Showing papers on "Nusselt number published in 1985"

Flow of a non-Newtonian fluid between heated parallel plates

Abstract: The flow of a fluid of grade three between heated parallel plates is examined for two cases. In the first instance we postulate constant heat flux at the walls and via a similarity transformation calculate the Nusselt number as a function of both Γ, the parameter controlling viscous dissipation, and Λ, the non-Newtonian parameter. In the second case we restrict the temperature to change only normal to the plates; solutions in this case are obtained for two temperature-viscosity models, μ = μ ( θ ).

Effect of Wall Heat Conduction on Natural Convection Heat Transfer in a Square Enclosure

Abstract: This paper presents numerical and experimental results for buoyancy-induced flow in a two-dimensional, fluid-filled enclosure. Rectangular cavities formed by finite conductance walls of different void fractions and aspect ratios are considered. Parametric heat transfer calculations have been performed and results are presented and discussed. Local and average Nusselt numbers along the cavity walls are reported for a range of parameters of physical interest. The temperatures in the walls were measured with thermocouples, and the temperature distributions in the air-filled cavity were determined using a Mach-Zehnder interferometer. Good agreement has been obtained between the measured and the predicted temperatures in both the solid wall and in the fluid using the mathematical model. Wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer.

Heat transfer characteristics of three phase fluidized beds

Abstract: Heat transfer characteristics of two (liquid-gas, liquid-solid) and three (liquid-gas-solid) phase fluidized beds have been studied in a 15.2 cm-ID column fitted with an axially mounted cylindrical healer. Effects of gas velocity (0-12 cm/s). liquid velocity (0-16cm/s), particle size (1.7-8.0 mm) and liquid viscosity (0.001-0.039 Pa s) on heat transfer coefficient were determined. The heat transfer coefficient increased with fluid velocities and particle size and it decreased with liquid viscosity in two and three phase fluidized beds. The bed porosity at which the maximum heat transfer occurred decreased with particle size but increased with liquid viscosity. The coefficient were correlated in terms of experimental variables. Modified Nusselt number from the present and previous studies has been correlated with modified Prandtl and Reynolds numbers.

Pattern Formation and Wave-Number Selection by Rayleigh-Bénard Convection in a Cylindrical Container

Abstract: We describe an apparatus and procedures for simultaneous heat transport measurements and computer enhanced shadowgraph flow-pattern imaging in a shallow horizontal layer of fluid heated from below. The heat transport measurements have a resolution of better than 0.1%, and the shadowgraph technique can detect the flow field for ≡ (R – Rc)/Rc as small as 10-2 (Rc is the critical value of the Rayleigh number R for onset of convection). The apparatus and procedures were used to study pattern and wave-number evolution in a cylindrical layer of water with radius-to-height ratio L = 7.5 and Prandtl number σ = 6.1. We found that dynamic sidewall forcing during the early thermal transients after a change in the heat current from a subcritical to a supercritical value establishes a cylindrical flow pattern. Once created, this pattern is stable in our apparatus over the wide range 0.16 8 even after the transients have decayed. With changing , adjustment in the wave number k takes place discontinuously by hysteretic changes at the cell center in the number of convection roll pairs. When is increased, the discontinuous changes at the cell center are towards smaller k and are preceded by a continuous loss of cylindrical symmetry (the middle roll pair moves off center). The selected wave numbers coincide neither with the zig-zag instability of the infinite system, as once suggested, nor with a linear extrapolation to = 0(1) of the recent prediction to lowest order in of Manneville and Piquemal and of Cross. Comparison of the selected k with measurements by others reveals no dependence upon L and σ. For < 0.16, the cylindrical pattern is unstable and decays on a time scale much longer than a horizontal diffusion time to patterns of rolls which tend to be perpendicular to the sidewalls and which contain defects. Once formed, these latter patterns will persist at large values of . These patterns also undergo a wave-number adjustment process with hysteretic changes mediated mostly by focus singularities near the walls. In these cases, larger values of also tend to produce smaller values of k.

Natural Convection in a Fully Partitioned, Inclined Enclosure

Abstract: Natural convection in an inclined enclosure with a centrally located, complete partition has been investigated by a finite-difference procedure. The thermal conditions along the partition are not known beforehand; rather, they are an outcome of the coupling of the natural convection systems on either side of the enclosure partition. To resolve this coupling, a consecutive calculation procedure is used in which the natural convection on either side of the enclosure is successively solved (until convergence) with information exchange in each cycle of solution. Results have been obtained for enclosures with overall aspect ratios of 1 and 2 for Rayleigh numbers up to 107 and for inclination angles of 30, 45, 60, and 90 degrees. Results indicate that the strength of the convective motion and the average Nusselt number are both considerably reduced owing to the presence of the partition. The partition temperature increases monotonically along its length. For a vertical enclosure, the non-uniformity in the parti...

