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Transient flow and heat transfer mechanism for Williamson-nanomaterials caused by a stretching cylinder with variable thermal conductivity

  • Hashim Email author
  • Aamir Hamid
  • Masood Khan
Technical Paper
  • 9 Downloads

Abstract

The utilization of nanometre-sized solid particles in working fluids has been seriously recommended due to their enhanced thermal characteristics. This suspension of solid particles in base fluids can significantly enhance the physical properties, such as, viscosity and thermal conductivity. They are widely used in several engineering processes, like, heat exchangers, cooling of electronic equipment, etc. In this exploration, we attempt to deliver a numerical study to simulate the nanofluids flow past a circular cylinder with convective heat transfer in the framework of Buongiorno’s model. A non-Newtonian Williamson rheological model is used to describe the behavior of nanofluid with variable properties (i.e., temperature dependent thermal conductivity). The leading flow equations for nanofluid transport are mathematical modelled with the assistance of Boussinesq approximation. Numerical simulation for the system of leading non-linear differential equations has been performed by employing versatile, extensively validated, Runge–Kutta Fehlberg scheme with Cash–Karp coefficients. Impacts of active physical parameters on fluid velocity, temperature and nanoparticle concentration is studied and displayed graphically. It is worth to mention that the temperature of non-Newtonian nanofluids is significantly enhanced by higher variable thermal conductivity parameter. One major outcome of this study is that the nanoparticle concentration is raised considerably by an increasing values of thermophoresis parameter.

List of symbols

a, β

Positive constants

t

Time

ρ

Density of the fluid

B0

Strength of magnetic field

μ

Viscosity at infinite shear rate

μ0

Viscosity at zero shear rate

β*

Viscosities ratio

x, r

Cylindrical polar coordinates

u, v

Velocity components

Uw

Stretching cylinder velocity

Γ

Relaxation time

ν

Kinematic viscosity

σ

Electrical conductivity

Tf

Temperature of hot fluid

hf

Heat transfer coefficient

T

Temperature of the fluid

C

Concentration of nanoparticles

T

Free stream temperature

C

Free stream nanoparticles concentration

DB

Brownian diffusion coefficient

DT

Thermophoretic diffusion coefficient

cp

Specific thermal capacity

k(T)

Variable thermal conductivity

τ

Ratio of effective heat capacities

ψ

Stream function

f

Dimensionless velocity

θ

Dimensionless temperature

φ

Dimensionless concentration

η

Dimensionless variable

γ

Curvature parameter

We

Weissenberg number

A

Unsteadiness parameter

Pr

Prandtl number

Sc

Schmidt number

Nt

Thermophoretic parameter

Nb

Brownian motion parameter

Re

Local Reynolds number

(ρc)f

Heat capacity of the fluid

(ρc)p

Heat capacity of nanoparticles

τw

Surface shear stress

Cf

Skin friction coefficient

Nu

Nusselt number

Sh

Sherwood number

qw

Surface heat flux

qm

Surface mass flux

γ1

Thermal Biot number

γ2

Concentration Biot number

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsRiphah International UniversityIslamabadPakistan
  2. 2.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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