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Applied Mathematics and Mechanics

, Volume 31, Issue 5, pp 557–564 | Cite as

Transient free convection flow of a viscoelastic fluid over vertical surface

  • H. M. DuwairiEmail author
  • R. A. Damseh
  • A. J. Chamkha
  • M. S. Abdel-Jaber
Article

Abstract

In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The governing equations are formulated and solved numerically using MackCormak’s technique. The results show excellent agreement with previously published results by a comparision. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.

Key words

viscoelastic flows transient free convection heat transfer 

Nomenclature

A1, A2

first two Rivlin-Ericksen tensors

Cf

local coefficient of friction

Cp

specific heat of the fluid at a constant pressure

g

acceleration magnitude for gravity

Gr

Grashof number, \( \frac{{g\beta (T_w - T_\infty )L^3 }} {{v^2 }} \)

h

heat transfer coefficient

k

thermal conductivity

k0

elastic parameter

kl*

dimensionless viscoelsatic parameter, \( \frac{{k_0 Gr^{\frac{1} {2}} }} {{L^2 }}; \)

L

characteristic length of plate

Nux

local Nusselt number

PI

spherical stress

Pr

Prandtl number, \( \frac{v} {\alpha } \);

τ

dimensionless time

T

temperature

Tw

wall temperature

T

ambient fluid temperature

u, υ

dimensionless velocities along the x-and y-axes, respectively

x, y

dimensionless coordinates

α

thermal diffusivity

α1, α2

material moduli

β

coefficient of thermal expansion

Θ

non-dimensional temperature

µ

dynamic viscosity

υ

kinematic viscosity

ρ

fluid density

Γ

Cauchy stress tensor

w

wallsurface

free stream condition

dimensional variables

Chinese Library Classification

O357 

2000 Mathematics Subject Classification

75A10 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • H. M. Duwairi
    • 1
    Email author
  • R. A. Damseh
    • 2
  • A. J. Chamkha
    • 3
  • M. S. Abdel-Jaber
    • 4
  1. 1.Mechanical Engineering Department, Faculty of Engineering and TechnologyThe University of JordanAmmanJordan
  2. 2.Mechanical Department, Al-Husun University CollegeAlbalqa Applied UniversityIrbidJordan
  3. 3.Manufacturing Engineering DepartmentThe Public Authority for Applied Education and TrainingShuweikhKuwait
  4. 4.Civil Engineering Department, Faculty of Engineering and TechnologyThe University of JordanAmmanJordan

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