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Showing papers on "Nusselt number published in 1974"


Journal ArticleDOI
TL;DR: In this paper, the problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered, and it is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes : a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity.
Abstract: The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes : a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A → 0, are derived.

289 citations



Journal ArticleDOI
TL;DR: From the analysis of a conjugate problem of convective heat transfer in a laminar incompressible flow around a flat plate of a finite thickness, the design formulas are suggested for a local Nusselt number Nux(Nux/Nux0)−1 = CBx, (0).

180 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived a heat and mass transfer law for fully turbulent flow along a rough wall, which is quite analogous to Millikan's (1939) derivation of a skin-friction law for smooth-and rough-wall flows.
Abstract: General dimensional and similarity arguments are applied to derive a heat and mass transfer law for fully turbulent flow along a rough wall. The derivation is quite analogous to Millikan's (1939) derivation of a skin-friction law for smooth-and rough-wall flows and to the derivation of the heat and mass transfer law for smooth-wall flows by Fortier (1968a, b) and Kader & Yaglom (1970, 1972).The equations derived for the heat or mass transfer coefficient (Stanton number) Ch and Nusselt number Nu include the constant term β of the logarithmic equation for the mean temperature or concentration of a diffusing substance. This term is a function of the Prandtl number, the dimensionless height of wall protrusions and of the parameters describing the shapes and spatial distribution of the protrusions. The general form of the function β is roughly estimated by a simplified analysis of the eddy-diffusivity behaviour in the proximity of the wall (in the gaps between the wall protrusions). Approximate values of the numerical coefficients of the equation for β are found from measurements of the mean velocity and temperature (or concentration) above rough walls. The equation agrees satisfactorily with all the available experimental data. It is noted that the results obtained indicate that roughness affects heat and mass transfer in two ways: it produces the additional disturbances augmenting the heat and mass transfer and simultaneously retards the fluid flow in the proximity of the wall. This second effect leads in some cases to deterioration of heat and mass transfer from a rough wall as compared with the case of a smooth wall at the same values of the Reynolds and Prandtl numbers.

175 citations


01 Nov 1974
TL;DR: In this article, the spacing between the hot solar absorber and successive glass covers should be in the range 4 to 8 cm to assure minimum gap conductance, based on the theory and some experimental measurements.
Abstract: A useful solar-thermal converter requires effective control of heat losses from the hot absorber to the cooler surroundings. Based upon the theory and some experimental measurements it is shown that the spacing between the tilted hot solar absorber and successive glass covers should be in the range 4 to 8 cm to assure minimum gap conductance. Poor choice of spacing can significantly affect thermal conversion efficiency, particularly when the efficiency is low or when selective black absorbers are used. Recommended data for gap Nusselt number are presented as a function of the Rayleigh number for the high aspect ratios of interest in solar collector designs. It is also shown that a rectangular cell structure placed over a solar absorber is an effective device to suppress natural convection, if designed with the proper cell spacing d, height to spacing ratio L/d and width to spacing ratio W/d needed to give a cell Rayleigh number less than the critical value.

172 citations


Journal ArticleDOI
TL;DR: In this paper, the Galerkin technique is used to treat the steady-state two-dimensional problem for Rayleigh numbers as large as ten times the critical value of the Rayleigh number.
Abstract: The properties of convective flow driven by an adverse temperature gradient in a fluid-filled porous medium are investigated. The Galerkin technique is used to treat the steady-state two-dimensional problem for Rayleigh numbers as large as ten times the critical value. The flow is found to look very much like ordinary Benard convection, but the Nusselt number depends much more strongly on the Rayleigh number than in Benard convection. The stability of the finite amplitude two-dimensional solutions is treated. At a given value of the Rayleigh number, stable two-dimensional flow is possible for a finite band of horizontal wavenumbers as long as the Rayleigh number is small enough. For Rayleigh numbers larger than about 380, however, no two-dimensional solutions are stable. Comparisons with previous theoretical and experimental work are given.

