scholarly journals Intensification of thermal stratification on dissipative chemically heating fluid with cross-diffusion and magnetic field over a wedge

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 877-888
Author(s):  
Adnan ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
Syed Tauseef Mohyud-Din ◽  
El-Sayed M. Sherif ◽  
...  
Keyword(s):  
Thermal Stratification ◽  
Thermal Characteristics ◽  
Shear Stresses ◽  
Similar Model ◽  
Cross Diffusion ◽  
Similarity Transformations ◽  
Dissipative Flow ◽  
Lorentz Forces ◽  
Self Similar ◽  
Physical Quantities

Abstract This paper aims to examine the heat and mass characteristics for thermally stratified chemically heated, dissipative flow under the cross-diffusion and imposed Lorentz forces. A self-similar model is obtained employing suitable similarity transformations. Then, the RK technique is used for mathematical analysis. The stimulations of pertinent physical quantities in the flow regimes, shear stresses, and the Nusselt number were examined graphically. It is noted that more radiative flow favors the thermal behavior of the fluid and increases in the Prandtl number causes the decrease in thermal characteristics. Moreover, decreases in mass characteristics were examined by the fluctuating chemical reaction and Schmidt parameters. Lastly, key outcomes of the work are pinpointed.

scholarly journals Impact of freezing temperature (Tfr) of Al2O3 and molecular diameter (H2O)d on thermal enhancement in magnetized and radiative nanofluid with mixed convection

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Adnan ◽  
Waqas Ashraf ◽  
Umar Khan ◽  
Amnah S. Al-Johani ◽  
Naveed Ahmed ◽  
...  
Keyword(s):  
Heated Surface ◽  
Velocity Slip ◽  
Freezing Temperature ◽  
Industrial Applications ◽  
Significant Rise ◽  
Shear Stresses ◽  
Magnetic Field Effects ◽  
Similarity Transformations ◽  
Lorentz Forces ◽  
Thermal Radiations

AbstractThe dynamics of nanofluid by considering the role of imposed Lorentz forces, thermal radiations and velocity slip effects over a vertically convectively heated surface is a topic of huge interest. Therefore, the said study is conducted for Al2O3-H2O nanofluid. Mathematical modelling of the problem is done via nanofluid effective correlations comprising the influences of freezing temperature, molecular diameter and similarity transformations. The results for multiple parameters are plotted and provide comprehensive discussion. From the analysis, it is examined that Al2O3-H2O nanofluid motion drops by strengthening Lorentz forces. The temperature in the nanofluid (Al2O3-H2O) is improved by inducing viscous dissipation effects (Ec number), surface convection (Biot number) and thermal radiations (Rd). Moreover, the shear stresses at the surface decreased due to higher magnetic field effects and rises due to velocity slip. A significant rise in Local Nusselt number is observed due to thermal radiations and Biot effects. Finally, enhanced heat transport mechanism in Al2O3-H2O is examined than a conventional liquid. Therefore, nanofluids are better for industrial applications and the uses of conventional liquids are limited due to low thermal conductivity.

scholarly journals Large-Eddy Simulation and Single-Column Modeling of Thermally Stratified Wind Turbine Arrays for Fully Developed, Stationary Atmospheric Conditions

2015 ◽  
Vol 32 (6) ◽  
pp. 1144-1162 ◽  
Author(s):  
Adrian Sescu ◽  
Charles Meneveau
Keyword(s):  
Thermal Stratification ◽  
Layer Structure ◽  
Potential Temperature ◽  
Surface Fluxes ◽  
Heat Fluxes ◽  
Shear Stresses ◽  
Column Model ◽  
Large Eddy ◽  
Single Column ◽  
Single Column Model

AbstractEffects of atmospheric thermal stratification on the asymptotic behavior of very large wind farms are studied using large-eddy simulations (LES) and a single-column model for vertical distributions of horizontally averaged field variables. To facilitate comparisons between LES and column modeling based on Monin–Obukhov similarity theory, the LES are performed under idealized conditions of statistical stationarity in time and fully developed conditions in space. A suite of simulations are performed for different thermal stratification levels and the results are used to evaluate horizontally averaged vertical profiles of velocity, potential temperature, vertical turbulent momentum, and heat flux. Both LES and the model show that the stratification significantly affects the atmospheric boundary layer structure, its height, and the surface fluxes. However, the effects of the wind farm on surface heat fluxes are found to be relatively small in both LES and the single-column model. The surface fluxes are the result of two opposing trends: an increase of mixing in wakes and a decrease in mixing in the region below the turbines due to reduced momentum fluxes there for neutral and unstable cases, or relatively unchanged shear stresses below the turbines in the stable cases. For the considered cases, the balance of these trends yields a slight increase in surface flux magnitude for the stable and near-neutral unstable cases, and a very small decrease in flux magnitude for the strongly unstable cases. Moreover, thermal stratification is found to have a negligible effect on the roughness scale as deduced from the single-column model, consistent with the expectations of separation of scale.

