This paper reviews basic results and recent developments in the field of small-scale gaseous hydrodynamics which has received significant attention in connection with small-scale science and technology. We focus on the modeling challenges arising from the breakdown of the Navier-Stokes description, observed when characteristic lengthscales become of the order of, or smaller than, the molecular mean free path. We discuss both theoretical results and numerical methods development. Examples of the former include the limit of applicability of the Navier-Stokes constitutive laws, the concept of second-order slip and the appropriate form of such a model, and how to reconcile experimental measurements of slipping flows with theory. We also review a number of recently developed theoretical descriptions of canonical nanoscale flows of engineering interest. On the simulation front, we review recent progress in characterizing the accuracy of the prevalent Boltzmann simulation method known as direct simulation Monte Carlo. We also present recent variance reduction ideas which address the prohibitive cost associated with the statistical sampling of macroscopic properties in low-speed flows.

http://absimage.aps.org/image/DFD05/MWS_DFD05-2005-020061.pdf

The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics

The purpose of this study is to determine the role of mixed convection, Brownian motion, and thermophoresis in the dynamics of Casson hybrid nanofluid in a bidirectional nonlinear stretching sheet. For the flow model, a combination of Tiwari and Das models, as well as Buongiornos model, is considered. The thermophysical characteristics of G r , T i O 2 , and blood are employed. With the assistance of relevant similarity transformation, the describing flow equations of a Casson hybrid nanofluid model are reformed in the form of a system with a single independent variable. The solution for these equations is obtained using the RKF-45 approach. The velocity, temperature, and concentration fields are visually developed for both linear and non-linear stretching sheets, and the implications of the major parameters are presented in detail. It is clear from the current investigation that heat and mass transfer characteristics of fluid are better in the case of linear stretching than non-linear stretching. Furthermore, the mixed convection parameter is found to enhance the fluid flow velocity. However, the trend is quite opposite in the thermal and concentration fields. Meanwhile, the increase in the yield stress caused due to the rise in the Casson parameter decreases the flow velocity.

Three dimensional mixed convection flow of hybrid casson nanofluid past a non-linear stretching surface: A modified Buongiorno’s model aspects

The present speculative investigation is concentrated to analyze the entropy generation and heat transfer phenomena in ciliary induced peristalsis of blood with the suspension of hybrid nanoparticles in a tube with heat source impact. The blood is assumed to contain copper (Cu) and silver (Ag) nanoparticles (NPs). The ciliary inner wall of the tube has been considered with small hair-like structures. The Phan-Thien-Tanner (PTT) fluid model is employed to describe the non-Newtonian rheological characteristics of blood. The conservative equations are normalized and simplified by utilizing scaling analysis with the assumption of low Reynolds number and large wavelength approximations. The analytical inspection exposes that the total entropy generation gets a decrement for mounting values of cilia length, while reversed impact is detected for an increment in heat source parameter. Hybrid nano-blood exhibits a greater total entropy number than mono nano-blood. This research study may be beneficial to medical experts and researchers in the field of embryology. Cysts in the ciliated fallopian tube, where embryos develop, are removed by using nanoparticles (nano-drug delivery).

Significance of entropy generation and heat source: the case of peristaltic blood flow through a ciliated tube conveying Cu-Ag nanoparticles using Phan-Thien-Tanner model.

In modern era, thermo-migration of microorganisms is an appealing research topic in bio-nanotechnology, bio engineering, and biomedical. In this context, a mathematical model describing thermo-bioconvection of Sutterby nanofluid flow including motile gyrotactic microorganisms near a perforated Riga plate under the physical impacts of heat radiation, and Arrhenius kinetics associated with binary chemical reaction is formulated and simulated here. The Darcy-Forchheimer (DF) law is applied to determine the porosity of porous media. The Grinberg term is taken for the Lorentz force owing to the parallel Riga plate wall. Appropriate translations are discharged to turn the constitutive partial differential equations (PDEs) into ordinary differential equations (ODEs), that are numerically computed by opting the Runge–Kutta-Fehlberg method (RKF-45) along with shooting strategy. The physical insights of various controlling variables on the transport profiles, Sherwood number, Nusselt number, and microorganisms density number are exemplified through requisite graphs and tables. It must be admitted that with enlarging Darcy number, the nanofluid velocity declines, while Forchheimer number has opposite consequence on it. The motile microorganisms density sharply decreases for improving values of activation parameter. The present modeling would provide preliminary guidances in a variety of biotechnological and industrial applications. 

