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Significances of Darcy–Forchheimer porous medium in third-grade nanofluid flow with entropy features

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Abstract

This work addresses the impact of magnetohydrodynamic Darcy–Forchheimer flow of third-grade nanofluid towards a linearly elastic sheet. Examination has been undertaken in the attendance of velocity slip, Newtonian heating, and non-Fourier heat and mass flux which has not been studied previously. Based on Darcy–Forchheimer model was implemented to illustrate the flow during the porous medium. The entropy minimization of the total system is calculated. Suitable variables are implemented to change the obtained mathematical models into an ODE models. Series solutions are derived by adopting homotopic simulation. After that, the complete investigation of the impact of flow regime on distinct thermofluidic parameters are conferred in the way of graphs and tables. To find the precision of the present solution scheme, a comparison table in limiting conditions is done between the previously available literature and the present results.

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Data Availability Statement

The raw data supporting the finishes of this article will be made accessible by the authors, without unjustifiable reservation.

Abbreviations

a :

Stretching rate \((s^{-1})\)

Be :

Bejan number

Br :

Brinkman number

\(B_{0}\) :

Constant magnetic field \((kgs^{-2}A^{-1})\)

C:

Concentration \((kgm^{-3})\)

\(C_{b}\) :

Drag coefficient

\(C_{p}\) :

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

\(C_{\infty }\) :

Ambient concentration \((kg m^{-3})\)

\(C_{w}\) :

Fluid wall concentration \((kg m^{-3})\)

\(Cf_{x}\) :

Skin friction coefficient

\(D_{B}\) :

Brownian diffusion coefficient \((m^{2}s^{-1})\)

\(D_{T}\) :

Thermophoretic diffusion coefficient \((m^{2}s^{-1})\)

EG :

Entropy generation parameter

\(f(\eta )\) :

Velocity similarity function

\(f_{w}\) :

Suction/injection parameter

Hg:

Heat generation parameter

\(h_{f}\) :

Surface heat transfer coefficient \((W m^{-2}K^{-1})\)

\(\alpha _{1}, \alpha _{2}, \beta \) :

Fluid parameters

k :

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

K:

Porous parameter

L:

Auxiliary linear operator

Le:

Lewis number

M:

Magnetic parameter

N:

Non-linear operator

Nb:

Brownian motion parameter

Nt:

Thermophoresis parameter

Nw:

Dimensionless Newtonian heating parameter

\(Nu_{x}\) :

Nusselt number

Pr:

Prandtl number

\(Q_{0}\) :

Dimensional heat generation/absorption coefficient

q :

Heat flux \((W m^{-2})\)

Rd:

Radiation parameter

Re:

Reynolds number

\(Sh_{x}\) :

Sherwood number

\(S^{'''}_{gen}\) :

Local volumetric entropy generation rate \((W m^{-3}K^{-1})\)

\(S^{'''}_{0}\) :

Characteristic entropy generation rate \((W m^{-3}K^{-1})\)

T :

Temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

\(T_{f}\) :

Convective surface temperature (K)

\(u_{w}\) :

Velocity of the sheet \((m s^{-1})\)

u, v :

Velocity components in (x, y) directions \((m s^{-1})\)

\(v_{w}>0\) :

Suction velocity

\(v_{w}<0\) :

Injection velocity

x, y :

Cartesian coordinates (m)

\(\chi _{m}\) :

Auxiliary parameter

\(\varphi (\eta )\) :

Concentration similarity function

\(\Gamma \) :

Slip parameter

\(\gamma \) :

Dimensionless heat thermal relaxation time

\(\gamma _{c}\) :

Dimensionless mass thermal relaxation time

\(\eta \) :

Similarity parameter

\(\lambda _{T}\) :

Thermal relaxation time

\(\lambda \) :

Dimensionless constant

v :

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

\(\Omega \) :

Dimensionless temperature difference

\(\theta (\eta )\) :

Temperature similarity function

\(\tau \) :

Ratio of the effective heat capacity

\(\rho \) :

Density \((kg m^{-1})\)

\(\sigma \) :

Electrical conductivity (S m)

\(\psi \) :

Stream function \((m s^{-1})\)

\(\zeta \) :

Dimensionless concentration difference

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Acknowledgements

This research was funded by the Deanship of Scientific Research at Princess Nourah Bint Abdulrahman University through the Fast-track Research Funding Program.

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Authors and Affiliations

  1. Department of Mathematics, Erode Arts and Science College, Erode, Tamil Nadu, 638 009, India

    K. Loganathan

  2. Department of Mathematical Sciences, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia

    Nazek Alessa

  3. Department of Mathematics, Government Arts College for Men, Krishnagiri, Tamil Nadu, 635 001, India

    K. Tamilvanan

  4. Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, 13318, Saudi Arabia

    Fehaid Salem Alshammari

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  1. K. Loganathan
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  2. Nazek Alessa
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  4. Fehaid Salem Alshammari
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All authors contributed equally to this work.

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Correspondence to K. Loganathan.

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Loganathan, K., Alessa, N., Tamilvanan, K. et al. Significances of Darcy–Forchheimer porous medium in third-grade nanofluid flow with entropy features. Eur. Phys. J. Spec. Top. 230, 1293–1305 (2021). https://doi.org/10.1140/epjs/s11734-021-00056-6

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