Falconer's formula for the Hausdorff dimension of a self-affine set in R2

1995 ◽  
Vol 15 (1) ◽  
pp. 77-97 ◽  
Author(s):  
Irene Hueter ◽  
Steven P. Lalley
Keyword(s):  
Hausdorff Dimension ◽  
Dimensional Hausdorff Measure ◽  
Similarity Transformations ◽  
Affine Mappings ◽  
Finite Set ◽  
Self Similar ◽  
Image Position ◽  
Affine Set ◽  
Small Overlap ◽  
Box Dimensions

Let A1, A2,…,Ak be a finite set of contractive, affine, invertible self-mappings of R2. A compact subset Λ of R2 is said to be self-affine with affinitiesA1, A2,…,Ak ifIt is known [8] that for any such set of contractive affine mappings there is a unique (compact) SA set with these affinities. When the affine mappings A1, A2,…,Ak are similarity transformations, the set Λ is said to be self-similar. Self-similar sets are well understood, at least when the images Ai(Λ) have ‘small’ overlap: there is a simple and explicit formula for the Hausdorff and box dimensions [12, 10]; these are always equal; and the δ-dimensional Hausdorff measure of such a set (where δ is the Hausdorff dimension) is always positive and finite.

scholarly journals Thermal-hydraulic behavior of physical quantities at critical velocities in a nuclear research reactor core channel using plate type fuel

2012 ◽  
Vol 27 (3) ◽  
pp. 229-238
Author(s):  
Ali Sidi ◽  
Zaki Boudali ◽  
Rachid Salhi
Keyword(s):  
Heat Flux ◽  
Critical Velocity ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Thermal Characteristics ◽  
Nuclear Research ◽  
Coolant Fluid ◽  
Critical Velocities ◽  
Set Up ◽  
Physical Quantities

The thermal-hydraulic study presented here relates to a channel of a nuclear reactor core. This channel is defined as being the space between two fuel plates where a coolant fluid flows. The flow velocity of this coolant should not generate vibrations in fuel plates. The aim of this study is to know the distribution of the temperature in the fuel plates, in the cladding and in the coolant fluid at the critical velocities of Miller, of Wambsganss, and of Cekirge and Ural. The velocity expressions given by these authors are function of the geometry of the fuel plate, the mechanical characteristics of the fuel plate?s material and the thermal characteristics of the coolant fluid. The thermal-hydraulic study is made under steady-state; the equation set-up of the thermal problem is made according to El Wakil and to Delhaye. Once the equation set-up is validated, the three critical velocities are calculated and then used in the calculations of the different temperature profiles. The average heat flux and the critical heat flux are evaluated for each critical velocity and their ratio reported. The recommended critical velocity to be used in nuclear channel calculations is that of Wambsganss. The mathematical model used is more precise and all the physical quantities, when using this critical velocity, stay in safe margins.

scholarly journals MULTIRESOLUTION CONTROL OF CURVES AND SURFACES WITH A SELF-SIMILAR MODEL

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 271-286 ◽  
Author(s):  
HOUSSAM HNAIDI ◽  
ERIC GUÉRIN ◽  
SAMIR AKKOUCHE
Keyword(s):  
Wavelet Transform ◽  
Control Point ◽  
Iterated Function Systems ◽  
Control Points ◽  
Similar Model ◽  
Surface Theory ◽  
Curves And Surfaces ◽  
Iterated Function ◽  
Resolution Level ◽  
Self Similar

This paper presents two self-similar models that allow the control of curves and surfaces. The first model is based on IFS (Iterated Function Systems) theory and the second on subdivision curve and surface theory. Both of these methods employ the detail concept as in the wavelet transform, and allow the multiresolution control of objects with control points at any resolution level.In the first model, the detail is inserted independently of control points, requiring it to be rotated when applying deformations. In contrast, the second method describes details relative to control points, allowing free control point deformations.Modeling examples of curves and surfaces are presented, showing manipulation facilities of the models.

scholarly journals Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

2019 ◽  
Vol 880 ◽  
pp. 239-283 ◽  
Author(s):  
Christoph Wenzel ◽  
Tobias Gibis ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Self Similar

A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter $\unicode[STIX]{x1D6FD}_{K}$ calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness $\unicode[STIX]{x1D6FF}_{99}$ and the skin-friction coefficient $c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar $\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same $\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same $\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium.

Similarity analysis of creep indentation tests

1992 ◽  
Vol 436 (1898) ◽  
pp. 617-630 ◽  
Keyword(s):  
Auxiliary Problem ◽  
Secondary Creep ◽  
Depth Of Penetration ◽  
Similarity Transformations ◽  
Similarity Relations ◽  
Hardness Tests ◽  
Wide Range ◽  
Indentation Tests ◽  
Nonlinear Elastic ◽  
Physical Quantities

The general theory of axisymmetric hardness tests on nonlinear media is approached from the standpoint of similarity transformations. It is shown how an entire process of indentation can be made to depend on the solution of just one boundary-value problem in scaled variables and with a fixed geometry. Once this single auxiliary solution has been obtained, the values of all physical quantities in the original problem can be generated readily at any stage without further numerical error. Even by themselves the similarity relations provide valuable information about (for example) an invariant connection between the depth of penetration and the radius of contact, or about the variation of penetration with time in a creep test under dead load. Two kinds of material behaviour are considered: (a) nonlinear elastic (modelling strain-hardening plasticity) and (b) nonlinear viscous (modelling secondary creep). In either category the constitutive specification is sufficiently flexible to represent a wide range of actual responses in the context of hardness testing. The analysis for case (a) extends a theory of ball indentation by Hill et al . to a class of indenters with shapes varying from flat to conical. It also prepares the ground for case (6) which is more difficult and calls for a quite different auxiliary problem.

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