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Examination of Couple Stress Hybrid Nanoparticles (CuO-Cu/Blood) as a Targeted Drug Carrier with Magnetic Effects Through Porous Sheet

  • General and Applied Physics
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Abstract

The focal target in current study is to examine the couple stress hybrid nanoparticles as a targeted drug carrier in a porous medium. The flow at stagnation point is exposed to effects of magnetic and induced magnetic fields that can be used in the field of biomedicines such as fluid motion through microcirculatory system and drug delivery system. The modelled equations are converted to dimensionless form through set of similar variables and are then solved with homotopy analysis method. In this work, it has noticed that the flow of fluid declines for augmentation in magnetic, inertial, and porosity parameters. Thermal flow increases with growth in thermophoretic, Brownian motion, radiation parameters, and with heat source, while it declines with Prandtl number and heat sink. Concentration profile increases with thermophoretic parameter and declines with growth in Brownian motion parameter and Schmidt number. Moreover, the impact of different emerging parameters upon engineering quantities of interest is determined numerically and presented in the tabular form.

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Abbreviations

\(u_{w}\) :

Stretching velocity \(\left( {\text{m/s}} \right)\)

u, v:

Velocity components along x- and y-axes \(\left( {\text{m/s}} \right)\)

\(H_{1}\) and \(H_{2}\) :

Magnetic field components along x- and y-axes

\(\eta_{0}\) :

Magnetic diffusivity

\(\beta\) :

Magnetic field parameter

\(\beta\) :

Volumetric thermal expansion coefficient

\(\rho_{hnf}\) :

Density of hybrid nanofluid \(\left( {{\text{kg/m}}^{ - 3} } \right)\,\)

\(\left( {\rho c_{p} } \right)_{hnf}\) :

Volumetric heat capacity of hybrid nanofluid \(\left( {{\text{m}}^{2} {\text{/s}}^{2} /K} \right)\,\)

\(Sh\) :

Sherwood number

\(\phi\) :

Nanoparticle volume fraction

\(\left( {c_{p} } \right)_{s}\) :

Specific heat at constant pressure of nanoparticles \(\left( {{\text{m}}^{2} /{\text{s}}^{2} /K^{1} } \right)\,\)

\(w_{1}\), \(w_{2}\) :

First and second nanoparticle

\(s\) :

Suction or injection parameter

\(\lambda\) :

Mixed convection or buoyancy parameter

\({\text{N}}_{b}\) :

Brownian motion parameter

\(\alpha\) :

Heat source parameter

\(Sc\) :

Schmidt number

\(\Pr\) :

Prandtl number

\(T_{w}\) :

Surface temperature \(\left( {\text{K}} \right)\)

\(C_{w}\) :

Surface concentration

\(G_{r}\) :

Grashof number

\(q_{r}\) :

Rosseland approximation

\(C\) :

Concentration of the fluid

\(V_{0}\) :

Suction/injection velocity

\(F_{1}\) :

Inertia coefficient

\(\theta \,\) :

Dimesionless temperature \(\left( - \right)\,\)

\(\rho_{f}\) :

Density \(\left( {{\text{kg/m}}^{3} } \right)\,\)

\(f^{\prime}\) :

Dimensionless velocity \(\left( - \right)\,\)

\(\left( {\rho c} \right)_{p}\) :

Effective heat capacity of nanoparticles \(\left( {{\text{m}}^{2} {\text{/s}}^{2} {\text{/K}}^{1} } \right)\,\)

\(T_{\infty } \,\) :

Ambient temperature \(\left( {\text{K}} \right)\)

\(T_{0}\) :

Reference temperature \(\left( {\text{K}} \right)\)

\(k\) :

Dimensional permeability

\(g\) :

Acceleration due to gravity \(\left( {{\text{m/s}}^{2} } \right)\)

\(\lambda_{1}\) :

Diffusive constant parameter

\(Q\) :

Volumetric rate of heat generation/absorption

\(\mu_{hnf}\) :

Viscosity of hybrid nanofluid

\(k_{hnf}\) :

Thermal conductivity of hybrid nanofluid

\(Re_{x}\) :

Reynolds number

\(\rho_{s}\) :

Density of nanoparticles

\(\phi_{1}\), \(\phi_{2}\) :

Volume fraction of first and second nanoparticles

\(w_{f}\) :

Base fluid masses

\(k_{1}\) :

Non-dimensional permeability parameter

\(\Lambda\) :

Reciprocal magnetic Prandtl number

\(N_{t}\) :

Thermophoretic parameter

\(K\) :

Coupled stress parameter

\(Nu_{x}\) :

Nusselt number

\(C_{f}\) :

Skin friction coefficient

\(k^{*}\) :

Mean absorption coefficient

\(\mu_{e}\) :

Magnetic permeability

\(l\) :

Characteristic length \(\left( {\text{m}} \right)\)

\(\sigma_{1}\) :

Stefan-Boltzmann constant

\(T\) :

Temperature of the fluid \(\left( {\text{K}} \right)\)

\(k_{{}}\) :

Thermal conductivity \(\left( {{\text{Wm}}^{1} /{\text{K}}^{1} } \right)\,\,\)

\(R\) :

Radiation parameter

\(\Phi\) :

Dimensionless concentration \(\left( - \right)\,\)

\(\eta\) :

Similarity variable

\(\nu_{f}\) :

Kinematic viscosity \(\left( {{\text{m}}^{2} {\text{/s}}^{1} } \right)\,\,\)

\(\mu_{f}\) :

Dynamic viscosity \(\left( {{\text{kg/m}}^{1} /{\text{s}}^{1} } \right)\,\)

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Authors and Affiliations

  1. Department of Mathematics, University of Swabi, Swabi, 23430, Pakistan

    Muhammad Jawad & Syed Azhar Ali Shah

  2. College of Aeronautical Engineering, National University of Sciences and Technology (NUST), Sector H-12, Islamabad, 44000, Pakistan

    Arshad Khan

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  1. Muhammad Jawad
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Correspondence to Arshad Khan.

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Jawad, M., Khan, A. & Shah, S.A.A. Examination of Couple Stress Hybrid Nanoparticles (CuO-Cu/Blood) as a Targeted Drug Carrier with Magnetic Effects Through Porous Sheet. Braz J Phys 51, 1096–1107 (2021). https://doi.org/10.1007/s13538-021-00930-7

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