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Thermal analysis of a reactive generalized Couette flow of power law fluids between concentric cylindrical pipes

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Abstract

In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton’s law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.

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Abbreviations

A :

Rate constant

B :

Planck’s number

Bi :

Biot number

Br :

Brinkmann number

C 0 :

Concentration of the reactant

E :

Activation energy

k :

Thermal conductivity

h :

Heat transfer coefficient

l :

Boltzmann’s constant

P :

Pressure

Q :

Heat of reaction

R :

Universal gas constant

r :

Radial distance

r 0 :

Inner pipe radius

r 1 :

Outer pipe radius

m :

Reaction exponent

n :

Power law index

Nu :

Nusselt number

T 0 :

Inner pipe temperature

T :

Absolute temperature

T a :

Ambient temperature

u :

Velocity component

U :

Inner pipe axial velocity

w :

Dimensionless velocity

z :

Axial distance

λ :

Frank-Kamenetskii

λ c :

Critical parameter

ε :

Activation energy parameter

γ :

Flow consistency index

ν :

Vibration frequency

δ :

Annulus parameter

Ψ :

Pressure gradient parameter

θ :

Dimensionless temperature

α :

Inner pipe temperature parameter

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Authors and Affiliations

  1. Faculty of Military Science, Stellenbosch University, Private Bag X2, 7395, Saldanha, South Africa

    O. D. Makinde

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  1. O. D. Makinde
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Correspondence to O. D. Makinde.

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Makinde, O.D. Thermal analysis of a reactive generalized Couette flow of power law fluids between concentric cylindrical pipes. Eur. Phys. J. Plus 129, 270 (2014). https://doi.org/10.1140/epjp/i2014-14270-4

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  • DOI: https://doi.org/10.1140/epjp/i2014-14270-4

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