Marangoni convection. Part 1. A cavity with differentially heated sidewalls

2000 ◽  
Vol 405 ◽  
pp. 79-110 ◽  
Author(s):  
M. HAMED ◽  
J. M. FLORYAN
Keyword(s):  
Heating Rate ◽  
Marangoni Convection ◽  
Contact Point ◽  
Reynolds Numbers ◽  
Critical Values ◽  
Tangency Condition ◽  
Oscillatory State ◽  
Prandtl Numbers ◽  
Dry Spot ◽  
Steady Convection

Marangoni convection in a cavity with differentially heated sidewalls has been investigated. The analysis includes the complete effects of interface deformation. The results determined for large Biot and zero Marangoni (zero Prandtl) numbers show that steady convection may exist for Reynolds numbers Re larger than, and for capillary numbers Ca and cavity lengths L smaller than, certain critical values. The main factor limiting the existence of steady convection involves the interface becoming tangential to the hot wall at the contact point (tangency condition). Unsteady analysis shows that the tangency condition defines the limit point for the system; its violation is most likely to lead to the formation of a dry spot at the hot wall. The critical values of Re, Ca, and L are mutually dependent and change with the heating rate (they reach a minimum for instantaneous heating). For a certain range of parameters, multiple (i.e. steady and oscillatory) states are possible. The oscillatory state has a form consisting of the steady mode with a simple harmonic sloshing motion superposed on it. A reduction in the heating rate permits heating of the liquid without triggering the oscillatory state. Transition between the steady and the oscillatory states involves a nonlinear instability process.

Marangoni convection. Part 2. A cavity subject to point heating

2000 ◽  
Vol 405 ◽  
pp. 111-129 ◽  
Author(s):  
M. HAMED ◽  
J. M. FLORYAN
Keyword(s):  
Marangoni Convection ◽  
Rapid Heating ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rupture Process ◽  
Critical Values ◽  
Interface Deformation ◽  
Prandtl Numbers ◽  
Steady Convection ◽  
Main Factor

Marangoni convection in a cavity subject to point (concentrated) heating has been investigated. The analysis includes the complete effects of the interface deformation. The results determined for large Biot and zero Marangoni (zero Prandtl) numbers show that steady convection may exist only for a limited range of Reynolds numbers Re (bounded from above and from below), and for capillary numbers Ca and cavity lengths L smaller than certain critical values. The main factor limiting the existence of steady convection involves the interface approaching the bottom of the cavity. Unsteady analysis shows that when the conditions guaranteeing the existence of steady convection are not met, an interface rupture process sets in leading, eventually, to the formation of a dryout at the bottom of the cavity. The initial stages of the rupture process are characterized by a rapidly accelerating growth of the interface deformation. The critical values of Re, Ca and L, which guarantee the existence of steady convection, are mutually dependent and change with the heating rate; they reach a minimum for instantaneous heating. Too rapid heating produces an oscillatory transient which always decays in the range of parameters studied.

scholarly journals MODELING HEAT EXCHANGE DEPENDING ON THE PRANDTL NUMBER FOR VARIOUS GEOMETRIC AND REGIME PARAMETERS

2020 ◽  
Vol 46 (4) ◽  
pp. 91-101
Author(s):  
I. E. Lobanov
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Prandtl Number ◽  
Energy Equation ◽  
Transport Model ◽  
Reynolds Numbers ◽  
Structured Grids ◽  
Shear Stress Transport Model ◽  
Small Reynolds Numbers ◽  
Prandtl Numbers

