solutions for the interfacial temperature distribution and the complete temperature field for the conjugated system. The analysis and the results of calculations for heat transfer between two immiscible films flowing down an adiabatic inclined plane are presented. It is shown that axial conduction can be included, and the effects of axial conduction in one stream are examined. The predicted Nusselt numbers are plotted versus axial position for various parameters, and the interfacial temperatures and mixed mean fluid temperatures for the two phases are plotted to elucidate the heat transfer characteristics.

Numerical solution of heat and mass transfer from spheroids in steady axisymmetric flow

Abstract: Heat (or mass) transfer from oblate and prolate spheroids with a ratio of minor to major axis of 0.2, as well as from a sphere, have been studied by numerically solving the energy (or diffusion) equation for constant fluid properties, in conjunction with the previously solved equations of continuity and motion, in spheroidal coordinates. A Reynolds number range of 1-100 was covered for a Prandtl number of 0.7, as well as creeping flow for Peclet numbers up to 70. Streamlines, isotherms, and local Nusselt numbers are presented. Surface mean Nusselt numbers computed for Pr = 0.7 are compared with experimental data in the literature, while those computed for creeping flow are compared with results by more approximate methods, and by analytical theory for limiting values of Peclet number, developed by other investigators.

On the second fundamental problem of combined free and forced convection through vertical noncircular ducts

Abstract: Analysis of combined free and forced convection through vertical noncircular ducts is carried out using a variational technique. Fully developed flow with uniform axial heat input and uniform peripheral heat flux is assumed. All fluid properties are considered invariant with temperature except the variation of density in the buoyancy term of the equation of motion. The condition of uniform peripheral heat flux is utilized in deriving the variational expression. This procedure releases the thermal boundary condition from satisfying exactly the condition at the wall. A finite-difference procedure is carried out. For pure forced convection case, a particularly simple variational expression is presented. Nusselt numbers for combined free and forced convection are computed for rectangular, rhombic and elliptical ducts. An exact solution is presented for laminar forced convection through elliptic ducts. Variational results are in agreement with this exact solution. The present results are compared with those in the published literature wherever possible, and good agreement is obtained.

Heat Transfer between Parallel Walls: An Interferometric Investigation

Abstract: The temperature fields and the transfer of heat within vertical, inclined and horizontal air layers are examined for each of three different heat transfer regimes. Experimental evidence is offered which explains the difference between the heat transfer correlations of previous investigations in which the Nusselt modulus is based on the heat flux leaving the heated wall and those in which the Nusselt number is based upon the rate at which heat is transferred to the cooled wall. It is also shown that some of the thermal boundary conditions which have generally been assumed in numerical studies are unrealistic.

Kinetics of heat transfer during the desiccation of moist materials

Abstract: A relation is established between the Rebinder number and the Nusselt number for the slowing-down stage of the desiccation process, also between the Nusselt number and the dimensionless desiccation rate during the first and the second stage of the process.

Thermal Instability in Differentially Heated Inclined Fluid Layers

Abstract: In an inclined adversely heated fluid layer confined between two rigid boundaries in a slot of large aspect ratio it is found that the unicellular base flow in the conduction regime becomes unstable with the formation of stationary secondary rolls with their axes along the line of inclination (x-rolls) for large Prandtl number fluids and axes perpendicular to the line of inclination (y-rolls) for small Prandtl number fluids However, for angles near the vertical, the curve of the critical Rayleigh number versus inclination for x-rolls rises above that for y-rolls even for large Prandtl number fluids so that in a vertical fluid layer only cross rolls (y-rolls) could develop The stability equations, as well as the results, reduce to those available for the horizontal fluid layer for which x-rolls are as likely to occur as y-rolls It is seen that even a small inclination to the horizontal is enough to assign a definite direction for these two-dimensional cells, this direction depending on the Prandtl number It is hoped that this basic information will be of help in the determination of the magnitude of the secondary cells in the postinstability regime and the heat transfer characteristics of the thin fluid layer