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Numerical Study on Hydromagnetic Oscillating Flow of Couple Stress Nanofluid in a Porous Channel with Cattaneo Christov Heat Flux

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Abstract

The present work discloses the oscillating hydromagnetic blood-based couple stress nanofluid flow in between porous walls by the means of Buongiorno nanofluid model with Cattaneo–Christov heat flux. Joule heating, chemical reaction, viscous dissipation, and thermal radiation are accounted in this study. The flow governing equations are simplified by adopting the perturbation method and then solved by using the Runge–Kutta fourth-order approach with aid of a shooting procedure. The obtained results show that the temperature increases with the augmenting viscous dissipation, thermophoresis, thermal radiation, and Brownian motion, whereas the rising couple stress viscosity dwindling the temperature. Heat transfer rate is enhanced with the increment in thermophoresis and Brownian motion parameters whereas the reverse is true with the rise in couple stress and thermal relaxation parameters.

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Data Availibility

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

\(x^{*},y^{*}\) :

Dimensional Cartesian coordinates

x, y :

Dimensionless Cartesian coordinates

\(u^{*} \) :

Dimensional velocity components in x-direction (m s\(^{-1}\))

u :

Dimensionless velocity component in x-direction

\(P^{*}\) :

Dimensional pressure (Kg m\(^{-1}\) S\(^{-1}\))

P :

Dimensionless pressure

\(t^{*}\) :

Dimensional time (s)

t :

Dimensionless time

\(\mu \) :

Dynamic viscosity

\(\sigma ^{*}\) :

Stefan–Boltzmann constant (W m\(^{-2}\) K\(^{-4}\))

\(\sigma \) :

Electrical conductivity \((\Omega \hbox {m})^{-1}\)

\(k^{*}\) :

Roseland mean absorption (m\(^{-1}\))

\(B_{0}\) :

Magnetic field

\(q_{r}^*\) :

Radioactive heat flux (W m\(^{-2}\))

\(T_{1},T_{0}\) :

Temperatures at top and bottom walls

\( T_m \) :

Mean temperature

\( D_T, D_B \) :

Diffusive coefficients of thermophoresis and Brownian motion

\( k_1 \) :

First order chemical reaction rate

\( \gamma \) :

Chemical reaction parameter

\(\rho \) :

Density (Kg m\(^{-3}\))

\(C_p\) :

Specific heat (J Kg\(^{-1}\) K\(^{-1}\))

\(\rho C_P\) :

Effective specific heat capacity

K :

Thermal conductivity (W m\(^{-1}\) K\(^{-1}\))

\(\eta \) :

Coefficient of couple stress viscosity

\( \lambda \) :

Couple stress parameter

\( \lambda _{0}\) :

Relaxation time for heat flux

\( \lambda _1 \) :

Thermal relaxation parameter

A :

Known constant

\(\epsilon (<<1)\) :

Positive quantity

\(T^{*}\) :

Temperature of the nanofluid (K)

h :

Distance between the walls (m)

\(\omega \) :

Frequency

H :

Frequency parameter

R :

Cross-flow Reynolds number

H :

Hartmann number

Pr :

Prandtl number

Nt :

Thermophoresis parameter

Nb :

Brownian motion parameter

Le :

Lewis number

Ec :

Eckert number

Rd :

Radiation parameter

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Author notes

  1. S. Rajamani and Rama Subba Reddy Gorla have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    S. Rajamani & A. Subramanyam Reddy

  2. Department of Mathematics, Einstein College of Arts and Science (Affiliated to Manonmaniam Sundaranar University), Seethaparpanallur, Tirunelveli, 627012, India

    S. Rajamani

  3. Department of Aeronautics and Astronautics, Air Force Institute of Technology, Dayton, OH, 45433, USA

    Rama Subba Reddy Gorla

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Correspondence to A. Subramanyam Reddy.

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Rajamani, S., Subramanyam Reddy, A. & Gorla, R.S.R. Numerical Study on Hydromagnetic Oscillating Flow of Couple Stress Nanofluid in a Porous Channel with Cattaneo Christov Heat Flux. Int. J. Appl. Comput. Math 9, 55 (2023). https://doi.org/10.1007/s40819-023-01532-4

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