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Heat transfer and flow induced by both natural convection and vibrations inside an open-end vertical channel

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Abstract

The effects of oscillatory motions that may present at a wall during vibrating conditions are studied on flow induced by natural convection and heat transfer inside an open-end vertical channel. The governing equations are non-dimensionalized and reduced to simpler forms. Analytical solutions are obtained for several limiting cases. The reduced governing equations are solved for various values of the controlling parameters. It is found that mean values of average Nusselt numbers are mainly affected by the Grashof number and the amplitude of the horizontal vibrations. Further, amplitudes of Nusselt numbers at the vibrated wall are decreased as the Grashof number increases for horizontal vibrations while they are increased as amplitudes of vibrations increase. It is also found that the squeezing/vibrational Reynolds number, Grashof number and amplitudes of vibrations have a great influence on the trends of stream lines and isotherms especially at low Grashof numbers. Finally, correlations that summarize the effects of the different controlling parameters are determined on the Nusselt numbers and their amplitudes at relatively low frequency of vibrations.

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Abbreviations

B:

height of the vertical channel

cp :

specific heat of the fluid

Gr:

Grashof number

H, h, ho :

dimensionless, dimensional and reference thickness of the channel

hc :

convective heat transfer coefficient

k:

thermal conductivity of the fluid

NuL, NuR :

local Nusselt number at the left and right walls

Pr:

Prandtl number

p:

fluid pressure

RS :

squeezing/vibrational Reynolds number

T, T1, T2 :

temperature in fluid, right and left wall temperatures

t:

time

U, u:

dimensionless and dimensional vertical velocities

V, v:

dimensionless and dimensional horizontal velocities

vo :

reference wall speed

X, x:

dimensionless and dimensional vertical coordinates

Y, y:

dimensionless and dimensional horizontal coordinates

Ω, Ω*:

dimensional and dimensionless vorticity

Ψ, Ψ*:

dimensional and dimensionless stream function

β:

dimensionless squeezing motion amplitude

βo :

thermal expansion coefficient

ɛ:

perturbation parameter

γ:

dimensionless frequency

η:

variable transformation for Y-coordinate

μ:

dynamic viscosity of the fluid

θ:

dimensionless temperature in flow field

θAVG :

dimensionless average temperature at a given X value

ρ:

density of the fluid

τ, τ*:

dimensionless time

υ:

kinematic viscosity

ω:

reference frequency of the vibration

ξ:

variable transformation for the X-coordinate

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Authors and Affiliations

  1. Department of Mechanical Engineering, The Ohio State University, Columbus OSU, Ohio 43210, USA

    A.-R. A. Khaled

  2. Department of Mechanical Engineering, University of California at Riverside UCR, Riverside, CA 92521, USA

    K. Vafai

Authors
  1. A.-R. A. Khaled
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  2. K. Vafai
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Correspondence to K. Vafai.

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Khaled, AR.A., Vafai, K. Heat transfer and flow induced by both natural convection and vibrations inside an open-end vertical channel. Heat and Mass Transfer 40, 325–337 (2004). https://doi.org/10.1007/s00231-002-0401-0

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