171 citations


Journal ArticleDOI
TL;DR: In this article, the thermal frequency response of beds packed with glass and metallic particles has been measured in the range of Reynolds numbers from 0·05 to 330 values of the coefficients of axial dispersion of heat, intraparticle thermal conductivity and fluid-particle heat transfer coefficients have been found by non-linear regression.

137 citations


Journal ArticleDOI
TL;DR: In this article, the curvature ratio (radius of bend/inside radius of tube) was included as an independent parameter and, for values as small as 10, was found to have a negligible effect on the peripherally averaged Nusselt number.
Abstract: Fully developed forced-convective heat transfer to viscous flow of a constant-property Newtonian fluid in curved circular tubes was studied theoretically for a uniform-wall-temperature boundary condition. Numerical solutions were obtained over a wide range of Prandtl numbers for Dean numbers as large as 1,200. The curvature ratio (radius of bend/inside radius of tube) was included as an independent parameter and, for values as small as 10, was found to have a negligible effect on the peripherally averaged Nusselt number. The average Nusselt numbers for the important Prandtl number range of 0.7 to 5 were correlated by NNu = 0.836 NDe0.5 NPr0.1 for NDe ≥ 80.

111 citations


Journal ArticleDOI
TL;DR: In this paper, experimental and numerically computed values for the Nusselt number for natural convection heat transfer in an inclined, square channel maintained at uniform temperature on one inclined side and at a lower uniform temperature in the opposing side were determined and found to be in agreement.

105 citations



Journal ArticleDOI
TL;DR: In this article, the effect of density inversion on free convective heat transfer in a porous layer heated from below was investigated by maintaining the upper boundary temperature at 0°C.

Journal ArticleDOI
TL;DR: In this paper, temperature profiles and Nusselt numbers are calculated for slow three-dimensional flow through a simple cubic array of isothermal spheres using a collocation method in a coordinate system which permits the surface temperature to be prescribed directly.

Journal ArticleDOI
01 Mar 1974
TL;DR: In this paper, the authors describe the convective heat transfer in a vertical space insulated with a permeable material and present a numerical solution to the problem for Ra0 ⩽ 200, which is the range of interest to building technologies.
Abstract: This article describes the natural convective heat transfer in a vertical space insulated with a permeable material. A numerical solution to the problem is given for Ra0 ⩽ 200, which is the range of interest to building technological applications. The variables and boundary conditions and their influence upon the convective heat transfer are discussed. Comparisons are made with previously published results.

Journal ArticleDOI
TL;DR: In this article, the authors describe a combined theoretical and experimental investigation into the heat transfer from a disk rotating close to a stator with a radial outflow of coolant, and obtain mean Nusselt numbers for the free disk, the disk rotating very close to an unshrouded stator, and for the stator itself.
Abstract: This paper describes a combined theoretical and experimental investigation into the heat transfer from a disk rotating close to a stator with a radial outflow of coolant. Experimental results are obtained from a 762 mm diameter disk, rotating up to 4000 rev/min at axial clearances from 2 to 230 mm from a stator of the same diameter, with coolant flow rates up to 0.7 kg/s. Mean Nusselt numbers are presented for the free disk, the disk rotating close to an unshrouded stator with no coolant outflow, the disk rotating close to a shrouded and unshrouded stator with coolant outflow, and for the unshrouded stator itself. Numerical solutions of the turbulent boundary layer equations are in satisfactory agreement with the experimentally determined mean Nusselt numbers for the air-cooled disk over a wide range of conditions. At large ratios of mass flow rate/rotational speed the mean Nusselt numbers for the air-cooled disk are independent of rotation, and both the numerical solutions and experimental results become asymptotic to an approximate solution of the boundary layer equations.

