Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary Layer

Blasius equation is very well known and it aries in many boundary layer problems of fluid dynamics. In this present article, the Blasius boundary layer is extended by transforming the stress strain term from Newtonian to non-Newtonian. The extension of Blasius boundary layer is discussed using some non-newtonian fluid models like, Power-law model, Sisko model and Prandtl model. The Generalised governing partial differential equations for Blasius boundary layer for all above three models are transformed into the non-linear ordinary differewntial equations using the one parameter deductive group theory technique. The obtained similarity solutions are then solved numerically. The graphical presentation is also explained for the same. It concludes that velocity increases more rapidly when fluid index is moving from shear thickninhg to shear thininhg fluid.MSC 2020 No.: 76A05, 76D10, 76M99

Entropy Generation Incorporating γ-Nanofluids under the Influence of Nonlinear Radiation with Mixed Convection

Nanofluids offer the potential to improve heat transport performance. In light of this, the current exploration gives a numerical simulation of mixed convection flow (MCF) using an effective Prandtl model and comprising water- and ethylene-based γγ−Al2O3 particles over a stretched vertical sheet. The impacts of entropy along with non-linear radiation and viscous dissipation are analyzed. Experimentally based expressions of thermal conductivity as well as viscosity are utilized for γγ−Al2O3 nanoparticles. The governing boundary-layer equations are stimulated numerically utilizing bvp4c (boundary-value problem of fourth order). The outcomes involving flow parameter found for the temperature, velocity, heat transfer and drag force are conferred via graphs. It is determined from the obtained results that the temperature and velocity increase the function of the nanoparticle volume fraction for H2O\C2H6O2 based γγ−Al2O3 nanofluids. In addition, it is noted that the larger unsteady parameter results in a significant advancement in the heat transport and friction factor. Heat transfer performance in the fluid flow is also augmented with an upsurge in radiation.

Determining Slope- and Free Air Flow Wind Profiles for WKB Prandtl Models.

During night time, when the air close to the surface cools-down and the atmosphere becomes stable, katabatic down-slope ows may occur in mountainous regions. Contrary, during day time, when the sun heats-up the air close to the surface, and the atmosphere becomes unstable, anabatic upslope ows are prevalent. Up to date, slope winds in the WKB Prandtl model are determined solely by means of specifying the height zj of the maximum turbulent jet above ground. Furthermore, depending on zj parameters K0 and h for a height-dependent eddy thermal diffusivity function KH(z) and a parameter C determining the amplitude for the Prandtl wind speeds must be specified. They are most often estimated from height-dependent wind speeds u, including slope angle α and fixed Prandtl number Pr = KM/KH with KH = KH(z) and KM the eddy viscosity. Having estimated those parameters, friction velocity u*, friction temperature θ* and sensible heat ux QH may be calculated. This article takes the reverse approach: From specified slope angle α, Pr, u*, θ*, QH and specified form of the eddy thermal diffusivity function KH(z) the corresponding WKB Prandtl model is identified. Furthermore, the relationship between u* and θ* calculated via Monin-Obukhov similarity theory for at terrain and those for the WKB Prandtl model are investigated. Using this relationship, we give hints how our new parametrization of the WKB Prandtl model may be used to determine slope ows and free air ows in a micro meteorological model of an alpine valley for pollutant dispersion calculations. We illustrate our derivations by applying our algorithms for the calculation of the WKB Prandtl model to four examples with two taken from Grisogono et al. (2015).

Global well-posedness of the 2-D magnetic Prandtl model in the Prandtl–Hartmann regime

In this paper, we prove the global well-posedness of the 2-D magnetic Prandtl model in the mixed Prandtl/Hartmann regime when the initial data is a small perturbation of the Hartmann layer in Sobolev space.

γ-Nanofluid Thermal Transport between Parallel Plates Suspended by Micro-Cantilever Sensor by Incorporating the Effective Prandtl Model: Applications to Biological and Medical Sciences

