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


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.


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

List of symbols


Axial and radial velocity components


Space coordinates

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

Thermal relaxation and retardation times


Kinematic viscosity


Reference velocity


Characteristic length


Radius of cylinder


Heat flux




Variable thermal conductivity


Thermal conductivity far away from stretched surface


Wall temperature


Ambient temperature


Thermal relaxation time of heat flux

p, cp)

Liquid density and specific heat at constant pressure


Thermal diffusivity

(G, H)

Chemical reactants

(g, h)

Concentration of chemical reactants

(kc, ks)

Rate constants

(DG, DH)

Diffusion of chemical reactants


Uniform concentration


Ratio of diffusion coefficient

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

Stretching velocities


Curvature parameter


Deborah numbers


Thermal conductivity


Prandtl number


Thermal relaxation parameter


Schmidt number


Measures of the strength of homogeneous–heterogeneous


Dimensionless variable


Dimensionless velocity


Dimensionless temperature


Dimensionless concentration



Ordinary differential equations


Partial differential equations



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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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