Showing papers on "Nusselt number published in 1999"

Dynamics and Heat Transfer Associated With a Single Bubble During Nucleate Boiling on a Horizontal Surface

Abstract: In this study, a complete numerical simulation of a growing and departing bubble on a horizontal surface has been performed. A finite difference scheme is used to solve the equations governing conservation of mass, momentum, and energy in the vapor-liquid layers. The vapor-liquid interface is captured by a level set method which is modified to include the influence of phase change at the liquid-vapor interphase. The disjoining pressure effect is included in the numerical analysis to account for heat transfer through the liquid microlayer. From the numerical simulation, the location where the vapor-liquid interface contacts the wall is observed to expand and then retract as the bubble grows and departs. The effect of static contact angle and wall superheat on bubble dynamics has been quantified. The bubble growth predicted from numerical analysis has been found to compare well with the experimental data reported in the literature and that obtained in this work

Evaporation of Acoustically Levitated Droplets

Abstract: The rate of heat and mass transfer at the surface of acoustically levitated pure liquid droplets is predicted theoretically for the case where an acoustic boundary layer appears near the droplet surface resulting in an acoustic streaming. The theory is based on the computation of the acoustic field and squeezed droplet shape by means of the boundary element method developed in Yarin, Pfaffenlehner & Tropea (1998). Given the acoustic field around the levitated droplet, the acoustic streaming near the droplet surface was calculated. This allowed calculation of the Sherwood and Nusselt number distributions over the droplet surface, as well as their average values. Then, the mass balance was used to calculate the evolution of the equivalent droplet radius in time. The theory is applicable to droplets of arbitrary size relative to the sound wavelength λ, including those of the order of λ, when the compressible character of the gas flow is important. Also, the deformation of the droplets by the acoustic field is accounted for, as well as a displacement of the droplet centre from the pressure node. The effect of the internal circulation of liquid in the droplet sustained by the acoustic streaming in the gas is estimated. The distribution of the time-average heat and mass transfer rate over the droplet surface is found to have a maximum at the droplet equator and minima at its poles. The time and surface average of the Sherwood number was shown to be described by the expression Sh = KB/√ω[Dscr ]0, where B = A0e/(ρ0c0) is a scale of the velocity in the sound wave (A0e is the amplitude of the incident sound wave, ρ0 is the unperturbed air density, c0 is the sound velocity in air, ω is the angular frequency in the ultrasonic range, [Dscr ]0 is the mass diffusion coefficient of liquid vapour in air, which should be replaced by the thermal diffusivity of air in the computation of the Nusselt number). The coefficient K depends on the governing parameters (the acoustic field, the liquid properties), as well as on the current equivalent droplet radius a.For small spherical droplets with a[Lt ]λ, K = (45/4π)1/2 = 1.89, if A0e is found from the sound pressure level (SPL) defined using A0e. On the other hand, if A0e is found from the same value of the SPL, but defined using the root-mean-square pressure amplitude (prms = A0e/√2), then Sh = KrmsBrms/ √ω[Dscr ]0, with Brms = √2B and Krms = K/√2 = 1.336. For large droplets squeezed significantly by the acoustic field, K appears always to be greater than 1.89. The evolution of an evaporating droplet in time is predicted and compared with the present experiments and existing data from the literature. The agreement is found to be rather good.We also study and discuss the effect of an additional blowing (a gas jet impinging on a droplet) on the evaporation rate, as well as the enrichment of gas at the outer boundary of the acoustic bondary layer by liquid vapour. We show that, even at relatively high rates of blowing, the droplet evaporation is still governed by the acoustic streaming in the relatively strong acoustic fields we use. This makes it impossible to study forced convective heat and mass transfer under the present conditions using droplets levitated in strong acoustic fields.

Prandtl number effects in convective turbulence

Abstract: The effect of Prandtl number on the dynamics of a convective turbulent flow is studied by numerical experiments. In particular, three series of experiments have been performed; in two of them the Rayleigh number spanned about two decades while the Prandtl number was set equal to 0.022 (mercury) and 0.7 (air). In the third series, in contrast, we fixed the Rayleigh number at 6×105 and the Prandtl number was varied from 0.0022 up to 15. The results have shown that, depending on the Prandtl number, there are two distinct flow regimes; in the first (Pr[lsim ]0.35) the flow is dominated by the large-scale recirculation cell that is the most important ‘engine’ for heat transfer. In the second regime, on the other hand, the large-scale flow plays a negligible role in the heat transfer which is mainly transported by the thermal plumes.For the low-Pr regime a model for the heat transfer is derived and the predictions are in qualitative and quantitative agreement with the results of the numerical simulations and of the experiments. All the hypotheses and the consequences of the model are directly checked and all the findings are consistent with the predictions and with experimental observations performed under similar conditions. Finally, in order to stress the effects of the large-scale flow some counter examples are shown in which the large-scale motion is artificially suppressed.

