Importance of heat generation in chemically reactive flow subjected to convectively heated surface

  • W A KhanEmail author
  • H Sun
  • M Shahzad
  • M Ali
  • F Sultan
  • M Irfan
Original Paper


Our main emphasis here is to scrutinize the Lorentz’s force aspects on the flow of cross-fluid in cylindrical surface. More specifically, heat transfer features are examined subject to heat sink–source and radiative flux. Furthermore, aspects of quartic autocatalysis analysis are considered. Non-dimensional variables are introducing to develop the physical model. The physical problem by employing Bvp4c scheme. Influences of rheological parameters for concentration, temperature and velocity are discussed. Additionally, computational analysis for Nusselt number and skin friction coefficient is presented through tables.


Time-dependent cross-fluid flow Thermal radiation Heat generation/absorption parameter Heterogeneous–homogeneous reactions 

List of symbols


Velocity components


Distance along the axial direction


Distance along the radial direction


Local similarity variable

\(b\left( t \right)\)

Radial of cylinder

\(B\left( t \right)\)

Strength of magnetic field


Positive constants


Kinematics viscosity

\(T_{\infty }\)

Ambient fluid temperature


Time material constant


Surface temperature


Fluid density

\(\lambda_{1} > 0\)

Stretching cylinder

\(\lambda_{1} < 0\)

Shrinking cylinder


Power law index


Fluid temperature






Thermal diffusivity

\(D_{\text{A}} ,D_{\text{B}}\)

Diffusion coefficient

\(\left( {\rho c} \right)_{\text{f}}\)

Heat capacity of fluid


Fluid density


Heat generation/absorption parameter

\(U_{\text{w}} \left( {x,t} \right)\)

Stretching velocity

\(U_{\text{e}} \left( {x,t} \right)\)

Free stream velocity


Magnetic field strength


Velocity ratio parameter


Velocity ratio parameter


Local Weissenberg number


Unsteadiness parameter


Heat source–sink parameter


Temperature ratio parameter


Radiation parameter


Prandtl number


Dimensionless suction parameter


Heterogeneous strength of reaction parameter


Strength coefficient of homogenous reaction


Thermal Biot number


Magnetic parameter


Schmidt number


Dimensionless velocities


Dimensionless temperature


Dimensionless concentration


Local Reynolds number


Skin friction


Local Nusselt number


47.10.A− 44.05.+e 44.10.+i 44.05 44.40.+a 



This project was funded by the postdoctoral international exchange program for incoming postdoctoral students, at Beijing Institute of Technology, Beijing, China.

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest.


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Copyright information

© Indian Association for the Cultivation of Science 2020

Authors and Affiliations

  • W A Khan
    • 1
    • 2
    Email author
  • H Sun
    • 1
  • M Shahzad
    • 2
    • 3
  • M Ali
    • 2
    • 3
  • F Sultan
    • 2
    • 3
  • M Irfan
    • 4
  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  2. 2.Department of MathematicsMohi-ud-Din Islamic UniversityNerian SharifPakistan
  3. 3.Department of Mathematics and StatisticsHazara UniversityMansehraPakistan
  4. 4.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan

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