Journal ArticleDOI
TL;DR: In this article, a Mach-Zehnder interferometer was used to stud two-dimensional Benard convection cells with Rayleigh numbers as great as 23400 and an overshoot of about 6% was observed at R/Rc = 9·2 and 13·8.
Abstract: A Mach-Zehnder interferometer was used to stud two-dimensional Benard convection cells. The experiments were performed with distilled water and sea water in the region where density is a linear function of temperature. Two-dimensional convection rolls were formed with Rayleigh numbers as great as 23400. Reversal in the temperature profile was obtained for R/Rc ≥ 3·8, and an overshoot of about 6% was observed at R/Rc = 9·2 and 13·8. This agrees with the values predicted theoretically by Veronis (1966) for stress-free boundaries and Royal (1969) for rigid boundaries. This disagrees with the experimental results of Gille (1967), who reports an overshoot of only 1 ½% at R/Rc = 16. Many of the other results agree with those of other experimenters, such as the relation between the cell height-to-width ratio and Rayleigh number, the relation between the Nusselt number and Rayleigh number, and the value of the critical Rayleigh number.

Journal ArticleDOI
TL;DR: In this article, experimental determinations of the local heat transfer by forced convection from model leaves heated by a constant energy flux were made in the laboratory under laminar and turbulent flow conditions.
Abstract: Experimental determinations of the local heat transfer by forced convection from model leaves heated by a constant energy flux were made in the laboratory under laminar and turbulent flow conditions. The results are expressed in a logarithmic dimensionless plot of the local Nusselt number, Nu d , against the local Reynolds number, Re d . For the laminar case, Nu d was only a linear function of Re d 1/2 downwind from the leading edge regions, although this relationship departed from that predicted theoretically due to the finite size and thickness of the model. For the turbulent case, a simple relationship between Nu d and Re d was found over a wide range of Reynolds numbers. The enhancement of heat transfer in the turbulent case depends primarily on the scale of turbulence rather than on the turbulent intensity. Past workers have discussed their results in relation to a factor β, defined as the ratio between the heat transfer predicted by the Polhausen equation, and that measured. The results suggest that β is not a unique parameter and may not be useful in describing the overall turbulent transfer process.

Journal ArticleDOI
TL;DR: In this paper, the effect of buoyancy forces on laminar forced convective heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall temperature is studied by a numerical method for the case of large Prandtl number fluids.

Journal ArticleDOI
TL;DR: In this article, a computational study of forced convection processes in ducts and packed beds at low Reynolds numbers has been made, and the results give a better understanding of these processes, especially for small Peclet numbers.

Journal ArticleDOI
TL;DR: In this article, an analysis has been carried out to determine the heat-transfer characteristics for turbulent flow in circular tube with circumferentially varying boundary conditions of first and second kind.

Journal ArticleDOI
01 Mar 1974
TL;DR: In this paper, a correlation of data is presented which shows the Nusselt number as a function not only of the Reynolds number but also in certain ranges of the Prandtl and Weber number.
Abstract: It is shown that a most consistent application of similarity parameters reduces the “random error” of experimental results in film condensation by 90%, in extreme situations even more. On the basis of physical considerations a correlation of data is presented which shows the Nusselt number as a function not only of the Reynolds number but also in certain ranges of the Prandtl and Weber number. Although the latter parameters varied only moderately in the experiments presented here the general idea is supported clearly. Further experiments will have to provide for quantitatively more reliable results.

Journal ArticleDOI
TL;DR: In this article, the Malkus hypothesis is used to show that the flow tends to transport the maximum amount of heat possible, subject to certain constraints, such as the Prandtl number and integral constraint.
Abstract: Turbulent convection for a rotating layer of fluid heated from below is studied in this paper. The boundaries of the fluid layer are taken to be free. The underlying principle, used is the Malkus hypothesis that the flow tends to transport the maximum amount of heat possible, subject to certain constraints. By taking the Prandtl number to be infinite, a linear differential constraint and an integral constraint are used. The variational problem that follows then depends on two dimensionless parameters, the Taylor number T and the Rayleigh number R.Asymptotic analysis for the turbulent regime shows that the flow arranges itself so as to tend to offset the stabilizing effect of the rotational constraint, at least in so far as the heat flux is concerned. The dimensionless heat flux, or the Nusselt number, has in general different dependence on T and R, depending on the particular region in the parameter space. For T [les ] O(R), the flow is essentially non-rotating. For O(R) [les ]T [les ] O(R4/3), the flow will always have finitely many horizontal wavenumbers, though the total number of modes increases as T increases in this region. For O(R4/3) [les ] T [les ] O (R3/2), the Nusselt number has a functional dependence proportional to R3/T2, having essentially infinitely many horizontal modes as both R and T increase indefinitely in this region. The last expression is particularly interesting, as it agrees qualitatively with results in finite-amplitude laminar convection. It is also linearly dependent on the layer thickness, as one might expect from dimensional argument. It is suggested that, in the context of the maximum principle, the result in this region of the parameter space may be applicable as well to the same fluid layer with rigid boundaries through the existence of an Ekman layer that is thinner than the thermal layer.