Objectives. The aim is to study the dependency of the distribution of integral heat transfer during turbulent convective heat transfer in a pipe with a sequence of periodic protrusions of semicircular geometry on the Prandtl number using the calculation method based on a numerical solution of the system of Reynolds equations closed using the Menter’s shear stress transport model and the energy equation on different-sized intersecting structured grids.Method. A calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations by factored finite-volume method closed with the help of the Menter shear stress transport model, as well as the energy equation on different-scaled intersecting structured grids (fast composite mesh method (FCOM)).Results. The calculations performed in the work showed that with an increase in the Prandtl number at small Reynolds numbers, there is an initial noticeable increase in the relative heat transfer. With additional increase in the Prandtl number, the relative heat transfer changes less: for small steps, it increases; for median steps it is almost stabilised, while for large steps it declines insignificantly. At large Reynolds numbers, the relative heat transfer decreases with an increase in the Prandtl number followed by its further stabilisation.Conclusion. The study analyses the calculated dependencies of the relative heat transfer on the Pr Prandtl number for various values of the relative h/D height of the turbulator, the relative t/D pitch between the turbulators and for various values of the Re Reynolds number. Qualitative and quantitative changes in calculated parameters are described all other things being equal. The analytical substantiation of the obtained calculation laws is that the height of the turbuliser is less for small Reynolds numbers, while for large Reynolds numbers, it is less than the height of the wall layer. Consequently, only the core of the flow is turbulised, which results in an increase in hydroresistance and a decrease in heat transfer. In the work on the basis of limited calculation material, a tangible decrease in the level of heat transfer intensification for small Prandtl numbers is theoretically confirmed. The obtained results of intensified heat transfer in the region of low Prandtl numbers substantiate the promising development of research in this direction. The theoretical data obtained in the work have determined the laws of relative heat transfer across a wide range of Prandtl numbers, including in those areas where experimental material does not currently exist. 

Convective Heat Transfer of the Flow through a Rotating Circular Straight Pipe

2001 ◽  
Vol 17 (2) ◽  
pp. 79-91
Author(s):  
U. Lei ◽  
Arthur C. Y. Yang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Reynolds Numbers ◽  
Straight Pipe ◽  
Constant Wall Temperature ◽  
Fully Developed Flow ◽  
Flow Through ◽  
Prandtl Numbers ◽  
Scaling Analyses ◽  
Gradient Condition

ABSTRACTLaminar heat transfer for large ranges of Reynolds numbers, rotational Reynolds numbers, and Prandtl numbers are studied numerically for incompressible fully developed flow in a circular straight pipe, which is rotating constantly about an axis perpendicular to its own axis under the constant wall temperature gradient condition. There exist four types of local Nusselt number distributions associated with the four different flow regimes for different parameters depending on the relative importance of different forces. Correlations of the averaged Nusselt number are also provided. When the Prandtl number is sufficiently large, the temperature distribution in the core is determined essentially by the secondary flow. Scaling analyses are provided for understanding the essential physics of the problem.

Convective Heat Transfer From a Sphere Due to Acoustic Streaming

1993 ◽  
Vol 115 (2) ◽  
pp. 332-341 ◽  
Author(s):  
A. Gopinath ◽  
A. F. Mills
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Acoustic Streaming ◽  
Reynolds Numbers ◽  
Materials Processing ◽  
Acoustic Levitation ◽  
Simple Experiment ◽  
Wide Range ◽  
Prandtl Numbers

Convective heat transfer from a sphere due to acoustic streaming is examined for large streaming Reynolds numbers. Analytical and numerical solution techniques are used to obtain Nusselt number correlations for a wide range of Prandtl numbers with particular emphasis on the case of Pr~1. A simple experiment performed to confirm some of the predictions is described. The results obtained can be used for the thermal analysis of containerless materials processing in space using acoustic levitation.

Numerical Analysis of Laminar Forced Convection in Sinusoidal-Wavy-, Rounded-Ellipse-, and Rounded-Vee-Shaped Corrugated-Plate Channels

2010 ◽  
Author(s):  
Dean Ferley ◽  
Scott J. Ormiston
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Numerical Analysis ◽  
Prandtl Number ◽  
Friction Factor ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Ansys Cfx ◽  
Prandtl Numbers ◽  
Laminar Forced Convection

