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Numerical Simulations of Time-Dependent Micro-Rotation Blood Flow Induced by a Curved Moving Surface Through Conduction of Gold Particles with Non-uniform Heat Sink/Source

  • Research Article-Mechanical Engineering
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Abstract

Cancer remains one of the leading healthcare problems in the world, and efforts continue not only to discover new therapies but also to find better ways to deliver medicines. The need to transmit cytotoxic agents selectively to cancer cells, to improve safety and efficacy, has prompted the application of nanotechnology in medicine. The latest explorations have revealed that gold nanomaterials can rectify and defeat it since they have a large atomic quantity to generate heat and contribute to malignant tumor therapy. The purpose of the present study is to investigate the consequence of heat transport through micropolar blood flow which contains gold nanomaterials in a moving shrinking/stretching curved surface. The mathematical modeling of micropolar nanofluid containing gold blood nanomaterials (AuNPs) toward the curved shrinking/stretching surface is simplified by utilizing suitable transformation. Numerical dual solutions are regulated for the temperature distribution and velocity field by using the bvp4c technique in MATLAB. Impacts of pertinent constants on temperature distribution and velocity are examined. Consequently, findings indicate that gold nanomaterials are useful for drug movement and delivery mechanisms, as velocity boundary is controlled by suction and unsteady parameters. Gold nanomaterials also raise the temperature field, so that cancer cells can be destroyed.

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Abbreviations

\(B_{0}\) :

Intensity of the magnetic field

\(B^{*} ,A^{*}\) :

Temperature- and space-dependent heat source/sink

c :

Constant rate

\(C_{F} {\text{Re}}_{s}^{0.5}\) :

Dimensionless friction factor

\(C_{m} {\text{Re}}_{s}\) :

Couple stress

\(F\) :

Dimensionless velocity

\(G\) :

Dimensionless micro-rotation

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{j}\) :

Micro-inertia

\(K_{1}\) :

Micropolar or material parameter

\(M\) :

Magnetic parameter

\(M_{m}\) :

Wall couple stress

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{N}\) :

Micro-rotation velocity

\({\text{Nu}}_{s} {\text{Re}}_{s}^{ - 0.5}\) :

Local Nusselt number

\(n_{0}\) :

Constant

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{p}\) :

Pressure

\(\Pr\) :

Prandtl number

\(Q^{*}\) :

Non-uniform heat sink or source

\(q\) :

Radius of curvature

\(q_{w}\) :

Flux of heat

\(R_{1}\) :

Radius of a circle

\(R_{d}\) :

Radiation parameter

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}_{w}\) :

Temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T}_{\infty }\) :

Ambient temperature

\(U_{w} \left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{s} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t} } \right)\) :

Stretching/shrinking velocity

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{V}_{w} \left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{s} } \right)\) :

Mass-flux velocity

\(\left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u}_{1} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{v}_{1} } \right)\) :

Velocity components

\(\left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{r} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{s} } \right)\) :

Curvilinear coordinates

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}\) :

Time

\(\beta\) :

Unsteadiness parameter

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\rho }_{{{\text{nf}}}}\) :

Nanoliquid density

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\gamma }_{{{\text{nf}}}}\) :

Nanofluid spin gradient

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{k}^{*}\) :

Mean proportion coefficient

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{k}_{{{\text{nf}}}}\) :

Nanoliquid thermal conductivity

\(\kappa\) :

Vortex viscosity

\(\lambda\) :

Stretching/shrinking constant

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\mu }_{{{\text{nf}}}}\) :

Nanoliquid viscosity

\(\phi\) :

Nanoparticle volume fraction

\(\xi\) :

Unsteadiness constant

\(\theta\) :

Dimensionless temperature

\(\left( {c_{p} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\rho } } \right)_{{{\text{nf}}}}\) :

Heat capacitance

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\sigma }^{*}\) :

Stefan–Boltzmann constant

\(\sigma_{e}\) :

Electrical conductivity

\(\tau_{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{r} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{s} }}\) :

Wall friction

nf:

Nanofluid

\({\text{f}}\) :

Base fluid

′:

Derivative w.r.t \(\eta\)

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Acknowledgment

The authors expressed sincere thanks to the reviewer for his valuable comments to improve the quality of the paper. Also, this research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, 11601485).

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Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  2. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

  3. Department of Mathematics and Social Sciences, Sukkur IBA University, Sukkur, Sindh, 65200, Pakistan

    Umair Khan

  4. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Anum Shafiq

  5. Department of Mathematical Sciences, Federal Urdu University of Arts, Science and Technology, Gulshan-e-Iqbal, Karachi, 75300, Pakistan

    A. Zaib

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  1. Yu-Ming Chu
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Chu, YM., Khan, U., Shafiq, A. et al. Numerical Simulations of Time-Dependent Micro-Rotation Blood Flow Induced by a Curved Moving Surface Through Conduction of Gold Particles with Non-uniform Heat Sink/Source. Arab J Sci Eng 46, 2413–2427 (2021). https://doi.org/10.1007/s13369-020-05106-0

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