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Numerical analysis of activation energy on MHD nanofluid flow with exponential temperature-dependent viscosity past a porous plate

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Abstract

The current investigation scrutinized the incompressible steady flow with temperature-dependent viscosity of magnetohydrodynamics nanofluid through a vertically stretched porous sheet. The Reynolds exponential model is employed to formulate the mathematical modeling. The momentum equation is further devised utilizing the Darcy–Brinkman–Forchheimer model. Electrically conducting nanofluids encompass uniformly suspended nanoparticles in the viscous base fluid. The Buongiorno model is adopted that aspects the behavior of thermophoretic forces and Brownian motion. The momentum, mass conservative, energy, and nanoparticle concentration equations are defined with magnetic body force. The looming nonlinear coupled differential equations are resolved numerically by employing the spectral local linearization method (SLLM). The SLLM algorithm is straightforward to develop and apply, as it is based on a smooth univariant linearization of nonlinear functions. The numerical performance of SLLM is more impressive as it grows a set of equations; those are successively solved by operating the results from the one equation into the subsequent equation. To accelerate and improve the convergence for the SLLM scheme, the successive over relaxation scheme has been utilized. The accuracy of the SLLM will be confirmed through the known methods, and convergence analysis is also presented. Graphical conduct for all the emerging parameters across temperature, velocity, and concentration distributions, as well as the Nusselt number, skin friction, and Sherwood number, is presented and discussed in detail. A comparative study of the novel proposed technique along with the preceding explored literature is also granted. It is costly to affirm that the spectral local linearization scheme is uncovered to be much stable and adaptable to solve the nonlinear problems.

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Abbreviations

\( B_{0} \) :

Magnetic field

\( U,V \) :

Components of velocity

\( \kappa \) :

Thermal conductivity

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

Thermophoretic coefficient

\( \bar{x},\bar{y} \) :

Cartesian coordinates along the surface

\( S_{\text{c}} \) :

Schmidt number

\( E \) :

Activation energy parameter

\( M \) :

Magnetic field parameter

\( \bar{g} \) :

Gravity

\( T_{\text{w}} \) :

Temperature at the wall

\( T_{\infty } \) :

Ambient temperature

\( \theta \) :

Dimensionless temperature profile

\( \phi \) :

Concentration profile

\( C_{\text{w}} \) :

Concentration at the wall

\( C_{\infty } \) :

Ambient concentration

\( \sigma \) :

Electrical conductivity

\( D_{\text{B}} \) :

Brownian diffusion coefficient

\( f \) :

Dimensionless stream function

\( {\text{Nu}}_{{{\bar{\text{x}}}}} \) :

Nusselt number

\( {\text{Sh}}_{{{\bar{\text{x}}}}} \) :

Sherwood number

\( C_{\text{F}} \) :

Forchheimer coefficient

\( m \) :

Dimensionless exponent

\( \beta_{\text{T}} \) :

Coefficient of thermal expansion

\( \alpha_{0} \) :

Variable viscosity parameter

\( P_{\text{r}} \) :

Prandtl number

\( C \) :

Nanoparticle concentration

\( \beta_{\text{C}} \) :

Coefficient of concentration expansion

\( N_{\text{t}} \) :

Thermophoresis parameter

\( \sigma_{1} \) :

Chemical reaction parameter

\( N_{\text{b}} \) :

Brownian motion parameter

\( B_{\text{r}} ,G_{\text{r}} \) :

Thermal and concentration Grashof numbers

\( \beta_{\text{D}} \) :

Dimensionless permeability parameter

d :

Constant

\( \nu \) :

Kinematic viscosity

ρ :

Density

\( k_{0} \) :

Boltzmann constant

\( \mu_{0} \) :

Viscosity at reference temperature

\( \text{Re}_{{{\bar{\text{x}}}}} \) :

Local Reynolds number

\( q_{w} , q_{m} \) :

Local heat and mass fluxes

\( C_{{{\text{f}}\bar{x}}} \) :

Skin friction coefficient

\( \tau_{\text{w}} \) :

Shear stress

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Authors and Affiliations

  1. College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    A. Shahid & H. L. Huang

  2. Department of Mathematical Sciences, International Institute of Symmetry Analysis and Mathematical Modeling, North West University, Mafikeng Campus, Mmabatho, South Africa

    C. M. Khalique & M. M. Bhatti

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, 266590, People’s Republic of China

    C. M. Khalique & M. M. Bhatti

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  1. A. Shahid
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Correspondence to M. M. Bhatti.

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Shahid, A., Huang, H.L., Khalique, C.M. et al. Numerical analysis of activation energy on MHD nanofluid flow with exponential temperature-dependent viscosity past a porous plate. J Therm Anal Calorim 143, 2585–2596 (2021). https://doi.org/10.1007/s10973-020-10295-9

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