Experimental Investigation of Free Convection in a Vertical Rod Bundle—A General Correlation for Nusselt Numbers

Abstract: Free convection in two vertical, enclosed rod bundles has been experimentally investigated for a wide range of Rayleigh numbers. A uniform power dissipation per unit length is supplied to each rod, and the enclosing outer cylinder is maintained at constant temperature. Nusselt numbers for each rod, as well as an overall value for each bundle, have been obtained as a function of Rayleigh number. Comparison of the results for air and water as the working fluid indicate that, for a fixed Rayleigh number, an increase in the Prandtl number produces a reduction in the Nusselt number. This is contrary to what has been reported for vertical cavities and is attributed to curvature effects. Furthermore, the data reveal the interesting fact that it is quite possible for the individual rods in the bundle to exchange energy with the working fluid via different but coexisting regimes at a given power dissipation. Also, as the Rayleigh number is increased, the rods each tend to assume nearly the same heat transfer coefficient. Finally, a correlation for the overall convective Nusselt number is developed in terms of Rayleigh number and geometric parameters.

Convective motions in a spherical shell

Abstract: We compute the axisymmetric convective motions that exist in a spherical shell heated from below with inner to outer radius ratio equal to 0.5. The boundaries are stress-free and gravity is directly proportional to radius. Accurate solutions at large Rayleigh numbers, O(100000), are made feasible by a spectral method that employs diagonal-mode truncation. By examining the stability of axisymmetric motions it is inferred that the preferred form of convection varies dramatically according to the value of the Rayleigh number. While axisymmetric motions with different patterns may exist for modestly nonlinear convection, only a single motion persists at sufficiently large values of the Rayleigh number. This circulation is symmetric about the equator and has two meridional cells with rising motion at the poles. Instability of this single axisymmetric motion determines that the preferred pattern of three-dimensional convection has one azimuthal wave.

On the effect of flow direction on mixed convection from a horizontal cylinder

Abstract: SUMMARY The influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two-dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re'. The results are compared with the available experimental data and the agreement is satisfactory. The problem of laminar mixed convective heat transfer from a circular cylinder is a fundamental problem which has received extensive attention because of its many engineering applications. Several experimental studies have been carried out to investigate the effect of different factors on the heat transfer process. Some of these studies resulted in experimental correlations; however, no correlation could successfully predict the overall heat transfer coefficient and take into consideration all the parameters involved in the process. The first experimental investigation on the influence of free stream direction on the rate of heat transfer from a horizontal cylinder was carried out by Hatton et al.l who studied the problem up to Reynolds number Re = 45 and Grashoff number Gr = 10. In their work a correlation based on the vectorial addition of the forced and natural heat transfer coefficients was proposed. The correlation was proved to be successful except for the cases when the forced flow approaches a direction opposite to that of natural convection. Oosthuizen and Madan' studied the same problem when the forced flow makes an angle of 0, 90°, 135" or 180" with the direction of natural convection. The study was conducted at relatively high Re and Gr values compared to the range in Reference 1. Other experimental studies are found in References 3-6. On the other hand, most of the theoretical studies found in the literature have dealt with the case when both forced flow and natural convection are in the same direction. For example, Acrivos' studied the problem of combined convection in laminar boundary-layer flow in order to obtain the Nusselt number distribution near a stagnation point for the two cases of Pr -+0 and Pr -+ co. The approach requires the existence of boundary-layer flow and is limited to the region surrounding the stagnation point, Sparrow and Lee8 obtained an approximate solution for the Nusselt number distribution in the neighbourhood of the forward stagnation point for the case of parallel flow past a circular cylinder. The solution is based on the boundary-layer flow assumption and the problem

The effects of a strongly temperature-dependent viscosity on Stokes's drag law: experiments and theory

