Elsevier

Chinese Journal of Physics

Volume 60, August 2019, Pages 676-687
Chinese Journal of Physics

A meta-analysis on the effects of haphazard motion of tiny/nano-sized particles on the dynamics and other physical properties of some fluids

https://doi.org/10.1016/j.cjph.2019.06.007Get rights and content

Highlights

  • Physical meaning of Brownian motion is explained.

  • A statistical method for analysis of results is explored.

  • Meta-analysis on the effects of haphazard motion of particles is presented.

  • Heat transfer rate is a decreasing property of Brownian motion.

  • Temperature distribution is an increasing function of Brownian motion.

Abstract

Decline in the theoretical and empirical review of Brownian motion is worth noticing, not just because its relevance lies in the field of mathematical physics but due to unavailability of statistical technique. The ongoing debate on transport phenomenon and thermal performance of various fluids in the presence of haphazard motion of tiny particles as explained by Albert Einstein using kinetic theory and Robert Brown is further clinched in this report. This report presents the outcome of detailed inspections of the significance of Brownian motion on the flow of various fluids as reported in forty-three (43) published articles using the method of slope linear regression through the data point. The technique of slope regression through the data points of each physical property of the flow and Brownian motion parameter was established and used to generate four forest plots. The outcome of the study indicates that an increase in Brownian motion corresponds to an enhancement of haphazard motion of tiny particles. In view of this, there would always be a significant difference between the corresponding effects when Brownian motion is small and large in magnitude. Maximum heat transfer rate can be achieved due to Brownian motion in the presence of thermal radiation, thermal convective and mass convective at the wall in three-dimensional flow. In the presence of heat convective and mass convective at the wall, and thermal radiation, a significant increase in Nusselt number due to Brownian motion is guaranteed. A decrease in the concentration of fluid substance due to an increase in Brownian motion is bound to occur. This is not achievable in the case of high entropy generation and homogeneous-heterogeneous quartic autocatalytic kind of chemical reaction.

Introduction

Historically, the literature reveals that Roman Poet Titus Lucretius Carus who lived within 99BC and 55BC discovered the motion of tiny particles in a sunbeam. According to Carus et al. [1], the so-called mingling motion of dust particles in sunbeams was traced to a significant difference in temperature or/and pressure (i.e. air currents). In the year 1785, irregular movement of tiny coal dust on the surface of alcohol was observed by Dutch physiologist, biologist and chemist Jan Ingenhousz who also started the broad work on photosynthesis. According to Lucretius Carus, this led to another school of thought that strongly believes impurity concentration on a vertical axis and heating are major factors leading to air currents and consequently mingling motion. More interestingly, it was until 1827 that the Scottish botanist Robert Brown observed the random motion of tiny particles suspended in gas or liquid. In fact, the concept of water conveying suspended pollen grains led to various research works (i.e. the motion of microorganism as in the case of phototaxis, hydrotaxis, and gyrotaxis). In the report of Einstein [2], the kinetic theory was adopted to explain the Brownian motion, one of the phenomena that prove the existence of molecules. Kinetic theory of gases postulates that molecules of gases move in a random pattern (which can be likened to a disorder or zig-zag motion), colliding with one another and with the walls of the container. Consequent to this collision is the generation of internal pressure, whose magnitude depends on the size and speed of the molecules. In a note on the existence of rotational motion over the surface of a sphere, Aydiner [3] remarked that all the components of the rotational relaxation during the process are exponential in nature when the influence of the inertia of the dipoles is insignificant. Tsekov and Lensen [4] once remarked that the migration of living cells, without any doubt, obeys the laws of Brownian motion which is a universal movement of matter. Four major modes of energy transport in any nanofluid according to Jang and Choi [5] are thermal interactions between nanoparticles and the molecules of the base fluid, collision between the molecules of base fluid, diffusion in the thermal property of the nanoparticles, and collision between the tiny particles due to the erratic random movement of these nano-sized particles. In the same report, it is revealed that there exists a connection between thermal behavior and Brownian motion of these particles. The aim of the study further led to the derivation of temperature-dependent thermal conductivity model and the major difference between solid/solid composites and solid/liquid suspensions which are useful in the designing of nano-engineered coolants with biomedical and industrial applications.

The report of Buongiorno [6] in the year 2006 on the transport phenomenon of nanofluids presents better model superior to dispersion and homogeneous models in which the properties/nature of nanoparticles and that of the base fluid are incorporated. Considering the fluid within the immediate fluid layers of the nanoparticles as a continuum, seven slip mechanisms including Brownian diffusion and thermophoresis are presented and discussed. Thereafter, several researchers were led to deliberate on the significance of Brownian diffusion and thermophoresis of tiny/nanoparticles within the thin boundary layer. For instance, Kuznetsov and Nield [7] explicitly explained the seven slip mechanisms reported by Buongiorno [6] and investigated the significance of Brownian motion and thermophoresis in the boundary-layer flow induced by natural convection. It was concluded that the Nusselt number is a decreasing property of buoyancy-ratio parameter (Nr, Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The same report of Buongiorno [6] can be referred to as the base idea of the aim and objectives of Khan and Pop [8] and other reports on the combined effects of thermophoresis and Brownian motion of tiny/nano-sized particles. Oztop et al. [9] deliberated on the flow of Cuo–Water nanofluid (the kind of Rayleigh–Benard problem) induced naturally by free convection with an attempt to know if thermophoresis and Brownian motion effects are significant in nanofluid heat transfer enhancement. Without any doubt, it was confirmed that the effects of Brownian and thermophoresis make the tiny particles to distribute non-uniformly in the domain, and consequently lead to higher heat transfer. In the absence of these two mechanisms, deterioration in heat transfer is ascertained. Nanofluids are the man-made colloidal suspension of tiny nanoparticles (i.e. alumina, gold, silica, and copper oxide) whose diameter is between the range of 1-100nm in a base fluid (i.e. water, ethanol, kerosene, and blood) without agglomeration (i.e assemblage of the nanoparticles). Sequel to all these, it is important to present a meta-analysis on the effects of haphazard motion of tiny/nano-sized particles on the dynamics and other physical properties of some fluids. The objectives are to extract published results on the effects of Brownian motion on various transport phenomena, introduce a statistical technique for quantifying the rate of increase or decrease, and scrutinize the corresponding effects.