The flow of nanofluid between infinite parallel plates suspended by micro-cantilever sensors is significant. The analysis of such flows is a rich research area due to the variety of applications it has in chemical, biological and medical sciences. Micro-cantilever sensors play a significant role in accurately sensing different diseases, and they can be used to detect many hazardous and bio-warfare agents. Therefore, flow water and ethylene glycol (EG) composed by γ-nanoparticles is used. Firstly, the governing nanofluid model is transformed into two self-similar nanofluid models on the basis of their effective models. Then, a numerical method is adopted for solution purposes, and both the nanofluid models are solved. To enhance the heat transfer characteristics of the models, the effective Prandtl model is ingrained in the energy equation. The velocity F’(η) decreases with respect to the suction of the fluid, because more fluid particles drags on the surface for suction, leading to an abrupt decrement in F’(η). The velocity F’(η) increases for injection of the fluid from the upper end, and therefore the momentum boundary layer region is prolonged. A high volume fraction factor is responsible for the denser characteristics of the nanofluids, due to which the fluids become more viscous, and the velocity F’(η) drops abruptly, with the magnetic parameters favoring velocity F’(η). An increase in temperature β ( η ) of Al2O3-H2O and γAl2O3-C2H6O2 nanofluids was reported at higher fraction factors with permeable parameter effects. Finally, a comparative analysis is presented by restricting the flow parameters, which shows the reliability of the study.

Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η ( γ ˙ ) , is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1 / γ ˙ .

Efficiency of hysteretic damper in oscillating systems

This paper is dedicated to comparative analysis of nonlinear damping in the oscillating systems. More specifically, we present the particular results for linear and nonlinear viscous dampers, fractional damper, as well as for the hysteretic damper in linear and nonlinear (Duffing-like) oscillating systems. We consider a constructive mathematical model of the damper with hysteretic properties on the basis of the Ishlinskii-Prandtl model. Numerical results for the observable characteristics, such as the force transmission function and the “force-displacement” transmission function are obtained and analyzed for both cases of the periodic affection, as well as for the impulse affection (in the form of δ-function). A comparison of an efficiency (in terms of the corresponding transmission functions) of the nonlinear viscous damper and the hysteretic damper is also presented and discussed.

The flow of ferromagnetic nanofluid over an extending surface under the effect of operative Prandtl model: A numerical study

The purpose of this research is to investigate the impact of magnetic dipole on the flow of nanofluids over the extending surface. This study is based on steady and non-porous medium with no-slip conditions. Two types of nanofluids are examined under the effect of operative Prandtl model and thermal convection. The experimental results comprising the spreading of [Formula: see text] and [Formula: see text] have been used from the existing literature with and without the magnetic dipole. The basic governing equations are transformed using the transformation into a set of nonlinear differential equations for both categories of nanofluids. The fourth-order Runge Kutta numerical scheme has been executed to solve the nonlinear ordinary differential equations. The impacts of the embedded parameters such as nanofluid volume fraction, Prandtl number, and dissipation term have been examined and discussed. The important features of the study such as Curie temperature, skin friction, and local Nusselt number are also analyzed physically and numerically. (1) It is perceived that ethylene glycol–based nanofluids are more effective due to their strong thermophysical properties compared to water-based nanofluids. By increasing the volume fraction [Formula: see text], the temperature of the nanofluids [Formula: see text] and [Formula: see text] is increased, and this is due to the fact that nanofluids exhibit high thermal conductivity compared to ordinary heat transfer fluids. (2) It is observed from the obtained results that the magnetic dipole is usually used to control the turbulence behavior of the fluid flow.

Stability of the Prandtl model for katabatic slope flows

We investigate the stability of the Prandtl model for katabatic slope flows using both linear stability theory and direct numerical simulations. Starting from Prandtl’s analytical solution for uniformly cooled laminar slope flows, we use linear stability theory to identify the onset of instability and features of the most unstable modes. Our results show that the Prandtl model for parallel katabatic slope flows is prone to transverse and longitudinal modes of instability. The transverse mode of instability manifests itself as stationary vortical flow structures aligned in the along-slope direction, whereas the longitudinal mode of instability emerges as waves propagating in the base-flow direction. Beyond the stability limits, these two modes of instability coexist and form a complex flow structure crisscrossing the plane of flow. The emergence of a particular form of these instabilities depends strongly on three dimensionless parameters, which are the slope angle, the Prandtl number and a newly introduced stratification perturbation parameter, which is proportional to the relative importance of the disturbance to the background stratification due to the imposed surface buoyancy flux. We demonstrate that when this parameter is sufficiently large, then the stabilising effect of the background stratification can be overcome. For shallow slopes, the transverse mode of instability emerges despite meeting the Miles–Howard stability criterion of $Ri>0.25$. At steep slope angles, slope flow can remain linearly stable despite attaining Richardson numbers as low as $3\times 10^{-3}$.