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A meshless numerical study of conjugate mixed convection of non-Newtonian nanofluids in an enclosure using non-homogeneous model

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Abstract

The present study deals with the conjugate mixed convection of a non-Newtonian nanofluid in an enclosure with a left thick side wall. We adopt Buongiorno’s non-homogeneous model to incorporate the effects due to Brownian motion and thermophoretic diffusion of the nanoparticles. The non-Newtonian behavior of the nanofluid is captured through the widely accepted power-law model. We employ the radial basis function (RBF)-based meshless numerical scheme for the simulation. In order to check the accuracy of the present numerical scheme, the simulated results are compared with the available numerical as well as experimental data. The excellent agreement of our results with the available ones ensures the capability of the newly adopted numerical tools to study the conjugate heat transfer problems. The results are presented by varying the pertaining parameters governing the undertaken conjugate mixed convection problem. Richardson number and Reynolds number are varied up to a moderate range with different permissible choices of the nanoparticle volume fractions, diameter of the nanoparticles, power-law index, and solid-to-fluid conductivity ratio, etc. The entropy generation and Bejan number are further evaluated to analyze the heat transfer characteristics. Results show that the degree of inhomogeneity of the nanoparticles depends strongly on the fluid behavior index. Rheological behavior of the nanofluid has substantial impact on the heat transfer rate and entropy generation, which can further be controlled through the value of the solid-to-fluid conductivity ratio. The pattern in Bejan number shows the predominance of the heat transfer irreversibility over the fluid friction irreversibility for all the cases considered in the study.

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Availability of data and materials

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Abbreviations

Be :

Bejan number, \(S_{h}/S_{gen}\)

D :

Dimensionless thickness of the solid wall

\(D_{B}\) :

Brownian diffusion coefficient

\(D_{T}\) :

Thermophoretic diffusion coefficient

\(d_{p}\) :

Diameter of the nanoparticle (m)

g :

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

Gr :

Grashof number, \(\left( \beta _{f}\rho _{f}^{2}V_{0}^{2-2n} H^{2n+1} (T_{h}-T_{c}) g \right) /m^{2}\)

H :

Enclosure height (m)

k :

Thermal conductivity (W/mK)

\(k_{B}\) :

Boltzmann constant (\(J K^{-1}\))

\(K_{r}\) :

Solid wall to nanofluid thermal conductivity ratio, \(k_{s}/k_{nf}\)

\(K_{ro}\) :

Solid wall to base fluid thermal conductivity ratio, \(k_{s}/k_{f}\)

m :

Flow consistency index

n :

Fluid behavior index

Nu :

Local Nusselt number

\(p^{*}\) :

Pressure (\(N/m^{2}\))

Pr :

Prandtl number, \(m(C_{p})_{f} V_{0}^{n-1}H^{1-n}/k_{f}\)

Re :

Reynolds number, \(\left( \rho _{f}V_{0}^{2-n}H^{n}\right) / m\)

Ri :

Richardson number, \(Gr/Re^{2}\)

\(S_{f}\) :

Dimensionless local entropy generation due to fluid friction irreversibility

\(S_{gen}\) :

Dimensionless total entropy generation

\(S_{h}\) :

Dimensionless local entropy generation due to heat transfer irreversibility

t :

Dimensionless time

T :

Temperature (K)

(u, v):

Dimensionless velocity components in x,y direction respectively

\(V_{0}\) :

Reference velocity (m/s)

\(\alpha\) :

Thermal diffusivity (\(m^{2}/s\))

\(\beta _{f}\) :

Coefficient of thermal expansion (\(K^{-1}\))

\(\theta\) :

Dimensionless temperature

\(\rho\) :

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

\(\phi\) :

Nanoparticle volume fraction

av :

Average

c :

Cold

f :

Clear fluid

h :

Hot

nf :

Nanofluid

p :

Solid particle

s :

Solid wall

\(*\) :

Dimensional quantity

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Funding

Partha P. Gopmandal gratefully acknowledges the financial support by the Science and Engineering Research Board, Govt. of India, through a project grant (File No. MTR/2018/001021).

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    S. K. Pal & P. Mandal

  2. Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, Japan

    H. Ohshima

  3. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, 713209, India

    Partha P. Gopmandal

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  1. S. K. Pal
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  2. P. Mandal
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Contributions

S.K.P and P.P.G conceive the research idea; S.K.P and P.M prepare the figures, S.K.P., P.M., P.P.G wrote the first draft and all the authors reviewed the manuscript.

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Correspondence to Partha P. Gopmandal.

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Pal, S.K., Mandal, P., Ohshima, H. et al. A meshless numerical study of conjugate mixed convection of non-Newtonian nanofluids in an enclosure using non-homogeneous model. Colloid Polym Sci 302, 517–538 (2024). https://doi.org/10.1007/s00396-023-05200-3

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