Infinite prandtl number convection

Abstract: We prove an inequality of the type N≤CR 1/3(1+log+ R)2/3 for the Nusselt number N in terms of the Rayleigh number R for the equations describing three-dimensional Rayleigh–Benard convection in the limit of infinite Prandtl number

Stagnation Region Heat Transfer of a Turbulent Axisymmetric Jet Impingement

Abstract: The turbulent heat transfer characteristics in a stagnation region were investigated experimentally for an axisymmetric submerged air jet impinging normal to a heated flat plate. The temperature distribution on the heated flat surface was measured by a thermochromic liquid crystal (TLC) with digital image processing technique. To get precise heat transfer data inside the stagnation region, a fully developed straight pipe nozzle was used in this study. The stagnation Nusselt number was correlated for the jet Reynolds number and the nozzle-to-plate spacing as Nu theta alpha Re 0.565(L/D)0.0384. For the nozzle-to-plate spacing of L/D=2, the stagnation Nusselt number varies according to Nu theta alpha Re 0.050 and the local heat transfer rates exhibit two maxima. The primary and secondary maxima are attributed to the accelerated radial flow and the transition from a laminar to a turbulent boundary layer, respectively. For larger nozzle-to-plate spacings (L/D<6), the local heat transfer decreases monotonica...

Heat transport in stagnant lid convection with temperature‐ and pressure‐dependent Newtonian or non‐Newtonian rheology

Abstract: A numerical model of two-dimensional Rayleigh-Benard convection is used to study the relationship between the surface heat flow (or Nusselt number) and the viscosity at the base of the lithosphere. Newtonian or non-Newtonian, temperature- and pressure-dependent rheologies are considered. In the high Rayleigh number time-dependent regime, calculations yield Nu ∝ RaBL1/3beff−4/3 where beff is the effective dependence of viscosity with temperature at the base of the upper thermal boundary layer and RaBL is the Rayleigh number calculated with the viscosity νBL (or the effective viscosity) at the base of the upper thermal boundary layer. The heat flow is the same for Newtonian and non-Newtonian rheologies if the activation energy in the non-Newtonian case is twice the activation energy in the Newtonian case. In this chaotic regime the heat transfer appears to be controlled by secondary instabilities developing in thermal boundary layers. These thermals are advected along the large-scale flow. The above relationship is not valid at low heat flow where a stationary regime prevails and for simulations forced into steady state. In these cases the Nusselt number follows a trend Nu ∝ RaBL1/5beff−1 for a Newtonian rheology, as predicted by the boundary layer theory. We argue that the equilibrium lithospheric thickness beneath old oceans or continents is controlled by the development of thermals detaching from the thermal boundary layers. Assuming this, we can estimate the viscosity at the base of the stable oceanic lithosphere. If the contribution of secondary convection to the surface heat flux amounts to 40 to 50 mW m−2, the asthenospheric viscosity is predicted to be between 1018 and 2×l019 Pa s.

Evaporation of acoustically levitated droplets

Abstract: The rate of heat and mass transfer at the surface of acoustically levitated pure liquid droplets is predicted theoretically for the case where an acoustic boundary layer appears near the droplet surface resulting in an acoustic streaming. The theory is based on the computation of the acoustic eld and squeezed droplet shape by means of the boundary element method developed in Yarin, Pfaenlehner & Tropea (1998). Given the acoustic eld around the levitated droplet, the acoustic streaming near the droplet surface was calculated. This allowed calculation of the Sherwood and Nusselt number distributions over the droplet surface, as well as their average values. Then, the mass balance was used to calculate the evolution of the equivalent droplet radius in time. The theory is applicable to droplets of arbitrary size relative to the sound wavelength , including those of the order of , when the compressible character of the gas flow is important. Also, the deformation of the droplets by the acoustic eld is accounted for, as well as a displacement of the droplet centre from the pressure node. The eect of the internal circulation of liquid in the droplet sustained by the acoustic streaming in the gas is estimated. The distribution of the time-average heat and mass transfer rate over the droplet surface is found to have a maximum at the droplet equator and minima at its poles. The time and surface average of the Sherwood number was shown to be described by the expression Sh= KB= p !D0, where B = A0e=(0c0) is a scale of the velocity in the sound wave (A0e is the amplitude of the incident sound wave, 0 is the unperturbed air density, c0 is the sound velocity in air, ! is the angular frequency in the ultrasonic range, D0 is the mass diusion coecient of liquid vapour in air, which should be replaced by the thermal diusivity of air in the computation of the Nusselt number). The coecientK depends on the governing parameters (the acoustic eld, the liquid properties), as well as on the current equivalent droplet radius a. For small spherical droplets with a , K = (45=4) 1=2 =1 :89, if A0e is found from the sound pressure level (SPL) dened using A0e. On the other hand, if A0e is found from the same value of the SPL, but dened using the root-mean-square pressure amplitude (prms = A0e= p

