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Impact of homogeneous–heterogeneous reactions and non-Fourier heat flux theory in Oldroyd-B fluid with variable conductivity

  • M. IrfanEmail author
  • M. Khan
  • W. A. Khan
Technical Paper
  • 48 Downloads

Abstract

This article scrutinizes the influence of chemical reactions on flow of an Oldroyd-B fluid due to stretched cylinder. In vision of non-Fourier heat flux model, the heat transfer phenomenon is scrutinized. This enhanced constitutive model anticipates the time space upper-convected derivative which is recycled to depicting heat conduction mechanism. Additionally, heat transfer scrutiny is considered with the influence of thermal conductivity which is temperature dependent. Apposite conversions are engaged to acquire ODEs which are then deciphered analytically via homotopic approach. To highlight their physical consequences, the graphical portrayal of diverse considerations on velocity, temperature and concentration fields is depicted and conferred. It is scrutinized from this study that all the profiles are higher in the instance of the cylinder as equated to a flat plate. This scrutiny also reported that the thermal relaxation parameter decreases the temperature field while the Schmidt number and homogeneous response parameter display the conflicting performance on concentration field. In addition, an assessment in restrictive instance is also presented in this exploration, which ensures us that our outcomes are more precise.

Keywords

Oldroyd-B fluid Variable thermal conductivity Non-Fourier heat flux relation Homogeneous–heterogeneous reactions Stretching cylinder 

List of symbols

\((u,\,w)\)

Axial and radial velocity components

\((r,\,z)\)

Space coordinates

\((\lambda_{1} ,\,\lambda_{2} )\)

Thermal relaxation and retardation times

\(\nu\)

Kinematic viscosity

\(U_{0}\)

Reference velocity

\(l\)

Characteristic length

\(R\)

Radius of cylinder

\(q\)

Heat flux

T

Temperature

K(T)

Variable thermal conductivity

k

Thermal conductivity far away from stretched surface

Tw

Wall temperature

T

Ambient temperature

δE

Thermal relaxation time of heat flux

p, cp)

Liquid density and specific heat at constant pressure

α1

Thermal diffusivity

(G, H)

Chemical reactants

(g, h)

Concentration of chemical reactants

(kc, ks)

Rate constants

(DG, DH)

Diffusion of chemical reactants

g0

Uniform concentration

λ*

Ratio of diffusion coefficient

w(z, r),u(z, r)

Stretching velocities

α

Curvature parameter

(β1,β2)

Deborah numbers

ε

Thermal conductivity

Pr

Prandtl number

γ

Thermal relaxation parameter

Sc

Schmidt number

k1,k2

Measures of the strength of homogeneous–heterogeneous

η

Dimensionless variable

f

Dimensionless velocity

θ

Dimensionless temperature

l

Dimensionless concentration

Abbreviations

ODEs

Ordinary differential equations

PDEs

Partial differential equations

Notes

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of MathematicsMohi-Ud-Din Islamic UniversityNerian Sharif Azad Jammu and KashmirPakistan

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