Themo-bioconvection of gyrotactic microorganisms in a polymer solution near a perforated Riga plate immersed in a DF medium involving heat radiation, and Arrhenius kinetics

Radiative CNT-based hybrid magneto-nanoliquid flow over an extending curved surface with slippage and convective heating

The present exploration examines the Cattaneo–Christov double diffusions theory in magneto-Cross nanomaterial flow conveying gyrotactic microorganisms over an extending horizontal cylinder/plate under the aspects of velocity slippage, and activation energy with chemically reacting features. The phenomena of thermophoresis, Brownian movement, and thermal radiation are also incorporated. Utilization of the adopted similarity transformations makes it convenient to transform our governing nonlinear higher-order coupled PDEs into ODEs which are further solved numerically by adopting well-known MATLAB function bvp4c. The quantitative outcomes of emerging thermo-physical and geometrical parameters on the associated non-dimensional profiles of interest are anatomized via requisite graphs and numerically erected tabular forms. It is detected that fluid velocity components decline due to upgraded magnetic field and velocity slippage parameter. When thermal time relaxation parameter varies from 0.0 to 0.9, Nusselt number augments about $$22.02\%$$
 for cylindrical surface and about $$23.61\%$$
 for plate surface. Likewise, with the same variations in thermal time relaxation parameter Sherwood number increases about $$17.32\%$$
 for cylindrical surface and about $$18.24\%$$
 for plate surface. Moreover, comparative exploration of the emerging flow features over a flat plate, and cylindrical surface is reported. It is visualized that flat plate offers less temperature than cylindrical surface when flow occurs. The results would offer primary guidance for many industrial, biological, medical and ecological challenges, for instance, bio-fuel, bio-diesel, ethanol, biological tissues, bio-fertilizers, bio-micro-systems, reproduction, infection, and marine life ecosystems, etc.

Investigation of Cattaneo–Christov Double Diffusions Theory in Bioconvective Slip Flow of Radiated Magneto-Cross-Nanomaterial Over Stretching Cylinder/Plate with Activation Energy

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation Flow formation is developed using the rheological expression of a power-law fluid,The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c The bvp4c function uses the finite difference code as the default This method is a fourth-order collocation method The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification,Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients An increase in the power-law index is observed to deplete velocity and temperature evolution The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid,The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic The results obtained in this work can be relevant in fluid mechanics and heat transfer applications,The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature A comparative study with the published works is conducted to verify the accuracy of the present study The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods

Hall effects on radiated magneto-power-law fluid flow over a stretching surface with power-law velocity slip effect

This paper aims to present the analytical investigation on an unsteady magneto-convective rotation of an electrically conducting non-Newtonian Casson hybrid nanoliquid past a vertical porous plate. The effects of thermal radiation, heat source/sink and hydrodynamic slip phenomenon are also taken into account. Ethylene glycol (EG) is adopted as a base Casson fluid. The Casson fluid model is accounted for to describe the rheological characteristics of non-Newtonian fluid. EG with copper and alumina nanoparticles is envisaged as a non-Newtonian Casson hybrid nanoliquid. The copper-alumina-ethylene glycol hybrid nanoliquid is considered as the regenerative coolant.,The perturbation method is implemented to develop the analytical solution of the modeled equations. Acquired solutions are used to calculate the shear stresses and the rate of heat transfer in terms of amplitudes and phase angles. Numerical results are figured out and tabled to inspect the physical insights of various emerging parameters on the pertinent flow characteristics.,This exploration discloses that the velocity profiles are strongly diminished by the slip parameter. Centrifugal and Coriolis forces caused by the plate rotation are found to significantly change the entire flow regime. The supplementation of nanoparticles is to lessen the amplitude of the heat transfer rate. A comparative study is carried out to understand the improvement of heat transfer characteristics of Casson hybrid nanoliquid and Casson nanoliquid. However, the Casson hybrid nanoliquid exhibits a lower rate of heat transfer than the usual Casson nanoliquid.,This proposed model would be pertinent in oceanography, meteorology, atmospheric science, power engineering, power and propulsion generation, solar energy transformation, thermoelectric and sensing material processing, tumbler in polymer manufacturing, etc. Motivated by such practical implications, the proposed study has been unfolded.,The novelty of this paper is to examine the simultaneous effects of the magnetic field, Coriolis force, suction/injection, slip condition and thermal radiation on non-Newtonian Casson hybrid nanoliquid flow past an oscillating vertical plate subject to periodically heating in a rotating frame of reference. A numerical comparison is also made with the existing published results under some limiting cases and it is found that the results are in good agreement with them. An in-depth review of the literature and the author’s best understanding find that such aspects of the problem have so far remained unexplored.

Asgar Ali

Papers

Investigation of Cattaneo–Christov Double Diffusions Theory in Bioconvective Slip Flow of Radiated Magneto-Cross-Nanomaterial Over Stretching Cylinder/Plate with Activation Energy

Significance of entropy generation and heat source: the case of peristaltic blood flow through a ciliated tube conveying Cu-Ag nanoparticles using Phan-Thien-Tanner model.

Radiative CNT-based hybrid magneto-nanoliquid flow over an extending curved surface with slippage and convective heating

Hall effects on radiated magneto-power-law fluid flow over a stretching surface with power-law velocity slip effect

Insight into the dynamics of magneto-casson hybrid nanoliquid caused by a plate rotation