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Thermal performance of micro-polymers containing nano-solid structures during transport phenomenon

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Abstract

The inclusion of solid nano-structures in the liquid changes its rheology and hence its thermal performance. This article considers the impact of nano-solid structure on the ability of the polymer to transport heat. Mathematical models for nano-solid structures and conservation laws are finite element method. The impact of nano-solid structures on transportation of heat is studied via computed solutions. The micro-rotation field increases with an increase in vortex viscosity. The wall shear stress and wall couple stress are increased for vortex viscosity. However, the rate of heat transfer has shown decreasing behavior as a function vortex viscosity.

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Abbreviations

u, v :

Velocity components (m s\(^{-1}\))

Pr :

Prandtl number

M :

Hartmann number

Ec :

Eckert number

\(B_\mathrm{i}\) :

Biot number

\(N_\mathrm{r}\) :

Radiation parameter

Gr :

Grashof number

\({Re}\) :

Reynolds number

A, d, a :

Consistency numbers

\(\beta _\mathrm{1}\) :

Volumetric expansion coefficient

K :

Micro-polar parameter

T :

Fluid temperature (K)

k :

Thermal conductivity (W m\(^{-1}\) K\(^{-1}\))

Q :

Heat generation/absorption coefficient

\({\mathbf {B}}\) :

Magnetic field (T)

\(k^{*}\) :

Absorption coefficient

\(\sigma ^{*}\) :

Stefan–Boltzmann constant

\(c_\mathrm{p}\) :

Specific heat (J kg\(^{-1}\) K\(^{-1}\))

\(B_\mathrm{0}\) :

Magnetic field strength

g :

Gravitational acceleration (m s\(^{-2}\))

\(\rho\) :

Density (kg m\(^{-3}\))

\(\sigma\) :

Electrical conductivity (\(\Omega ^{-1}\) m\(^{-1}\))

\(\varphi\) :

Volume fraction

\(\mu\) :

Dynamic viscosity (kg m\(^{-1}\) s\(^{-1}\))

\(\eta\) :

Independent similarity function

\(\beta\) :

Heat generation/absorption parameter

\(\lambda\) :

Unsteadiness parameter

\(\gamma\) :

Spin gradient viscosity

f:

Fluid

w:

Wall

p:

Particles

s:

Solid particles

nf:

Nano-fluid

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

    Saima Batool, M. Nawaz & Shafia Rana

  2. Department of Humanities and Sciences, School of Electrical Engineering and Computer Sciences (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Rai Sajjad Saif

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  1. Saima Batool
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  2. M. Nawaz
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Correspondence to M. Nawaz.

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Batool, S., Nawaz, M., Saif, R.S. et al. Thermal performance of micro-polymers containing nano-solid structures during transport phenomenon. J Therm Anal Calorim 146, 1323–1333 (2021). https://doi.org/10.1007/s10973-020-10017-1

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