Abstract: This is an experimental and theoretical study of the slow translation of a hot sphere through a fluid at rest at infinity The viscosity depends strongly on temperature, ie, if Δ T = T 0 − T ∞ is the applied temperature difference and γ = |(d/d T 0 ) lnμ( T 0 )|, then the parameter θ = γ Δ T is large: it is about 65 in the experiments and is taken as infinite in the theory The flow is determined by two large parameters, namely the Nusselt number N and the modified viscosity ratio e −1 = ν ∞ /(ν 0 θ 3 ) The qualitative state of the flow is observed to depend on the relation between N and e If e −1 → ∞ ( N fixed, possibly large) previous analysis (Morris 1982) shows that all the shear occurs in a thin low-viscosity film coating the sphere; this film and the associated thermal layer separate at the equator, and a separation bubble of low-viscosity fluid trails the sphere (ii) If N → ∞ (e −1 ) large but fixed) even the most viscous fluid deforms, and both the drag and heat losses are found to be controlled by this highly viscous flow The present work maps the major asymptotic states which separate these two end-states for small e The drag and heat-transfer laws are determined experimentally and theoretically: in addition it is shown that separation of the thermal layer ceases when the drag is controlled by the most viscous fluid, even though the heat transfer in this case can be still controlled by the dynamics of the least-viscous fluid The heat-transfer and drag laws are also given for a sphere moving in a spherical container of finite radius This model is shown to give a close estimate of wall effects for a sphere moving in a cylindrical container For state (i) the theory predicts the heat transfer to within 20% and, for the smallest e, the drag to within 30% In the experiments e is small enough for all limiting states to be evident but, apart from state (i), a design flaw prevents a quantitative test of the theory For the other states, the theory is compared with numerical results from Daly & Raefsky (1985) Although the values of e in the calculations are not small enough for the limiting states to be achieved, the theory predicts the drag to within 8% and the heat transfer to within 10 %

Analysis of buoyancy effect on fully developed laminar heat transfer in a rotating tube

Abstract: Laminar heat transfer is analyzed in a tube rotating about an axis perpendicular to the tube axis. The solution applies for flow that is either radially outward from the axis of rotation, or radially inward toward the axis of rotation. The conditions are fully developed, and there is uniform heat addition at the tube wall. The analysis is performed by expanding velocities and temperature in power series using the Taylor number as a perturbation parameter. Coriolis and buoyancy forces caused by tube rotation are included, and the solution is calculated through second-order terms. The secondary flow induced by the Coriolis terms always tends to increase the heat transfer coefficient; this effect can dominate for small wall heating. For radial inflow, buoyancy also tends to improve heat transfer. For radial outflow, however, buoyancy tends to reduce heat transfer; for large wall heating this effect can dominate, and there is a net reduction in heat transfer coefficient.

The effect of density ratio on the film-cooling of a flat plate

Abstract: Influence du rapport de densite (entre le refrigerant et le gaz a refroidir) dans le cas du refroidissement par film d'une plaque plate

Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli

Abstract: The influence of various Prandtl numbers on the laminar convection flow between concentric and vertically eccentric cylinders is studied numerically. To overcome the difficulties associated with the complex physical domains a numerical transformation method is used to map this region on a rectangle. Although two independent computer programs which are based on different formulations of the governing equations were used, nearly identical results were obtained. Local heat transfer results are presented for a wide range of Rayleigh numbers for the first time. Local heat transfer rates are found to depend on the Prandtl number in addition to the Rayleigh number dependence.

High Rayleigh number convection with strongly variable viscosity: A comparison between mean field and two‐dimensional solutions

Abstract: We have studied single-mode mean field equations associated with variable viscosity convection for both steady state and time-dependent situations. Steady state mean field solutions can be obtained by treating the governing mean field equations as two coupled fourth-order differential systems, which are solved as a series of coupled two-point boundary value problems with underrelaxation. Steady solutions can be achieved in which there can exist viscosity contrasts exceeding 108 and interior Rayleigh numbers of 0(109). For comparison with two-dimensional solutions we have employed results derived from two finite element methods. Both temperature-dependent and temperature- and pressure-dependent viscosity with the surface viscosity fixed have been studied. Our results show that the differences between the two approaches grow with both viscosity contrast and convective vigor. The steady state Nusselt numbers and interior temperatures are greater in the case of mean field solutions. The power law index β governing the relationship between the interior Rayleigh number and the Nusselt number is larger for the mean field. Comparison of time-dependent solutions shows that one can monitor rather faithfully the evolution of the averaged interior temperature and surface heat flow over a long time scale with the mean field method. Initially, thermal instabilities originating from the mean field boundary layers are found to be correlated with two-dimensional boundary layer instabilities and are much more violent in character and cause large oscillations of the surface heat flow. The time scales associated with the secular variations of the Urey number, representing the ratio of the heat production and the surface heat loss, agree well between the two approaches. These results suggest that the mean field equations may serve as an efficient vehicle for studying planetary convection with complicated physics.