Section snippets

Theoretical/conceptual review

In this subsection, the outcome of the theoretical/conceptual review of the forty-three (43) reports on the significance of Brownian motion is presented. The governing equation which models the two-dimensional flow of Brownian motion across nanofluid flow over a horizontal stretchable surface was non-dimenzionalized and solved numerically by Khan and Pop [8]. The Brownian motion within nanofluid over an isothermal sphere in a confined saturated porous medium was investigated by Chamkha et al.

Systematic review procedure

Step-by-step procedure of meta-analysis suggested by Neyeloff et al. [53] was considered but not suitable. This could be traced to the fact that calculations of weighted effect size (w × es), outcome size, test measures of heterogeneity, variance (Var), individual study weights (w), standard error (SE) and a number to quantify the heterogeneity of all the reported studies on the effects of Brownian motion of tiny/nano-sized particles in the flow of various fluids are not realistic. In this

Discussion of observed results

Physically, an increase in Brownian motion simply implies enhancement of haphazard motion of tiny particles. Whenever there is no irregular motion of such tiny particles, heat transfer can be easily enhanced. The decrease in Nusselt number which is directly proportional to heat transfer due to Brownian motion can be traced to the disturbance of heat transfer owing to the haphazard motion of tiny particles. In the presence of heat convective and mass convective at the wall of three-dimensional

Concluding remarks

Based on the outcome of the theoretical/conceptual and systematic review procedure of all the suitable published reports on the effects of Brownian motion of tiny/nano-sized particles in various nanofluids, it can be concluded that

  • 1.

    Increase in the magnitude of haphazard motion of particles implies an increase in the internal pressure on the tiny/nano-sized particles. In such a case, collision between the particles is bound to occur.

  • 2.

    In the same trends with Jang and Choi [5], the relentless and

Acknowledgments

All the authors would like to appreciate the support of Olabiyi A. S., Bankole T. D., and Ijirinmoye Abiodun. Special thanks to the reviewers for their constructive and logical comments.

References (58)

  • O.D. Makinde et al.

    MHD couple stress nanofluid flow in a permeable wall channel with entropy generation and nonlinear radiative heat

    J. Therm. Sci. Technol.

    (2017)
  • S. Qayyum et al.

    Mixed convection and heat generation/absorption aspects in MHD flow of tangent-hyperbolic nanoliquid with newtonian heat/mass transfer

    Radiat. Phys. Chem.

    (2018)
  • R.A. Subba et al.

    Hydromagnetic non-newtonian nanofluid transport phenomena from an isothermal vertical cone with partial slip:aerospace nanomaterial enrobing simulation

    Heat Transfer - Asian Res.

    (2018)
  • H. Kh et al.

    Hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates by analytical method

    Int. J. Mech. Mater.Eng.

    (2018)
  • T.L. Carus et al.

    On the Nature of Things

    (1952)
  • A. Eistein et al.

    Investigation on the theory of the brownian movement

    Sci. Mon.

    (1956)
  • E. Aydiner

    Rotational brownian motion on sphere surface and rotational relaxation

    Chin. Phys. Lett.

    (2006)
  • R. Tsekov et al.

    Brownian motion and the temperament of living cells

    Chin. Phys. Lett.

    (2013)
  • S.P. Jang et al.

    Role of brownian motion in the enhanced thermal conductivity of nanofluids

    Appl. Phys. Lett.

    (2004)
  • J. Buongiorno

    Convective transport in nanofluids

    J. Heat Transfer

    (2006)
  • A. Chamkha et al.

    Non-similar solution for natural convective boundary layer flow over a sphere embedded in a porous medium saturated with a nanofluid

    Transp. Porous Media

    (2011)
  • W.A. Khan et al.

    Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid

    J. Heat Transfer

    (2011)
  • M.J. Uddin et al.

    Thermophoresis and brownian motion effect on chemically reacting MHD boundary layer slips flow of a nanofluid

    AIP Conference Proc.

    (2012)
  • N. Anbuchezhian et al.

    Thermophoresis and brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

    Appl. Math. Mech.

    (2012)
  • M. Mustafa et al.

    MHD boundary layer flow of second grade nanofluid over a stretching sheet with convective boundary conditions

    J. Aerosp. Eng.

    (2012)
  • W. Ibrahim et al.

    Boundary-layer flow and heat transfer of nanofluid over a vertical plate with convective surface boundary condition

    J. Fluids Eng.

    (2012)
  • G. RSR et al.

    Natural convective boundary-layer flow over a vertical cylinder embedded in a porous medium saturated with a nanofluid

    J. Nanotechnol. Eng. Med.

    (2012)
  • M.J. Uddin et al.

    Scaling group transformation for MHD boundary layer slip flow of a nanofluid over a convectively heated stretching sheet with heat generation

    Math. Prob. Eng. 2012

    (2012)
  • S. Nadeem et al.

    Boundary layer flow of nanofluid over an exponentially stretching surface

    Nanoscale Res. Lett.

    (2012)
  • Cited by (138)

    View all citing articles on Scopus
    View full text