scholarly journals Energy balance of the airflow boundary layer in the brake disc ventilation

2021 ◽  
Vol 2131 (2) ◽  
pp. 022050
Author(s):  
I A Yaitskov ◽  
A E Litvinov ◽  
P A Polyakov ◽  
A A Golikov ◽  
R S Tagie ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Energy Balance ◽  
Thermal Boundary Layer ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Energy Balance Equation ◽  
Polar Coordinates ◽  
Brake Disc ◽  
Air Supply ◽  
Ventilation Ducts

Abstract Airflow through the brake disc ventilation causes the formation of a boundary layer at the walls. It affects both the dynamic processes related to air exchange in the space between the walls and thermal processes associated with air insulation of the heated surfaces of the ventilation ducts. The present paper aims to develop a model for calculating plane airflow in a ventilation duct in polar coordinates. Using the Navier-Stokes equations and the equations of the energy balance of the airflow boundary layer, we succeeded in determining the elements that affect the intensity of changes in the air masses in the boundary layer and the elements that are responsible for the thermal conductivity of the thermal boundary layer of the airflow. Besides, we obtained an energy balance equation, which takes into account the enthalpy and thermodynamic parameters of the thermal boundary layer, as well as found the possibilities of influencing the heat exchange processes by minimizing factors of the heat-insulating boundary layer. Finally, we specified the dependence of the boundary layer temperature on the temperature of the walls of the brake disc ventilation. The obtained dependences lay the ground for formulating variants of the influence on the heat-insulating boundary layer of the airflow, namely, the design of a forced air supply system at different angles of attack into the ventilation cavity of the brake disc or the manufacture of ventilation ducts with complex geometry.

Numerical Modelling of Hydrodynamic Instabilities in Supercritical Fluids

2021 ◽  
pp. 32-54
Author(s):  
Sakir Amiroudine
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Stokes Equations ◽  
Gravitational Instability ◽  
Heat Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stability Diagrams ◽  
The Stability ◽  
Rayleigh Benard

The case of a supercritical fluid heated from below (Rayleigh-Bénard) in a rectangular cavity is first presented. The stability of the two boundary layers (hot and cold) is analyzed by numerically solving the Navier-Stokes equations with a van der Waals gas and stability diagrams are derived. The very large compressibility and the very low heat diffusivity of near critical pure fluids induce very large density gradients which lead to a Rayleigh–Taylor-like gravitational instability of the heat diffusion layer and results in terms of growth rates and wave numbers are presented. Depending on the relative direction of the interface or the boundary layer with respect to vibration, vibrational forces can destabilize a thermal boundary layer, resulting in parametric/Rayleigh vibrational instabilities. This has recently been achieved by using a numerical model which does not require any equation of state and directly calculates properties from NIST data base, for instance.

On the sensitivity of heat transfer in the stagnation-point boundary layer to free-stream vorticity

1963 ◽  
Vol 16 (4) ◽  
pp. 497-520 ◽  
Author(s):  
S. P. Sutera ◽  
P. F. Maeder ◽  
J. Kestin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Stokes Equations ◽  
Point Boundary ◽  
Oncoming Flow ◽  
Flat Plates

Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.

Numerical analysis of non-isothermal viscous jet with peripheral heat transfer

2016 ◽  
Vol 07 (03) ◽  
pp. 1650012
Author(s):  
Sulagna Chatterjee ◽  
Trisha Sen ◽  
Anindya Mitra
Keyword(s):  
Heat Transfer ◽  
Energy Balance ◽  
Balance Equation ◽  
Stokes Equations ◽  
Numerical Study ◽  
Energy Balance Equation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Isothermal Model ◽  
Jet Velocity

A fluid jet ejected from micron size nozzle is a commonly occurring phenomenon in biomedical engineering, printing technology and micro-fluidic applications. Disintegration of a jet into drops occurs due to disturbances induced by external sources. This work explores the various sources of perturbation and their effect on jet disintegration through numerical simulation of a two-dimensional non-isothermal model. The mathematical approach uses a novel technique to combine analytical solutions for the energy balance equation in the radial direction to solve the complete two dimensional problem. The two dimensional energy balance equation is simultaneously solved together with the axi-symmetric Navier–Stokes equations using the slender-jet approximation to predict jet velocity. The energy balance takes into account of peripheral heat transfer to the environment through analytical expressions derived from radial approximations. The model helps in understanding the factors in dynamic temperature variations that eventually render the jet unstable. The distinguishing aspect of this work is the analysis of the effect of a periodic thermal perturbation applied at any point in the domain of a progressive jet, a situation typically encountered in thermal inkjet printers and not considered previously. Results presented for non-isothermal jets which are both stationary and moving illustrate the effect of jet velocity in propagation of perturbation and subsequent drop formation. The major contribution of this numerical study is that it provides an insight on novel ways of controlling droplet formation in bubble jet printers. This study demonstrates that thermal disturbance propagating from periodic heating can be manipulated to shape the droplets and control their breakage point along the jet.

Numerical Modelling of Hydrodynamic Instabilities in Supercritical Fluids

2017 ◽  
pp. 33-54
Author(s):  
Sakir Amiroudine
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Stokes Equations ◽  
Gravitational Instability ◽  
Heat Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stability Diagrams ◽  
The Stability ◽  
Rayleigh Benard

The case of a supercritical fluid heated from below (Rayleigh-Bénard) in a rectangular cavity is first presented. The stability of the two boundary layers (hot and cold) is analyzed by numerically solving the Navier-Stokes equations with a van der Waals gas and stability diagrams are derived. The very large compressibility and the very low heat diffusivity of near critical pure fluids induce very large density gradients which lead to a Rayleigh–Taylor-like gravitational instability of the heat diffusion layer and results in terms of growth rates and wave numbers are presented. Depending on the relative direction of the interface or the boundary layer with respect to vibration, vibrational forces can destabilize a thermal boundary layer, resulting in parametric / Rayleigh vibrational instabilities. This has recently been achieved by using a numerical model which does not require any equation of state and directly calculates properties from NIST data base (NIST, 2000) for instance.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

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