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Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk

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A Commentary to to this article was published on 03 January 2017

Abstract

In this paper we have studied the effects of temperature dependent fluid properties such as density, viscosity and thermal conductivity and variable Prandtl number on unsteady convective heat transfer flow over a porous rotating disk. Using similarity transformations we reduce the governing nonlinear partial differential equations for flow and heat transfer into a system of ordinary differential equations which are then solved numerically by applying Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. Comparison with previously published work for steady case of the problem were performed and found to be in very good agreement. The obtained numerical results show that the rate of heat transfer in a fluid of constant properties is higher than in a fluid of variable properties. The results further show that consideration of Prandtl number as constant within the boundary layer for variable fluid properties lead unrealistic results. Therefore, modeling thermal boundary layers with temperature dependent fluid properties Prandtl number must treated as variable inside the boundary layer.

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Abbreviations

a, b :

Constants

Cf :

Skin-friction coefficient

c p :

Specific heat at constant pressure

d :

Constant

F :

Dimensionless radial velocity

G :

Dimensionless tangential velocity

H :

Dimensionless axial velocity

Nu :

Nusselt number

p :

Pressure within the boundary layer

p ∞ :

Pressure of the ambient fluid

Pr:

Variable Prandtl number

Pr∞ :

Ambient Prandtl number

q w :

Surface heat flux

R :

Rotational parameter

Re:

Rotational Reynolds number

r :

Cylindrical radial coordinate

t :

Time

T :

Temperature within the boundary layer

T w :

Temperature at the surface of the disk

T ∞ :

Temperature of the ambient fluid

u, v, w :

Velocities along radial, tangential and axial direction, respectively

w s :

Non-dimensional suction/injection velocity

w w :

Dimensional suction/injection velocity

z :

Cylindrical vertical coordinate

γ :

Relative temperature difference parameter

ρ :

Density of the fluid

ρ ∞ :

Density of the ambient fluid

μ :

Coefficient of dynamic viscosity

μ ∞ :

Dynamic viscosity of the ambient fluid

κ :

Thermal conductivity

κ ∞ :

Thermal conductivity of the ambient fluid

η :

Similarity variable

υ ∞ :

Kinematic viscosity of the ambient fluid

δ :

Time dependent length scale

λ :

Unsteadiness parameter

φ :

Tangential coordinate

τ r :

Radial shear stress

τ t :

Tangential shear stress

θ :

Dimensionless temperature

Ω:

Angular velocity

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Authors and Affiliations

  1. Department of Mathematics, Jagannath University, Dhaka, 1100, Bangladesh

    M. S. Alam & S. M. Chapal Hossain

  2. Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P. C. 123 Al-Khod, Muscat, Sultanate of Oman

    M. M. Rahman

Authors
  1. M. S. Alam
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  2. S. M. Chapal Hossain
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  3. M. M. Rahman
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Correspondence to M. M. Rahman.

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Alam, M.S., Hossain, S.M.C. & Rahman, M.M. Effects of temperature dependent fluid properties and variable Prandtl number on the transient convective flow due to a porous rotating disk. Meccanica 49, 2439–2451 (2014). https://doi.org/10.1007/s11012-014-9995-9

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  • DOI: https://doi.org/10.1007/s11012-014-9995-9

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