Heat transfer enhancement due to nanoparticles, magnetic field, thermal and exponential space-dependent heat source aspects in nanoliquid flow past a stretchable spinning disk

Abstract

This study explores the heat transfer characteristics of nanoliquid flowing over a rotating disk in the presence of the applied magnetic field and convective boundary condition. The nanoliquid is flowing due to the rotation of the disk with uniform stretching of a disk along the radial direction. Effects of ESHS (exponential space-related heat source) and THS (thermal-related heat source) are the focal concern of this article. The effective thermal conductivity of ethylene glycol (EG)-based graphene oxide (GO) nanoliquid is estimated by using Nan’s model whereas effective dynamic viscosity is calculated through Brinkman model. The partial differential system which governed the problem is transformed by using Von-Karman stretching transformations to the ordinary differential system. The subsequent two-point ODBVP (ordinary differential boundary value problem) is treated numerically. The consequence of effective parameters of the problem on different flow fields is illustrated graphically. The numerical values of shear stress and heat transfer rate (Nusselt number) are also calculated. Further, the slope of the data points is determined to quantify the outcome. Validation of the present results is made by direct comparison with the available results and an excellent agreement is found. It is found that the rate of heat transfer increased with nanoparticle volume fraction at the rate 0.4153 and the friction factor increased by increasing nanoparticle volume fraction at the rate 3.0681. The fluctuation rate of Nusselt number due to the variation of the ESHS parameter is almost three times more than that of THS parameter.

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Abbreviations

Ω:

Angular velocity

Bi:

Biot number

T f :

Convective fluid temperature (K)

h f :

Convective heat transfer coefficient

H(ξ):

Dimensionless normal velocity

F(ξ):

Dimensionless radial velocity

G(ξ):

Dimensionless tangential velocity

n :

Exponential index

Q*E :

Exponential space-dependent heat source coefficient

Q E :

Exponential space-dependent heat source or sink parameter

Re:

Local Reynolds number

B 0 :

Magnetic field strength

M :

Magnetic parameter

Nux :

Nusselt number

Pr:

Prandtl number

P :

Pressure

r :

Radial axes

C f :

Skin friction coefficient

S :

Stretching rate

c :

Stretching strength parameter

L ii :

Geometrical factor

T :

Temperature of the fluid (K)

k f :

Thermal conductivity (W m−1 K−1)

Q*T :

Thermal-dependent heat source coefficient

Q T :

Thermal-dependent heat source/sink parameter

(u,v,w):

Velocity components along r, s, z directions (m s−1)

z :

Vertical axis in the cylindrical coordinates system

T :

Ambient temperature (K)

p :

Constant pressure

ρ :

Density (kg m−3)

θ(ξ):

Dimensionless temperature

ξ :

Dimensionless variable

µ :

Dynamic viscosity (kg m−1 s−1)

σ :

Electrical conductivity (S m−1)

ν :

Kinematic viscosity (m2 s−1)

κ :

Nanoparticle volume fraction

τ wr :

Radial shear stress at the surface

c p :

Specific heat (J kg−1 K−1)

σ*:

Stefan-Boltzmann constant (Wm2 K4)

q w :

Surface heat flux

α :

Thermal diffusivity

τ w κ :

Transversal shear stress at the surface

β ii :

Symbol used represents expression

nf :

Nanomaterial

f :

Base fluid

s :

Nanoparticles

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Acknowledgements

The author (B.Mahanthesh) gratefully acknowledges the support of the Management, CHRIST (Deemed to be University), Bangalore, INDIA for pursuing this work. Also, we are very grateful for the Editor and reviewer for their constructive suggestions.

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Correspondence to Giulio Lorenzini.

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Mahanthesh, B., Shashikumar, N.S. & Lorenzini, G. Heat transfer enhancement due to nanoparticles, magnetic field, thermal and exponential space-dependent heat source aspects in nanoliquid flow past a stretchable spinning disk. J Therm Anal Calorim (2020). https://doi.org/10.1007/s10973-020-09927-x

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Keywords

  • Exponential space-based heat source (ESHS)
  • Nanoliquid
  • Magnetic field
  • Thermal-based heat source (THS)
  • Rotating disk
  • Nanoparticles