Journal ArticleDOI
TL;DR: In this article, the effects of uniform transpiration on heat transfer and on temperature and velocity profiles were predicted using the finite difference procedure of Patankar and Spalding (1967).

Journal ArticleDOI
TL;DR: In this paper, Cebeci et al. presented some numerical predictions of the turbulent flow of a mixture of CC1 4 vapour and air over a vertical plate onto which the vapour condenses.

Journal ArticleDOI
C.A. Hieber1
TL;DR: In this paper, it was shown by means of a global energy-rate balance that the leading edge effect upon the total heat transfer rate is given by a1kΔT where a1 has the value 0·625 at a Prandtl number of 0·72.

Journal ArticleDOI
HK Hendrik Kuiken1
TL;DR: In this article, a coordinate expansion is used to converge for all values of the expansion variable, and an alternative series expansion is derived to derive solutions valid for small or large values of Prandtl number.
Abstract: infinite expanse of viscous fluid. The heat resistance of the sheet is assumed to ble so small that the temperature can be considered uniform across the sheet. Precise conditions for this assumption to be valid are derived. The problem is solved first by means of a coordinate expansion, which can be proved to converge for all values of the expansion variable. Since this series cannot be used numerically downstream, an alternative series expansion, which applies downstream, is also derived. Special sections are devoted to deriving solutions valid for small or large values of the Prandtl number. Finally, expressions are obtained for the Nusselt number and the cooling length. It is found that cooling is determined by the smaller of two diffusivities, namely, the kinematic viscosity and the thermal diffusivity.

Journal ArticleDOI
01 Jul 1974
TL;DR: In this article, asymptotic expressions for the Nusselt number for very small and very large Prandtl numbers were found for a sheet and a cylinder moving in a fluid at rest.
Abstract: Heat transfer from a sheet and a cylinder (at constant temperature) moving in a fluid at rest is examined. Asymptotic expressions for the Nusselt number are found for very small and very large Prandtl numbers.


Journal ArticleDOI
TL;DR: In this article, two independent methods were used to measure the rate of heat transfer from a hot gas to the walls of a cylindrical combustion chamber in which large-amplitude combustion-driven oscillations accompanied a mean flow.
Abstract: Two independent methods were used to measure the rate of heat transfer from a hot gas to the walls of a cylindrical combustion chamber in which large-amplitude combustion-driven oscillations accompanied a mean flow. The results obtained from the two methods were in good agreement and indicated a definite increase in the heat transfer in the presence of oscillations. The increase was found to vary approximately as the square root of the oscillation amplitude and as the fourth root of the frequency. A correlation in terms of dimensionless variables was obtained using the thickness of the acoustic boundary layer as the appropriate length scale.

Journal ArticleDOI
TL;DR: In this paper, a theory was developed for heat transfer to liquid metals when the heat transfer surface is covered with gas bubbles, and the system analysed is that of constant heat flux to slug flow in a circular pipe.

Journal ArticleDOI
TL;DR: In this article, a convective heat transfer for steady laminar flow between two confocal elliptic pipes with longitudinal uniform wall temperature gradient under various heating conditions is presented in analytical closed form utilizing the exact solutions of the Navier-Stokes and energy equations.