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

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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.

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Abbreviations

\(u,v\) :

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

B 0 :

Magnetic field strength

S :

Velocity ratio parameter

λ 1 :

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

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Acknowledgements

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

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Correspondence to W A Khan.

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Cite this article

Khan, W.A., Sun, H., Shahzad, M. et al. Importance of heat generation in chemically reactive flow subjected to convectively heated surface. Indian J Phys (2020). https://doi.org/10.1007/s12648-019-01678-2

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Keywords

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

PACS Nos.

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