Bivariate Spectral Local Linearisation Method (BSLLM) for Unsteady MHD Micropolar-Nanofluids with Homogeneous–Heterogeneous Chemical Reactions Over a Stretching Surface

  • Hloniphile Sithole
  • Hiranmoy MondalEmail author
  • Vusi Mpendulo Magagula
  • Precious Sibanda
  • S. Motsa
Original Paper


A mathematical model of MHD micropolar-nanofluid flow deformed by a stretchable surface is presented with a homogeneous–heterogeneous reactions given by isothermal cubic autocatalator kinetics and first order kinetics. We assumed the existence of an induced magnetic field. The basic microrotation flow and heat mass transfer nonlinear equations are solved using the bivariate spectral local linearisation method. An analysis of the accuracy of the method is given using residual errors, and the influence of certain variables on the fluid properties are discussed. The results show, that the concentration distribution is reduced by an increase in the homogeneous reaction parameter while it increases with the Schmidt number. The rate of heat transfer is enhanced by larger values of the Prandtl number and the thermophoresis parameter.


Nanofluids Homogeneous–heterogeneous reactions Micropolar fluid Thermophoresis Brownian motion 

List of Symbols

\(C_a, C_b\)

Concentration of homogeneous–heterogeneous reactions species

\(C_{fx }\), \(Nu_{x}\), \(Sh_{x}\)

Local skin friction, Nusselt and Sherwood number

\(C_{\infty }\)

Species concentration far away from the wall

\(T_{\infty }\)

Temperature of the fluid far away from the wall


Specific heat at constant pressure


Mass diffusivity


Dimensionless stream function


Hartmann number


Material parameter


Heterogeneous reaction parameter


Thermal conductivity of the fluid


Angular velocity


Heat generation coefficient


Prandtl number


Brownian diffusion coefficient


Thermophoretic diffusion coefficient


Brownian motion parameter


Thermophoresis parameter


Scidth number


Velocity component

Greek Symbols

\(\psi \)

Stream function

\(\lambda \)

Homogeneous reaction rate parameter

\(\rho \)

Density of the fluid

\(\mu \)

Dynamic viscosity of the fluid

\(\nu \)

Kinematic viscosity

\(\xi , \eta \)

Transformed variables

\(\epsilon \)

Ratio of the diffusion coefficient







Conditions at the wall

\(\infty \)

Free stream condition



This work was supported by a Claude Leon Foundation Postdoctoral Fellowship, and the University of KwaZulu-Natal, South Africa.

Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interests regarding the publication of this article.


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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  • Hloniphile Sithole
    • 1
  • Hiranmoy Mondal
    • 1
    Email author
  • Vusi Mpendulo Magagula
    • 2
  • Precious Sibanda
    • 1
  • S. Motsa
    • 1
    • 2
  1. 1.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalPietermaritzburgSouth Africa
  2. 2.Department of Mathematics, Faculty of Science and EngineeringUniversity of SwazilandMatsaphaSwaziland

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