The cooling of a low-heat-resistance sheet moving through a fluid

1974 ◽  
Vol 341 (1625) ◽  
pp. 233-252 ◽  
Keyword(s):  
Nusselt Number ◽  
Thermal Diffusivity ◽  
Viscous Fluid ◽  
Prandtl Number ◽  
Heat Resistance ◽  
Series Expansion ◽  
Kinematic Viscosity ◽  
Flat Sheet

In this paper we consider the cooling of a flat sheet moving through a semiinfinite expanse of viscous fluid. The heat resistance of the sheet is assumed to be 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.

scholarly journals Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere (part II: For small Prandtl number)

1995 ◽  
Vol 18 (3) ◽  
pp. 579-590 ◽  
Author(s):  
Hadi Y. Alkahby
Keyword(s):  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Gravity Waves ◽  
Kinematic Viscosity ◽  
Cutoff Frequency ◽  
Temperature Perturbation ◽  
Solar Photosphere ◽  
Acoustic Gravity Waves ◽  
Exponential Increase ◽  
Isothermal Atmosphere

In part one of these series we investigated the effect of Newtonian cooling on acoustic-gravity waves in an isothermal atmosphere for large Prandtl number. It was shown that the atmosphere can be divided into two regions connected by an absorbing and reflecting layer, created by the exponential increase of the kinematic viscosity with height, and if Newtonian cooling coefficient goes to infinity the temperature perturbation associated with the wave will be eliminated. In addition all linear relations among the perturbation quantities will be modified. In this paper we will consider the effect of Newtonian cooling on acoustic-gravity waves for small Prandtl number in an isothermal atmosphere. It is shown that if the Newtonian cooling coefficient is small compared to the adiabatic cutoff frequency the atmosphere may be divided into three distinct regions. In the lower region the motion is adiabatic and the effect of the kinematic viscosity and thermal diffusivity are negligible, while the effect of these diffusivities is more pronounced in the upper region. In the middle region the effect of the thermal diffusivity is large, while that of the kinematic viscosity is still negligible. The two lower regions are connected by a semitransparent reflecting layer as a result of the exponential increase of the thermal diffusivity with height. The two upper regions are joined by an absorbing and reflecting barrier created but the exponential increase of the kinematic viscosity. If the Newtonian cooling coefficient is large compared to the adiabatic cutoff frequency, the wavelengths below and above the lower reflecting layer will be equalized. Consequently the reflection produced by the thermal conduction is eliminated completely. This indicates that in the solar photosphere the temperature fluctuations may be smoothed by the transfer of radiation between any two regions with different temperatures. Also the heat transfer by radiation is more dominant than the conduction process.

scholarly journals Effect of Prandtl number on heat transfer characteristics in an axisymmetric sudden expansion: A numerical study

2007 ◽  
Vol 11 (4) ◽  
pp. 171-178
Author(s):  
Khalid Alammar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Study ◽  
Sudden Expansion ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Simulated Effect

Using the standard k-e turbulence model, an incompressible, axisymmetric turbulent flow with a sudden expansion was simulated. Effect of Prandtl number on heat transfer characteristics downstream of the expansion was investigated. The simulation revealed circulation downstream of the expansion. A secondary circulation (corner eddy) was also predicted. Reattachment was predicted at approximately 10 step heights. Corresponding to Prandtl number of 7.0, a peak Nusselt number 13 times the fully-developed value was predicted. The ratio of peak to fully-developed Nusselt number was shown to decrease with decreasing Prandtl number. Location of maximum Nusselt number was insensitive to Prandtl number.

scholarly journals Non-Boussinesq Low-Prandtl-number Convection with a Temperature-dependent Thermal Diffusivity

2021 ◽  
Vol 907 (1) ◽  
pp. 56
Author(s):  
Ambrish Pandey ◽  
Jörg Schumacher ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Temperature Dependent

scholarly journals Upper bounds on Nusselt number at finite Prandtl number

2016 ◽  
Vol 260 (4) ◽  
pp. 3860-3880 ◽  
Author(s):  
Antoine Choffrut ◽  
Camilla Nobili ◽  
Felix Otto
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Upper Bounds

scholarly journals Stellar Convection as a Low Prandtl Number Flow

1991 ◽  
Vol 130 ◽  
pp. 57-61
Author(s):  
Josep M. Massaguer
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Heat Transport ◽  
Large Scale ◽  
Shear Layers ◽  
Turbulent Convection ◽  
The Sun ◽  
Stellar Convection ◽  
Cool Stars ◽  
Number Flow

AbstractThermal convection in the Sun and cool stars is often modeled with the assumption of an effective Prandtl number σ ≃ 1. Such a parameterization results in masking of the presence of internal shear layers which, for small σ, might control the large scale dynamics. In this paper we discuss the relevance of such layers in turbulent convection. Implications for heat transport – i.e. for the Nusselt number power law – are also discussed.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

The cooling of a low-heat-resistance cylinder moving through a fluid

1975 ◽  
Vol 346 (1644) ◽  
pp. 23-35 ◽  
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Heat Resistance ◽  
Series Expansions

A solution is presented for the cooling of a cylinder moving through a semi-infinite fluid region. The heat resistance of the material of the cylinder is assumed to be so low that the temperature can be taken as uniform across the cylinder. Special attention is given to both small and large values of the Prandtl number. In each case the problem is solved by two different series expansions, one valid near the orifice, where the cylinder enters the fluid region, and one downstream, where the boundary layer is thick in comparison with the radius of the cylinder.

Validation and Development of DNS Database for Low Prandtl Numbers in Rod Bundle

2019 ◽  
Author(s):  
Jonathan K. Lai ◽  
Elia Merzari ◽  
Yassin A. Hassan ◽  
Aleksandr Obabko
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Heat Transfer Characteristics ◽  
Reynolds Analogy ◽  
Transfer Characteristics ◽  
Rod Bundle ◽  
High Thermal Diffusivity ◽  
Prandtl Numbers

Abstract Difficulty in capturing heat transfer characteristics for liquid metals is commonplace because of their low molecular Prandtl number (Pr). Since these fluids have very high thermal diffusivity, the Reynolds analogy is not valid and creates modeling difficulties when assuming a turbulent Prandtl number (Prt) of near unity. Baseline problems have used direct numerical simulations (DNS) for the channel flow and backward facing step to aid in developing a correlation for Prt. More complex physics need to be considered, however, since correlation accuracy is limited. A tight lattice square rod bundle has been chosen for DNS benchmarking because of its presence of flow oscillations and coherent structures even with a relatively simple geometry. Calculations of the Kolmogorov length and time scales have been made to ensure that the spatial-temporal discretization is sufficient for DNS. In order to validate the results, Hooper and Wood’s 1984 experiment has been modeled with a pitch-to-diameter (P/D) ratio of 1.107. The present work aims at validating first- and second-order statistics for the velocity field, and then analyzing the heat transfer behavior at different molecular Pr. The effects of low Pr flow are presented to demonstrate how the normalized mean and fluctuating heat transfer characteristics vary with different thermal diffusivity. Progress and future work toward creating a full DNS database for liquid metals are discussed.

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