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Heat transfer enhancement and entropy generation of two working fluids of MHD flow with titanium alloy nanoparticle in Darcy medium

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Abstract

This article aims to study entropy generation and heat transfer due to free convection. Two types of base fluids (water and kerosene oil) are taken with a suspension of titanium alloy nanoparticles. An external magnetic field is applied in a perpendicular direction and the induced magnetic field is neglected. Scientific analysis is performed on magnetohydrodynamic flow through a Darcy medium. Free convection and the sudden motion of the heated plate cause the fluid to flow. The problem is formulated in terms of differential equations with associated physical conditions. Relations for entropy generation and Bejan numbers are also provided. The Laplace transform technique has been used for finding the exact solution to the problem. Results are plotted using Mathcad software and a comparison is made between water-titanium alloy and kerosene oil-titanium alloy nanoparticles for velocity, temperature, entropy generation, and Bejan number. It is concluded that kerosene oil base fluid has a greater velocity and temperature profile in all parametric studies as compared to water-based fluid. While in the case of entropy generation and Bejan number, near to the plate and for away the plate the behaver is distinct. Entropy generation and Bejan number are boosting up via using different base fluid. For larger estimation of Brinkman number, both Bejan number and entropy rate have the opposite effect. The volume fraction of nanofluid enhance the rate of heat transfer in case of both nanofluid. While the water base nanofluid enhance the rate of heat transfer up to 19.14% and kerosene oil base fluid is enhanced up to 30.01%.

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Abbreviations

\(\rho\) :

Density

\(\Theta_{\rm w}\) :

Wall temperature

\(u\left( {y_{1} ,t_{1} } \right)\) :

Velocity of fluid

\(U_{0}\) :

Constant velocity

\(\mu\) :

Dynamic viscosity

\(\Omega\) :

Dimensionless temperature difference

\(g\) :

Gravitation acceleration

\(\phi\) :

Volume fraction

\(\beta_{\Theta }\) :

Thermal conductivity

\(N_{\rm H}\) :

Entropy generation due to heat transfer

\(\Theta \left( {y_{1} ,t_{1} } \right)\) :

Temperature profile

\(C_{\rm p}\) :

Specific heat capacitance

\(B_{0}^{2}\) :

Magnetic field

\(N_{\rm F}\) :

Entropy generation due to fluid friction

\(\Theta_{\infty }\) :

Imbedded temperature

\(\sigma\) :

Electrical conductivity

\(\psi\) :

Porous medium

\(Ns\) :

Entropy generation

\(k\) :

Permeability of the porous medium

\(\Pr\) :

Prandtl number

\(\left(\right)_{\rm f}\) :

Base fluid

\(B_{{\text{e}}}\) :

Bejan number

\(\left(\right)_{{\text{s}}}\) :

Nanoparticles

\(K\) :

Pours medium permeability

\(\left(\right)_{{{\text{nf}}}}\) :

Nanofluid

\(Gr\) :

Grashof number

\(M\) :

Magnetic parameter

\(\nu\) :

Kinematic viscosity

\(Br\) :

Brinkman number

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Acknowledgements

The authors acknowledge the financial support provided by the Centre of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. The authors wish to thank the anonymous referees for their comments and suggestions.

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Authors and Affiliations

  1. Center of Excellence in Theoretical and Computational Science (TaCS‐CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Dolat Khan, Poom Kumam & Wiboonsak Watthayu

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  3. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia

    Ilyas Khan

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  1. Dolat Khan
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Contributions

DK model the problem. DK and IK solved the modeled problem analytically. DK and IK draw the graphs. Results and discussions have reviewed by PK and WW reviewed the whole manuscript. Proof reading has performed by DK and PK. All authors reviewed the final manuscript.

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Correspondence to Poom Kumam.

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Khan, D., Kumam, P., Watthayu, W. et al. Heat transfer enhancement and entropy generation of two working fluids of MHD flow with titanium alloy nanoparticle in Darcy medium. J Therm Anal Calorim 147, 10815–10826 (2022). https://doi.org/10.1007/s10973-022-11284-w

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