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Analysis of Natural Convection Bionanofluid Between Two Vertical Parallel Plates

  • Ahmad Hajizadeh
  • Nehad Ali ShahEmail author
  • F. D. Zaman
  • I. L. Animasaun
Article

Abstract

In this paper, natural convection flow of non-Newtonian bionanofluid flow between two vertical flat plates is considered. Sodium alginate (SA) is considered the base non-Newtonian fluid, and nanoparticles such as titania (TiO2) and alumina (Al2O3) were added to them. Analytical solutions for temperature and velocity field are determined by means of integral transform (Laplace transform) method. The influences of some physical parameters non-dimensional velocity and temperature profiles are graphically underlined.

Keywords

Natural convection Bionanofluid Laplace transform Vertical plates 

Nomenclature

u

The fluid velocity [LT−1]

T

The fluid temperature [K]

g

The acceleration due to the gravity [LT−2]

ρnf

The density of the nanofluid [ML−3]

βnf

The thermal expansion coefficient of the nanofluid [K−1]

μnf

The dynamic viscosity of the nanofluid [ML−1T−1]

Q

The dimensional heat generation/absorption coefficient [WL−3K−1]

(cp)nf

The specific heat of the nanofluid at constant pressure [L2MT−1K−1]

knf

The thermal conductivity of the bionanofluid [WL−1K−1]

d

The distance between plates [L]

φ

The nanoparticle volume fraction

f and s

Fluid and solid particles, respectively

Notes

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no Conflict of Interest and authors receive no fund.

Research Involving Humans and Animals Statement

None.

Informed Consent

None.

Funding Statement

None.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ahmad Hajizadeh
    • 1
    • 2
  • Nehad Ali Shah
    • 3
    Email author
  • F. D. Zaman
    • 4
  • I. L. Animasaun
    • 5
  1. 1.FASTUniversity Tun Hussein Onn MalaysiaParit RajaMalaysia
  2. 2.Public Authority of Applied Education and Training, Applied Science DepartmentCollege of Technological StudiesShuwaikhKuwait
  3. 3.Department of MathematicsLahore Leads UniversityLahorePakistan
  4. 4.Abdus Salam School of Mathematical SciencesGC UniversityLahorePakistan
  5. 5.Department of Mathematical SciencesFederal University of TechnologyAkureNigeria

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