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MHD mixed convection of non-Newtonian power-law ferrofluid in a wavy enclosure

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Abstract

The present study focuses on numerical simulations of magnetohydrodynamic mixed convection and entropy formation in a lid-driven wavy enclosure filled with non-Newtonian power-law ferrofluid. The physical model is a two-dimensional wavy square chamber with thermally adiabatic horizontal boundaries, while the right and left vertical walls maintain a constant temperature of the \(T_{\rm C}\) and \(T_{\rm H}\), respectively. For mapping the wavy domain to a simple square domain the Cartesian curvilinear coordinates are used. The governing equations are solved using the finite volume method to explore the mixed convection characteristics in terms of heat transport, velocity, streamlines, isotherms, and entropy formation. Pertinent non-dimensional parameters, such as the Reynolds number (Re), Hartmann number (Ha), power-law index (n), ferroparticle volume fraction (\(\phi \)), and a fixed Prandtl number (\({\rm Pr} = 6.8377\)), are used for the numerical simulation. According to the findings, the mean Nusselt numbers (\({\overline{\rm Nu}}\)) grow when Ha is reduced and Re, n and \(\phi \) are augmented, and the highest magnitude of \({\overline{\rm Nu}}\) is found, while \(4\%\) ferroparticles are added to the base fluid. The influence of key variables on total entropy production \((E_{\rm s})_{\rm t}\) reduced by raising Ha.

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Data availability

The data are available based on request.

Abbreviations

Be:

Bejan number (local)

\(B_0\) :

Magnetic force, \({\rm kg}\,{\rm s}^{-2}\,{\rm A}^{-1}\)

\(C_{\rm p}\) :

Specific heat, \({\rm Jkg}^{-1}\,{\rm K}^{-1}\)

E :

Entropy production, \({\rm J m}^{-3}\,{\rm s}^{-1}\,{\rm K}^{-1}\)

Gr:

Grashof number

g :

Gravitational acceleration, \({\rm ms}^{-2}\)

Ha:

Hartmann number

k :

Thermal conductivity, \({\rm J m}^{-1}\,{\rm s}^{-1}\,{\rm K}^{-1}\)

Nu:

Nusselt number (local)

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

Nusselt number (average)

Pr:

Prandtl number

Re:

Reynolds number

Ri :

Richardson number

T :

Temperature, K

\(T_{\rm o}\) :

Bulk temperature, K

\(\bar{u}\),\(\bar{v}\) :

Dimensional mid-x and mid-y velocity components, \({\rm ms}^{-1}\)

u, v :

Dimensionless mid-x and mid-y velocity components

\(\bar{x},\bar{y}\) :

Dimensional coordinates, m

x, y :

Dimensionless coordinates

\(\alpha \) :

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

\(\beta \) :

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

\(\mu \) :

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

\(\nu \) :

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

\(\rho \) :

Fluid density, \({\rm kg m}^{-3}\)

\(\sigma \) :

Electrical conductivity, \({\rm Am}^{-2}\)

\(\phi \) :

Volume fraction

\(\psi \) :

Dimensionless stream function

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Acknowledgements

This research is conducted by using the High-Performance Computing (HPC) facility of the School of Engineering and Physical Sciences (SEPS), North South University (NSU), Bangladesh. M. M. Molla would like to thank the NVIDIA Corporation, USA, for granting the TESLA K40 GPU.

Funding

The authors acknowledge gratefully to the North South University for the financial support as a faculty research grant  (Grant No.: CTRG-22-SEPS-09). The last authors also acknowledge the Ministry of Science and Technology (MOST), the government of Bangladesh, for providing the financial support for this research  (Grant No.: EAS/SRG-222427).

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Authors and Affiliations

  1. Department of Mathematics and Physics, North South University, Dhaka, 1229, Bangladesh

    Amzad Hossain & Md. Mamun Molla

  2. Center for Applied and Computational Sciences (CACS), North South University, Dhaka, 1229, Bangladesh

    Md. Mamun Molla

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  1. Amzad Hossain
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Correspondence to Md. Mamun Molla.

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Hossain, A., Molla, M. . MHD mixed convection of non-Newtonian power-law ferrofluid in a wavy enclosure. J Therm Anal Calorim 148, 11871–11892 (2023). https://doi.org/10.1007/s10973-023-12485-7

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