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Thermosolutal discharge of double diffusion mixed convection flow with Brownian motion of nanoparticles in a wavy chamber

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Abstract

In this paper, we have conducted a numerical investigation to investigate thermal and solutal performances of thermosolutal mixed convection flow in a wavy chamber with the influence of Brownian motion of nanoparticles. The Cu-water nanofluid is used to fill the chamber. The bottom boundary is nonuniformly concentrated and heated while the other boundaries of the chamber are fixed at constant low concentration and cold temperature. The upper and lower walls of the chamber are in motion with constant velocity. Depending on the directions of motion of the upper and lower walls, we have considered four cases. The governing equations representing incompressible viscous flows are the Navier–Stokes (N–S) equations in the form of mass, momentum, temperature and concentration equations. A compact finite difference scheme is adopted to solve those equations. We have applied KKL model of Koo-Kleinstreuer and Li for taking into account the effects of Brownian motion of Cu-water nanofluid properties in addition to the effective thermal conductivity and the dynamic viscosity. The numerical results are explored for getting a better understanding of the effects of thermal Grashof number (\({\mathrm{Gr}}_{\mathrm{T}}=10^{4}\)), Buoyancy ratio number (\(N=1\)), Richardson number (\(0.1\le {\mathrm {Ri}}\le 10.0\)), Lewis number (\(1\le {\mathrm{Le}}\le 10\)), the wavy surface amplitude (\(0.0\le \lambda \le 0.06\)), solid volume fraction (\(0.0\le \phi \le 0.04\)) and undulation number of the vertical walls (\(0\le d \le 2\)). Results reveal that nanoparticles are responsible for the enhancement of heat transfer and the decrement of mass transfer.

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Abbreviations

L :

Length of cavity (m)

Pr:

Prandtl number

Re:

Reynolds number

Ri:

Richardson number

D :

Mass diffusivity (\(\hbox {m}^2\)   \(\hbox {s}^{-1}\))

d :

Undulation of the wavy wall

g :

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

Le:

Lewis number, \({\mathrm{Le}}=\frac{\alpha }{D}\)

N :

Buoyancy ratio parameter, \(N=\frac{{\mathrm{Gr}}_{\mathrm{C}}}{{\mathrm{Gr}}_{\mathrm{T}}}\)

k :

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

p :

Dimensional pressure (\(\hbox {N m}^{-2}\))

P :

Dimensionless pressure

T :

Dimensional temperature

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

Volumetric expansion coefficients with temperature

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

Volumetric expansion coefficient with mass (concentration) fraction

C :

Dimensional concentration

c :

Dimensionless concentration

\(\kappa _{\mathrm{b}}\) :

Boltzmann constant

\(C_{\mathrm{p}}\) :

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

Nu:

Local Nusselt number

Sh:

Local Sherwood number

\({\overline{\mathrm{Nu}}}\) :

Average Nusselt number

\({\overline{\mathrm{Sh}}}\) :

Average Sherwood number

\({\mathrm{Gr}}_{\mathrm{C}}\) :

Grashof number due to mass diffusion, \(\displaystyle {\frac{g\beta _{\mathrm{C}}(C_{\mathrm{h}}-C_{\mathrm{c}})L^{3}}{\nu ^{2}}}\)

\({\mathrm{Gr}}_{\mathrm{T}}\) :

Grashof number due to thermal diffusion, \(\displaystyle {\frac{g\beta _{\mathrm{T}}(T_{\mathrm{h}}-T_{\mathrm{c}})L^{3}}{\nu ^{2}}}\)

x, y :

Dimensional Cartesian coordinates (m)

X, Y :

Dimensionless Cartesian coordinates

u, v :

Dimensional velocities in x, y directions, respectively (\(\hbox {m s}^{-1}\))

U, V :

Dimensionless velocities in X, Y directions, respectively

\(\xi\), \(\eta\) :

Dimensionless coordinate in computational plane

\(\alpha\) :

Thermal diffusivity (\(\hbox {m}^{2}\) \(\hbox {s}^{-1}\))

\(\beta\) :

Thermal expansion coefficient (\(\hbox {K}^{-1}\))

\(\phi\) :

Volume fraction of the nanoparticles

\(\rho\) :

Nanofluid density(kg \(\hbox {m}^{-3}\))

\(\nu\) :

Kinematic viscosity (\(\hbox {m}^2\) \(\hbox {s}^{-1}\))

\(\mu\) :

Dynamic viscosity (Pa s)

\(\lambda\) :

Amplitude of the waviness

\(\psi\) :

Streamfunction

\(\zeta\) :

Vorticity

\(\theta\) :

Dimensionless temperature

i,j:

Cell faces

c:

Cold

h:

Hot

f:

Fluid

nf:

Nanofluid

static:

Magnitudes without considering the Brownian motion

Brownian:

Magnitudes considering also the Brownian motion

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Authors and Affiliations

  1. Integrated Science Education and Research Centre (ISERC), Visva-Bharati, Santiniketan, West Bengal, 731235, India

    Samrat Hansda & Swapan K. Pandit

  2. Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Republic of China

    Tony W. H. Sheu

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  1. Samrat Hansda
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Hansda, S., Pandit, S.K. & Sheu, T.W.H. Thermosolutal discharge of double diffusion mixed convection flow with Brownian motion of nanoparticles in a wavy chamber. J Therm Anal Calorim 147, 7007–7029 (2022). https://doi.org/10.1007/s10973-021-10971-4

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