Numerical analysis of steady, two-dimensional, laminar forced convection in corrugated-plate channels is performed using a commercial CFD code: ANSYS CFX. The flow domain consists of six modules in each of three wall corrugations: sinusoidal-wavy-shaped (SWS), rounded-ellipse-shaped (RES), and rounded-vee-shaped (RVS). One ratio of minimum-to-maximum plate spacings and one module length-to-height ratio is considered. Fluid flow and heat transfer are repeating in the modules and the results are examined in a typical module in the fully-developed region for Reynolds numbers in the range of 25 to 300 for Prandtl numbers of 0.7 (air), 2.29 (water), and 34.6 (ethylene glycol). The RES corrugation produced the highest peak value of local Nusselt number as well as the highest friction factor. The SWS corrugation produced the highest average Nusselt number, except at a Prandtl number of 34.6 at higher Reynolds number where the RES corrugation had the highest value. The RVS corrugation had the lowest friction factor for the geometric configuration considered. The highest heat transfer rate per unit pumping power was found at the highest Prandtl number for the RES corrugation.

The effect of shear and stratification on the stability of a rotating fluid layer

1973 ◽  
Vol 59 (2) ◽  
pp. 369-390 ◽  
Author(s):  
A. R. Brunsvold ◽  
C. M. Vest
Keyword(s):  
Stratified Flow ◽  
Reynolds Numbers ◽  
Travelling Wave ◽  
Taylor Number ◽  
Critical Parameters ◽  
Rotating Fluid ◽  
Critical Mode ◽  
Shear Rates ◽  
Prandtl Numbers ◽  
The Stability

The stability of a layer of Newtonian fluid confined between two horizontal disks which rotate with different angular velocities is studied. Both isothermal and adversely stratified fluids are considered for small shear rates at low to moderate Taylor numbers. The linearized formulation of the stability problem is given a finite-difference representation, and the resulting algebraic eigenvalue problem is solved using efficient numerical techniques. The critical parameters and disturbance orientations are determined as a function of the Taylor number for the isothermal flow, and for the stratified flow for Prandtl numbers of 0·025, 1·0 and 6·0.At high Taylor numbers, the unstratified fluid flows in Ekman-like layers near the disks, and two modes of instability are noted: the viscous-type ‘class A’ travelling wave, whose existence depends on Coriolis forces, and the inflexional ‘class B’ mode, which is nearly stationary with respect to the nearer bounding disk. As the Taylor number is decreased, the Ekman layers coalesce to form a fully developed flow. In this regime there is a Taylor number below which the class A waves are always damped. The critical Reynolds number for the class B waves increases rapidly as the Taylor number approaches zero.For Prandtl numbers of 1·0 and 6·0, the adversely stratified flow exhibits two distinct types of instability: convective and dynamical. At low Reynolds numbers, a stationary mode associated with Bénard convection in a rotating fluid is critical. It is stabilized and given orientation by the shear. At higher Reynolds numbers, the critical mode is a travelling wave of the nature of either the class A or class B waves, depending upon the Taylor number. For a Prandtl number of 0·025, the critical mode resembles oscillatory convection at small Reynolds numbers and a class A wave at larger shear rates.

Evaporation of Pure Liquids at High Prandtl Numbers in a Scale-Up Capable Falling Film Evaporator

2010 ◽  
Author(s):  
Stefanie Arndt ◽  
Stephan Scholl
Keyword(s):  
Heat Transfer ◽  
Scale Up ◽  
Reynolds Numbers ◽  
Temperature Sensitive ◽  
Turbulent Regime ◽  
Falling Film ◽  
Film Evaporator ◽  
Laminar And Turbulent Flow ◽  
Falling Film Evaporation ◽  
Prandtl Numbers

In industrial application heat transfer to temperature sensitive products in falling film evaporation is often linked to the evaporation at elevated viscosities. In the present study a scale-up capable falling film evaporator has been used to investigate the heat transfer to liquids with Prandtl numbers up to 150. The focus was on heated falling films during surface evaporation. Film-Reynolds numbers were varied from 48 to 10,000. As pure liquids water and cyclohexanol were used. In the results a distinct transition zone between laminar and turbulent flow can be observed for elevated Prandtl numbers. The comparison to literature models shows that more parameters have to be taken into account to properly predict the heat transfer in falling film evaporators for different equipment and fluids. The optical monitoring of the film on the inside of the evaporation tube through an endoscope showed that the fully turbulent regime could not been reached for high viscosities.

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