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Effects of aspect ratio on unsteady solutions through curved duct flow

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Abstract

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ⩽ Gr ⩽ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1 ⩽ γ ⩽ 3. Water is taken as a working fluid (Pr = 7.0). It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.

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Abbreviations

Dn :

Dean number

g :

gravitational acceleration

u :

velocity component in the x-direction

Gr :

Grashof number

v :

velocity component in the y-direction

h :

half height of the cross section

w :

velocity component in the z-direction

d :

half width of the cross section

x :

horizontal axis

L :

radius of the curvature

y :

vertical axis

Pr :

Prandtl number

z :

axis in the main flow direction

t :

time

λ :

resistance coefficient

η :

curvature of the duct

ν :

kinematic viscosity

ρ :

density

κ :

thermal diffusivity

ψ :

sectional stream function

µ:

viscosity

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Authors and Affiliations

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

    R. N. Mondal

  2. Mathematics Discipline, Khulna University, Khulna, 9208, Bangladesh

    S. Islam

  3. Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

    K. Uddin & A. Hossain

Authors
  1. R. N. Mondal
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  2. S. Islam
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  3. K. Uddin
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  4. A. Hossain
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Correspondence to R. N. Mondal.

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Mondal, R.N., Islam, S., Uddin, K. et al. Effects of aspect ratio on unsteady solutions through curved duct flow. Appl. Math. Mech.-Engl. Ed. 34, 1107–1122 (2013). https://doi.org/10.1007/s10483-013-1731-8

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  • DOI: https://doi.org/10.1007/s10483-013-1731-8

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2010 Mathematics Subject Classification

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