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Hall and Ion Slip Effects on Rotating Casson Nanofluid Flow Past a Deformable Sheet with Multiple Slips and Activation Energy: Modern Impressions of Non-linear Radiation and Convection

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Abstract

The primary aim of the present investigation is to explore the impressions of Hall current and ion slip effects on heat and mass transport phenomena in a rotating and 3-dimensional steady flow of incompressible Casson nanofluid over an exponentially elongating sheet with multiple slip conditions at the surface boundary. Furthermore, quadratically varying heat and mass convections, internal heat source, viscous–Ohmic dissipation, nonlinear thermal radiation and activation energy with binary chemical reaction are also taken into consideration. Such a flow problem has several scientific and engineering applications in polymer processing, bio-sensors, geothermal engineering, thermal energy storage systems, conductive coatings, food processing, space vehicles, high temperature and cooling processes, combustion chambers, etc. Appropriate similarity transformations are introduced to non-dimensionalize the governing model equations and boundary conditions. The converted boundary value problem is then solved numerically using a shooting technique based on Runge–Kutta Cash–Karp method. The velocity, temperature and concentration profiles are drawn to visualize the impacts of several worthy parameters on momentum, thermal and mass distributions. The variations in surface drag force, rates of heat and mass transport at the bounding surface are also illustrated and presented in graphical form. Moreover, a comparative study of numerical data is performed to validate the correctness of the obtained results. The results show that the Hall current and ion slip accelerate the flow momentum. The temperature profile is escalated with respect to the thermal radiation parameter.

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Data Availability

Enquiries about data availability should be directed to the authors.

Abbreviations

\({\tilde{U}},{\tilde{V}},{\tilde{W}}\) :

Velocity components

\({\tilde{X}},{\tilde{Y}},{\tilde{Z}}\) :

Space coordinates

\(K_2\) :

Chemical reaction coefficient

\(E_a\) :

Activation energy

\(c_p\) :

Specific heat at constant pressure

Kr :

Chemical reaction parameter

\(U_{\text {wall}}\),\(V_{\text {wall}}\) :

Stretching velocities

\(k_1\) :

Thermal conductivity

\(Q_1\) :

Heat generation coefficient

\(D_B\) :

Mass diffusivity

Rd :

Thermal radiation parameter

Pr :

Prandtl number

\(\text {g}\) :

Gravitational acceleration

\(E_1\) :

Activation energy parameter

\({\tilde{T}},{\tilde{C}}\) :

Temperature and concentration respectively

Nt :

Thermophoresis parameter

\(Re_{{\tilde{X}}}, Re_{{\tilde{Y}}}\) :

Local Reynolds numbers

Q :

Heat generation parameter

Nb :

Brownian motion parameter

\(N_3,N_4\) :

Velocity slip coefficients

\(d_3,d_4\) :

Thermal and solutal jump coefficients respectively

H :

Magnetic parameter

\(k^*\) :

Boltzmann constant

\({\tilde{T}}_0, {\tilde{C}}_0\) :

Constant temperature and concentration

\({\tilde{U}}_0, {\tilde{V}}_0\) :

Reference velocities

n :

Temperature exponent parameter

K :

Rotation parameter

\(N^*\) :

Ratio of concentration to thermal buoyancy forces

Ec :

Eckert number

A :

Velocity ratio parameter

Sc :

Schmidt number

\(Gr_{{\tilde{x}}}\) :

Thermal Grashof number

\(Gc_{{\tilde{x}}}\) :

Solutal Grashof number

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

Coefficient of thermal diffusion

\(k^*\) :

Mean absorption coefficient

\(\sigma ^*\) :

Stefan–Boltzmann constant

\(\beta \) :

Cassonparameter

\(\Theta \) :

Dimensionless temperature

\(\nu \) :

Kinematic viscosity

\(\Phi \) :

Dimensionless concentration

\(\eta \) :

Similarity variable

\(\mu \) :

Dynamic viscosity

\(\delta _1,\delta _2\) :

Velocity slip parameters

\(\Lambda _1,\Lambda _2\) :

Quadratic convection parameters for temperature and concentration

\(\delta _3, \delta _4\) :

Dimensionless temperature and concentration jump parameters

\(\sigma \) :

Electrical conductivity

\(\Theta _r\) :

Temperature ratio parameter

\(\lambda _1\) :

Mixed convection parameter

\(\left( \rho c_p\right) _f\) :

Heat capacity of base fluid

\(\beta _1, \beta _2\) :

Linear and non-linear concentration expansion coefficients

\(\alpha _1, \alpha _2\) :

Linear and non-linear thermal expansion coefficients

\(\beta _e\) :

Hall current parameter

\(\rho _f\) :

Density of the base fluid

\(\alpha _e\) :

Ion slip parameter

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Acknowledgements

The first author is grateful to the University of Petroleum and Energy Studies, and the second author is grateful to the National Institute of Technology Meghalaya for providing all kinds of research facilities needed to complete this work.

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Authors and Affiliations

  1. Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, 248007, India

    Susmay Nandi

  2. Department of Mathematics, National Institute of Technology Meghalaya, Shillong, 793003, India

    Bidyasagar Kumbhakar

  3. Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India

    Gauri Shanker Seth

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  1. Susmay Nandi
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SN Methodology, software, writing- original draft preparation, data curation and validation BK: Conceptualization, supervision, formal analysis, visualization, investigation GSS: Conceptualization, supervision, data curation.

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Correspondence to Bidyasagar Kumbhakar.

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Nandi, S., Kumbhakar, B. & Seth, G.S. Hall and Ion Slip Effects on Rotating Casson Nanofluid Flow Past a Deformable Sheet with Multiple Slips and Activation Energy: Modern Impressions of Non-linear Radiation and Convection. Int. J. Appl. Comput. Math 10, 65 (2024). https://doi.org/10.1007/s40819-024-01691-y

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