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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
  • 8 Downloads

Abstract

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.

Keywords

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

List of symbols

\(u,v\)

Velocity components

\(x\)

Distance along the axial direction

\(r\)

Distance along the radial direction

\(\eta\)

Local similarity variable

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

Radial of cylinder

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

Strength of magnetic field

\(c,b_{0}\)

Positive constants

\(\nu\)

Kinematics viscosity

\(T_{\infty }\)

Ambient fluid temperature

\(\varGamma\)

Time material constant

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

Surface temperature

\(\rho_{\text{f}}\)

Fluid density

\(\lambda_{1} > 0\)

Stretching cylinder

\(\lambda_{1} < 0\)

Shrinking cylinder

\(n\)

Power law index

\(T\)

Fluid temperature

t

Time

\(\sigma^{*}\)

Stefan–Boltzmann

\(\alpha_{\text{m}}\)

Thermal diffusivity

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

Diffusion coefficient

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

Heat capacity of fluid

\(\rho_{\text{f}}\)

Fluid density

\(Q_{0}\)

Heat generation/absorption parameter

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

Stretching velocity

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

Free stream velocity

B0

Magnetic field strength

S

Velocity ratio parameter

λ1

Velocity ratio parameter

We

Local Weissenberg number

A

Unsteadiness parameter

Λ

Heat source–sink parameter

\(\theta_{\text{w}}\)

Temperature ratio parameter

\(N_{\text{R}}\)

Radiation parameter

Pr

Prandtl number

S

Dimensionless suction parameter

\(K_{\text{s}}\)

Heterogeneous strength of reaction parameter

K

Strength coefficient of homogenous reaction

\(\gamma\)

Thermal Biot number

M

Magnetic parameter

Sc

Schmidt number

\(f\)

Dimensionless velocities

\(\theta\)

Dimensionless temperature

\(\phi\)

Dimensionless concentration

Re

Local Reynolds number

\(C_{\text{f}}\)

Skin friction

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

Local Nusselt number

PACS Nos.

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

Notes

Acknowledgements

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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