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Entropy generation on double-diffusive MHD slip flow of nanofluid over a rotating disk with nonlinear mixed convection and Arrhenius activation energy

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Abstract

The present study deals with the swirling flow problem for the nanoliquid over a radially stretchable rotating disk with the consideration of nonlinear mixed convection and chemical reaction defined by Arrhenius model. The surface of the stretchable rotating disk concedes with the Navier’s velocity slip condition. The temperature jump condition due to imperfect liquid–solid energy interaction is also considered. The flow model is established by incorporating the well-known Buongiorno’s nanofluid model and therefore, Brownian motion and thermophoretic diffusion are incorporated in the mathematical modeling. Heat transport is performed taking into account the heat generation owing to viscous and Joule dissipations and internal energy generation/absorption of the fluid. The coupled nonlinear partial differential equations (PDEs) are converted to the non-dimensional ordinary differential equations (ODEs) through the similarity transformation. These ODEs together with the physical conditions are then solved by the “bvp4c” technique. The impact of present flow characteristics on the entropy generation and Bejan number, flow fields (axial and radial velocities), temperature and concentration profiles are presented graphically. Moreover, the surface drag force, strength of energy and mass transport are calculated and presented in tabular forms. The outcomes show that an increase in magnetic and slip parameter values decrease the fluid velocities (axial and radial). Entropy generation gets improved with the increase in either Brinkman number or magnetic parameter values.

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Abbreviations

\(\omega \) :

Angular velocity

\({{\hat{C}}_{{\hat{W}}}}\) :

Concentration at the disk surface

\({{\hat{C}}_\infty }\) :

Free stream concentration

\({{\mathrm{Re}}^{m}}\) :

Magnetic Reynolds number

\({\hat{U}},\,\,{\hat{V}}\) :

Velocities in \(\left( {r,\,\,\phi } \right) \) directions

g :

Gravitational acceleration

\({\sigma _f}\) :

Electrical conductivity

\({c_p}\) :

Heat capacitance

\(Q'\) :

Heat generation/absorption parameter

s :

Constant of fitted rate

\({D_{{\hat{T}}}}\) :

Thermophoresis diffusion coefficient

\({k_r}\) :

Chemical reaction strength

\(\lambda _1,\,\,\lambda _2\) :

Linear and nonlinear heat expansion parameters

\(\gamma _1,\,\,\gamma _2\) :

Slip coefficient for velocity components \(\left( {{\hat{U}},\,\,{\hat{V}}} \right) \)

\(\varepsilon \) :

Boltzmann constant

b :

Stretching constant

\({l_3}\) :

Thermal slip parameter

M :

Magnetic parameter

Pr:

Prandtl number

\(B_0\) :

Strength of magnetic field

\({{\hat{T}}_{{\hat{W}}}}\) :

Temperature at the disk surface

\({{\hat{T}}_\infty }\) :

Free stream temperature

\({D_m}\) :

Diffusivity of the magnetic field

\({\upsilon _f}\) :

Kinematic viscosity

\({\rho _f}\) :

Density

\({\hat{T}}\) :

Temperature

\({\mu _f}\) :

Dynamic viscosity

\(A_c\) :

Coefficient of activation energy

\({k_f}\) :

Thermal conductivity

\({\hat{C}}\) :

Concentration

\({D_B}\) :

Brownian diffusion coefficient

\(\lambda _3,\,\,\lambda _4\) :

Linear and nonlinear concentration expansion parameters

Ng :

Entropy generation rate

\({\gamma _3}\) :

Thermal slip coefficient

\(l_1,\,\,l_2\) :

Velocity slip parameters

\(\chi \) :

Mixed convection variable

\({B_t}\) :

Nonlinear convection parameters due to temperature

Nt :

Thermophoretic parameter

Q :

Heat generation/absorption parameter

Re:

Reynolds number

Nb:

Brownian motion parameter

\(\delta \) :

Temperature ratio parameter

A :

Activation energy parameter

\({\mathrm{{C}}_f}\) :

Skin friction coefficient

\(S{h_x}\) :

Mass transference rate

\({\Upsilon _w}\) :

Heat flux

\({\tau _w}\) :

Shear stress

\({\alpha _a}\) :

Temperature difference parameter

Ec:

Eckert number

Sc:

Schmidt number

\(K_c\) :

Chemical reaction parameter

\({B_c}\) :

Nonlinear convection parameters due to concentration

N :

Ratio of concentration to temperature buoyancy force

\(N{u_x}\) :

Heat transference rate

L :

Diffusive variable

\({\Upsilon _m}\) :

Mass flux

Br :

Brinkman parameter

\({\alpha _b}\) :

Concentration difference parameter

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Acknowledgements

The first two authors are thankful to the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Govt. of India, for providing the financial support through the research Project with No.: ECR/2017/001754 dated 31-07-2018.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, VPO.- Kamand, Mandi, 175005, India

    Amit Kumar & Rajendra K. Ray

  2. Laboratory on Convective Heat and Mass Transfer, Tomsk State University, Tomsk, Russia, 634050

    Mikhail A. Sheremet

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  1. Amit Kumar
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Correspondence to Rajendra K. Ray.

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Kumar, A., Ray, R.K. & Sheremet, M.A. Entropy generation on double-diffusive MHD slip flow of nanofluid over a rotating disk with nonlinear mixed convection and Arrhenius activation energy. Indian J Phys 96, 525–541 (2022). https://doi.org/10.1007/s12648-021-02015-2

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