Progress in the use of non-linear two-equation models in the computation of convective heat-transfer in impinging and separated flows

Abstract: The paper considers the application of the Craft et al. [6]non-linear eddy-viscosity model to separating and impinging flows. The original formulation was found to lead to numerical instabilities when applied to flow separating from a sharp corner. An alternative formulation for the variation of the turbulent viscosity parameterc μ with strain rate is proposed which, together with a proposed improvement in the implementation of the non-linear model, removes this weakness. It does, however, lead to worse predictions in an impinging jet, and a further modification in the expression for c μ is proposed, which both retains the stability enhancements and improves the prediction of the stagnating flow. The Yap [24] algebraic length-scale correction term, included in the original model, is replaced with a differential form, developed from that proposed by Iacovides and Raisee [10]. This removes the need to prescribe the wall-distance, and is shown to lead to superior heat-transfer predictions in both an abrupt pipe flow and the axisymmetric impinging jet. One predictive weakness still, however, remains. The proposed model, in common with other near-wall models tested for the abrupt pipe expansion, returns a stronger dependence of Nusselt number on the Reynolds number than that indicated by the experimental data.

Effect of Surface Radiation on Natural Convection in a Square Enclosure

Abstract: Results of an experimental study of heat transfer by natural convection and surface radiation in an air-e lled squareenclosureusingadifferentialinterferometerarereported.Theenclosurecomprisestwodifferentiallyheated vertical walls and two horizontal adiabatic walls. The suppression of natural convection in the presence of surface radiation has been demonstrated experimentally. For the case of an enclosure with highly emissive walls, mean Nusselt number correlations for convection and radiation, as well as combined convection and radiation, are also presented in terms of Grashof number in the laminar range. Nomenclature d = width of the enclosure, m Gr = Grashof number, gb (Th i Tc)d 3 /m 2 h = local heat transfer coefe cient along the hot wall, W/m 2 K N h = average heat transfer coefe cient along the hot wall, W/m 2 K km = thermal conductivity of air at Tm, W/m K N Nuc = Nusselt number (mean) due to convection, [(qcd)]/[(Th i Tc)km] N Nur = Nusselt number (mean) due to radiation, [(qrd)]/[(Th i Tc)km] N Nur qc = convective heat e ux entering the enclosure from the hot wall, W/m 2 qr = radiative heat e ux entering the enclosure from the hot wall, W/m 2 qt = total heat e ux entering the enclosure, (qc C qr), W/m 2

Coupled heat and mass transfer by free convection over a truncated cone in porous media: VWT/VWC or VHF/VMF

Abstract: The heat and mass transfer characteristics of natural convection about a truncated cone embedded in a saturated porous medium subjected to the coupled effects of thermal and mass diffusion is numerically analyzed. The surface is maintained at variable wall temperature/concentration (VWT/VWC) or variable heat/mass flux (VHF/VMF). The transformed governing equations are solved by Keller box method. Numerical data for the dimensionless temperature profiles, the dimensionless concentration profiles, the local Nusselt number and the local Sherwood number are presented for wide range of dimensionless distance ξ, the Lewis number Le, the exponent λ, and buoyancy ratioN (orN*). In general, it has been found that when the buoyancy ratio is increasing both the local Nusselt number and the local Sherwood number increase. Increasing the value of λ and ξ increases the local surface heat and mass transfer rates. The local Nusselt (Sherwood) number increases (decreases) with decreasing the Lewis number. Furthermore, it is shown that the local Nusselt number and the local Sherwood number of the truncated cone approach those of inclined plate (full cone) for the case of ξ=0 (ξ→∞).

Anti-Icing System Simulation Using CANICE

Abstract: A mathematical model of a hot air anti-icing system and its implementation in the ice accretion simulation code CANICEarepresented.Theicing codeisusedto predictthesurfacetemperatureandtheamount ofrunbackwater for given atmospheric conditions and heat e ux distribution from an anti-icing device. The external boundary layer is modeled with an integral method. Velocity and temperature distribution in the water e lm are estimated using a polynomial approximation. Conduction in the airfoil skin is taken into account with a one-dimension model. Numerical results are compared with experimental and numerical results from NASA for three different icing conditions. The comparison shows that surface temperatures are very sensitive to the water droplet impingement limits. The integral method used here failed to predict correctly the heat transfer coefe cients in the transition region of the boundary layer. When experimental heat transfer coefe cients are used, the model gives satisfactory results.