Thermal boundary layer thickness for laminar forced convection to flat plates with uniform heating and uniform wall temperature

AIChE Journal ◽  
1973 ◽  
Vol 19 (1) ◽  
pp. 177-178 ◽  
Author(s):  
Stuart W. Churchill ◽  
Hiroyuki Ozoe
Keyword(s):  
Boundary Layer ◽  
Wall Temperature ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Thermal Boundary Layer Thickness ◽  
Uniform Heating ◽  
Flat Plates ◽  
Uniform Wall Temperature ◽  
Uniform Wall ◽  
Laminar Forced Convection

Momentum and Thermal Boundary-layer Thickness in a Stagnation Flow Chemical Vapor Deposition Reactor

1997 ◽  
Vol 12 (4) ◽  
pp. 1112-1121 ◽  
Author(s):  
David S. Dandy ◽  
Jungheum Yun
Keyword(s):  
Boundary Layer ◽  
Chemical Vapor Deposition ◽  
Layer Thickness ◽  
Vapor Deposition ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Chemical Vapor ◽  
Square Root ◽  
Thermal Boundary Layer Thickness

Explicit expressions have been derived for momentum and thermal boundary-layer thickness of the laminar, uniform stagnation flows characteristic of highly convective chemical vapor deposition pedestal reactors. Expressions for the velocity and temperature profiles within the boundary layers have also been obtained. The results indicate that, to leading order, the momentum boundary-layer thickness is inversely proportional to the square root of the Reynolds number, while the thermal boundary-layer thickness is inversely proportional to the square root of the Peclet number. Values computed using the approximate expressions are compared directly with numerical solutions of the equations of motion and thermal energy equation, for a specific set of conditions typical of diamond chemical vapor deposition. Because values of the Lewis number do not vary significantly from unity for many different chemical vapor deposition systems, the expression derived here for thermal boundary-layer thickness may be used directly as an approximate concentration boundary-layer thickness.

Linear stability and energetics of rotating radial horizontal convection

2016 ◽  
Vol 795 ◽  
pp. 1-35 ◽  
Author(s):  
Gregory J. Sheard ◽  
Wisam K. Hussam ◽  
Tzekih Tsai
Keyword(s):  
Boundary Layer ◽  
Potential Energy ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Baroclinic Instability ◽  
Mean Flow ◽  
Thermal Boundary Layer Thickness ◽  
Available Potential Energy ◽  
Horizontal Convection ◽  
The Mean

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

Time-Resolved Thermal Boundary-Layer Structure in a Pulsatile Reversing Channel Flow

2001 ◽  
Vol 123 (4) ◽  
pp. 655-664 ◽  
Author(s):  
Sean P. Kearney ◽  
Anthony M. Jacobi ◽  
Robert P. Lucht
Keyword(s):  
Boundary Layer ◽  
Channel Flow ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Layer Structure ◽  
Laminar Regime ◽  
Thermal Boundary Layer Thickness ◽  
Reversed Flow ◽  
Time Resolved ◽  
Primary Impact

In this paper, the results of an experimental study of the time-resolved structure of a thermal boundary layer in a pulsating channel flow are presented. The developing laminar regime is investigated. Two techniques were used for time-resolved temperature measurements: a nonintrusive, pure-rotational CARS method and cold-wire anemometry. Results are presented for differing degrees of flow reversal, and the data show that the primary impact of reversed flow is an increase in the instantaneous thermal boundary-layer thickness and a period of decreased instantaneous Nusselt number. For the developing laminar parameter space spanned by the experiments, time-averaged heat-transfer enhancements as high as a factor of two relative to steady flow are observed for nonreversing and partially reversed pulsating flows. It is concluded that reversal is not necessarily a requirement for enhancement.

A CFD Evaluation of Multiple RANS Turbulence Models for Prediction of Boundary Layer Flows on a Turbine Vane

2013 ◽  
Author(s):  
Thomas E. Dyson ◽  
David G. Bogard ◽  
Sean D. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Turbulence Models ◽  
Experimental Measurements ◽  
Thermal Boundary Layer Thickness ◽  
Mean Velocity ◽  
High Turbulence

There is a growing trend toward the use of conjugate CFD for use in prediction of turbine cooling performance. While many studies have evaluated the performance of RANS simulations relative to experimental measurements of the momentum boundary layer, no studies have evaluated their performance in prediction of the accompanying thermal boundary layer. This is largely due to the fact that, until recently, no appropriate experimental data existed to validate these models. This study compares several popular RANS models — including the realizable k-ε and k-ω SST models — with a four equation k-ω model (“Transition SST”) and experimental measurements at selected positions on the pressure and suction sides of a model C3X vane. Comparisons were made using mean velocity and temperature in the boundary layer without film cooling under conditions of high and low mainstream turbulence. The best performing model was evaluated using modification of the turbulent Prandtl number to attempt to better match the data for the high turbulence case. Overall, the models did not perform well for the low turbulence case; they greatly over-predicted the thermal boundary layer thickness. For the high turbulence case, their performance was better. The Transition SST model performed the best with an average thermal boundary layer thickness within 15% of the experimentally measured values. Prandtl number variation proved to be an inadequate means of improving the thermal boundary layer predictions.

Significance of Prandtl Number on the Heat Transport and Flow Structure in Rotating Rayleigh–Bénard Convection

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Vishnu Venugopal T ◽  
Arnab Kumar De ◽  
Pankaj Kumar Mishra
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flow Structure ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Thermal Boundary Layer Thickness ◽  
Rotation Rates ◽  
Conduction State ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract A direct numerical simulation of rotating Rayleigh–Bénard convection (RBC) for different fluids (Pr=0.015,0.7,1,7,20, and 100) in a cylindrical cell of aspect ratio Γ=0.5 is carried out in this work. The effect of rotation on the heat transfer rate, flow structures, their associated dynamics, and influence on the boundary layers are investigated. The Rayleigh number is fixed to Ra=106 and the rotation rates are varied for a wide range, starting from no rotation (Ro→∞) to high rotation rates (Ro≈0.01). For all the Prandtl numbers (Pr=0.015–100), a reduction in heat transfer with increase in rotation is observed. However, for Pr=7 and 20, a marginal increase of the Nusselt number for low rotation rates is obtained, which is attributed to the change in the flow structure from quadrupolar to dipolar state. The change in flow structure is associated with the statistical behavior of the boundary layers. As the flow makes a transition from quadrupolar to dipolar state, a reduction in the thermal boundary layer thickness is observed. At higher rotation rates, the thermal boundary layer thickness shows a power law variation with the rotation rate. The power law exponent is close to unity for moderate Pr, while it reduces for both lower and higher Pr. At extremely high rotation rates, the flow makes a transition to the conduction state. The critical rotation rate (1/Roc) for which transition to the conduction state is observed depends on the Prandtl number according to 1/Roc∝Pr0.5.

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