Variable-viscosity flows in channels with high heat generation

1977 ◽  
Vol 83 (1) ◽  
pp. 191-206 ◽  
Author(s):  
J. R. A. Pearson
Keyword(s):  
Boundary Layer ◽  
Heat Generation ◽  
Thermal Boundary Layer ◽  
Variable Viscosity ◽  
Plane Channel ◽  
High Heat ◽  
Maximum Temperature ◽  
Mean Velocity ◽  
Channel One ◽  
Plane Channel Flow

This paper presents a similarity solution for plane channel flow of a very viscous fluid, whose viscosity is exponentially dependent upon temperature, when heat generation is very large. A dimensionless formulation of the problem involves two length scales (the depthhand lengthl, respectively, of the channel), one velocity scale (the mean velocityVof the fluid along the channel), the thermal conductivityk, thermal diffusivitykand viscosityVof the fluid, and the temperature coefficientbof the viscosity. From these, two important dimensionless groups arise, the Graetz number (Gz = Vh2/kl) and the Nahme–Griffith number (G= μV2b/k). In the case of steady flow withG−1[Lt ]Gz−1[Lt ] 1 a thin thermal boundary layer of thickness proportional toGz−½arises at each wall with an even thinner shear layer, detached from the wall and embedded in the thermal boundary layer, of thickness proportional toGz−½(lnG)−1, coinciding with the region of maximum temperature (lnG)/b. The similarity variable is (Pe½y/x½) wherePeis the Péclet number (Vh/k) andyandxare measured away from and along (either) boundary wall. The analogous unsteady uniform flow solution is also given.

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.

Revisiting Forced Convection Flow Through a Porous Medium Saturated Channel Using Singular Perturbation Analysis

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
G. M. Chen
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Porous Medium ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Shape Factor ◽  
Thermal Boundary Layer ◽  
Brinkman Model ◽  
Interfacial Heat Transfer

Abstract Accounting for the fact that thermal conductivity of fluid is much less than the thermal conductivity of solid in most of the porous medium-related applications, this study applies perturbation approach in analyzing forced convection through a parallel plate channel under local thermal nonequilibirum (LTNE) condition by denoting the thermal conductivity ratio of fluid to solid as the small parameter, suggesting leading order solutions to solve the two-equation energy model, by incorporating Darcy model and Brinkman model for large porous medium shape factor, respectively, in the presence of heat generation in both fluid and solid. This study provides important fluid temperatures, solid temperatures, and heat transfer coefficient approximations, which enables further analysis on the fluid and solid temperature gradient at the boundary and hence delineate the roles of thermal conductivities and interfacial heat transfer in LNTE mode. The results signify competition between the heat conduction from the wall through fluid conduction and interfacial heat transfer from solid to fluid in the thermal boundary layer. The effect of thermal boundary layer is intensified with the attendant increase in porous medium shape factor and heat generation in solid. The results for Brinkman model also establish conditions for temperature bifurcations to take place whereby in such cases, an increase in viscous dissipation in fluid attributes to the detachment of thermal boundary layer as the porous medium shape factor, S decreases. The phenomenon caused by insufficient convection rate to overcome viscous dissipation bears much resemblance to the separation point in the momentum boundary layer.

On the resonant nature of the breakdown of a laminar boundary layer

1987 ◽  
Vol 184 ◽  
pp. 43-74 ◽  
Author(s):  
Yu. S. Kachanov
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
High Frequency ◽  
Plane Channel ◽  
Secondary Instability ◽  
Breakdown Mechanism ◽  
Physical Experiments ◽  
Wave Resonance ◽  
History Of ◽  
Plane Channel Flow

The first part of this paper (§2) briefly reviews the history of the idea of the resonant nature of laminar-boundary-layer breakdown. In the second part a new wave-resonance concept of the breakdown mechanism is proposed. The existing experimental data on the laminar boundary layer (and plane channel flow) breakdown are analysed from the viewpoint of this concept and are compared with the well-known local high-frequency secondary-instability concept. The results testify to the correctness of the proposed wave-resonant concept for the initial stages of breakdown, in particular for the K-regime of transition up to the spike formation and its doubling.Within the framework of the wave-resonance concept, before constructing the corresponding theory, many important features of the disturbance development can be qualitatively explained and understood. Concerning the understanding of the spike appearance, the wave-resonance concept complements the local high-frequency secondary-instability one and represents by itself a new fruitful viewpoint on this phenomenon. The development of the wave-resonance concept and its application to the analysis of numerical and physical experiments, together with the construction on this basis of the corresponding theory, can give an essential impetus towards the better understanding of the breakdown nature.

Heat transfer of temperature-sensitive magnetic fluids around single heating pipe

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1039-1046
Author(s):  
Yuhiro Iwamoto ◽  
Hayaki Nakasumi ◽  
Yasushi Ido ◽  
Xiao-Dong Niu
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transport ◽  
Thermal Boundary Layer ◽  
High Heat ◽  
Temperature Sensitive ◽  
Long Distance ◽  
Nanoparticle Suspension ◽  
Single Heating

Temperature-sensitive magnetic fluid (TSMF) is a magnetic nanoparticle suspension with strong temperature-dependent magnetization even at room temperature. TSMF is a refrigerant that enables high heat transport capability and pumpless long-distance heat transport. To enhance the heat transport capacity of the magnetically-driven heat transport device using TSMF, it is effective to use a heating body with a very large heat exchange surface such as a heat sink or a porous medium. In the present study, the thermal flow of TSMF around a single heating pipe under a magnetic field was investigated. Visualization of the temperature field by infrared thermography showed that the application of the magnetic field dramatically developed the thermal boundary layer and improved heat transfer. It was clarified by numerical analysis that this dramatic variation in the thermal boundary layer was associated with several vortexes generated by magnetic force in the vicinity of the heating pipe.

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