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Entropy generation optimization in a radiative hybrid nanofluid (engine oil + NiZnFe2O4 + MnZnFe2O4) flow through a convectively heated microchannel with cross-diffusion effects

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Abstract

The vertical microchannels phenomenon is useful in the cooling process of microelectronic devices, fuel cells and MHD (magnetohydrodynamic) micro-pumps. The understanding of this phenomenon makes these flows crucial in industries and engineering products. Objective of this paper is how Dufour, Soret and chemical reaction affect the characteristics of hybrid nanofluid (engine oil + manganese zinc ferrite (\(({\text{MnZnFe}}_{2} {\text{O}}_{4} )\) + nickel zinc ferrite \(({\text{NiZnFe}}_{2} {\text{O}}_{4} )\))) flow in a microchannel with two vertical parallel plates. The irreversibility analysis is considered. The bvp4c solver in MATLAB is implemented to compute the transformed system derived from the equations used to describe the present problem. The heat transfer rate and other physical parameters of relevance near both plates are explained using graphs. It has been observed that as the Brinkman number and Dufour numbers increased, the entropy production rate is significantly changed. It is noticed that there is a reduction in Bejan number with the escalation in volume fraction of \({\text{NiZnFe}}_{2} {\text{O}}_{4}\) (\(\phi_{{{\text{Ni}}}}\)). The skin-friction factor declined with the rate of 0.03114 at \(0 \le {\text{Mn}} \le 3\) (near left plate) and decreased in the friction factor is 2.45896 when \(\phi_{{{\text{Ni}}}}\) is in the range \(0 \le \phi_{{{\text{Ni}}}} \le 0.09\) (near right plate). It is detected that when Dufour number (\({\text{Du}}\)) is at \(0 \le {\text{Du}} \le 0.6\), heat transmission rate cuts down by 0.06935 (near the left plate). Sherwood number risen by 0.043153 (near the left plate) when Soret number (\({\text{Sr}}\)) is set to \(0 \le {\text{Sr}} \le 0.6\).

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Abbreviations

\(u,v\) :

Velocity components in \(x,y\) directions

\(p\) :

Pressure

\(\kappa\) :

Permeability of porous medium

\(k_{{\text{T}}}\) :

Thermal mean temperature

\({\text{Br}}\) :

Brinkman number

\(c_{{\text{s}}}\) :

Concentration susceptibility

\(\mu\) :

Dynamic viscosity

\(\rho\) :

Density

\(\sigma\) :

Electrical conductivity

\({\text{St}}\) :

Schmidt number

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

Specific heat capacity

\(\Pr\) :

Prandtl number

\(k*\) :

Mean absorption coefficient

\(k_{0}\) :

Chemical reaction rate parameter

\(\upsilon\) :

Kinematic viscosity

\(k\) :

Thermal conductivity

\(\phi_{1}\) :

Volume fraction of \({\text{NiZnFe}}_{2} {\text{O}}_{4}\)

\({\text{Sr}}\) :

Soret number

\(\phi_{2}\) :

Volume fraction of \({\text{MnZnFe}}_{2} {\text{O}}_{4}\)

\(\eta\) :

Similarity variable

\(\sigma *\) :

Stefan–Boltzmann constant

\(T_{{\text{m}}}\) :

Fluid mean temperature

\(\delta\) :

Pressure gradient parameter

\(\Lambda\) :

Porosity parameter

\({\text{Cr}}\) :

Reaction rate parameter

\(D_{{\text{m}}}\) :

Molecular diffusivity

\({\text{Mn}}\) :

Magnetic field parameter

\({\text{Bi}}_{1}\) :

Biot number near left plate

\({\text{Bi}}_{2}\) :

Biot number near right plate

\(h_{{\text{i}}}\) :

Convective heat transfer coefficient

\({\text{Rd}}\) :

Thermal radiation parameter

\(\tilde{R}\) :

Universal gas constant

\(E_{{\text{G}}}\) :

Entropy generation parameter

\(G\) :

Diffusion parameter

\({\text{Re}}\) :

Reynolds number

\({\text{Du}}\) :

Dufour number

\(\beta\) :

Concentration ratio parameter

\(\alpha\) :

Temperature difference parameter

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Authors and Affiliations

  1. Department of Mathematics, Matrusri Engineering College, Saidabad, Hyderabad, Telangana, 500059, India

    Darapuneni P. C. Rao

  2. Department of Mathematics, S.V.A Government College, Srikalahasti, Andhra Pradesh, 517644, India

    M. Jayachandra Babu

  3. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    S. A. Shehzad & S. Qaisar

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  1. Darapuneni P. C. Rao
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  2. M. Jayachandra Babu
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  3. S. A. Shehzad
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  4. S. Qaisar
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Contributions

DPCR was involved in the investigation, data curation and formal analysis. MJB contributed to writing—original draft, data curation and software. SAS assisted in the validation, visualization, technical review and visualization. SQ contributed to the visualization, supervision and conceptualization.

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Correspondence to M. Jayachandra Babu or S. A. Shehzad.

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Rao, D.P.C., Babu, M.J., Shehzad, S.A. et al. Entropy generation optimization in a radiative hybrid nanofluid (engine oil + NiZnFe2O4 + MnZnFe2O4) flow through a convectively heated microchannel with cross-diffusion effects. J Therm Anal Calorim 148, 10907–10916 (2023). https://doi.org/10.1007/s10973-023-12412-w

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