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Natural convection enhancement by a discrete vibrating plate and a cross-flow opening: a numerical investigation

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Abstract

In this study, a unique combination of a vibrating plate and a cross-flow passage is proposed as a means of enhancing natural convection cooling. The enhancement potential was estimated based on numerical studies involving a representative model which includes a short, transversely oscillating plate, placed over a transverse cross-flow opening in a uniformly heated vertical channel wall dividing two adjacent vertical channels. The resulting velocity and temperature fields are analyzed, with the focus on the local thermal effects near the opening. The simulation indicates up to a 50% enhancement in the local heat transfer coefficient for vibrating plate amplitudes of at least 30% of the mean clearance space and frequencies of over 82 rad/s.

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Abbreviations

A :

Oscillation amplitude Eq. (1), m

b :

Channel width Fig. 1b, m

Fig. 1
figure 1

Combined cross-flow passage-transverse oscillating plate cooling method: (a) model under investigation; (b) geometric specifications. Note gravity is acting in the negative x direction as indicated by the g

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BT :

Board thickness Fig. 1b, m

C :

Instantaneous clearance Fig. 1b, m

CM :

Mean clearance Eq. (1), m

c p :

Specific heat, J/kg K

d :

Nomenclature Eq. (10c)

d os :

Instantaneous displacement of oscillating plate Eq. (1), m

g :

Gravitational acceleration, m/s2

Gr :

Grashof number \( Gr = {{\beta g\Updelta T_{ref} L_{ref}^{3} }/{v^{2} }} \)

h :

Heat transfer coefficient Eq. (15), W/m2 K

HL :

Length of hole or opening Fig. 1b, m

k :

Thermal conductivity, W/m K

L :

Reference length in x direction, m

n :

Normal direction

P D :

Dynamic pressure, Pa

PL :

Length of oscillating plate Fig. 1b, m

Pr :

Prandtl number \( Pr = v/(k/\rho c_{p} ) \)

PT :

Thickness of oscillating plate Fig. 1b, m

q, q a :

Heat flux, applied heat flux Eq. (14), W/m2

t :

Time, s

T :

Temperature, K

TL :

Total channel length Fig. 1b, m

x, y:

Coordinates, m

u, v:

x, y components of velocity, m/s

\( \overrightarrow {V} \) :

Velocity vector, m/s

V :

Nomenclature of Eq. (10c)

V os :

Instantaneous velocity of oscillating plate Eq. (1) m/s

β :

Coefficient of thermal expansion, 1/K

μ :

Absolute viscosity, N s/m2

ν :

Kinematic viscosity, m2/s

ρ :

Density, kg/m3

ω :

Oscillation frequency, rad./s, nomenclature in Eq. (10)

\( \left( {} \right)^* \) :

Dimensionless

\( \overline{{\left( {} \right)}} \) :

Average

\( \overrightarrow {{\left( {} \right)}} \) :

Vector

\( \left( {} \right)_{comp} \) :

x or y component

\( \left( {} \right)_{o} \) :

Related to ambient

\( \left( {} \right)_{os} \) :

Related to oscillating plate

\( \left( {} \right)_{ref} \) :

Reference for non-dimensionalization

\( \left( {} \right)_{s} \) :

Related to solid

\( \nabla \) :

Del operator

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Authors and Affiliations

  1. Department of Mechanical Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA

    L. A. Florio & A. Harnoy

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  1. L. A. Florio
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  2. A. Harnoy
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Correspondence to L. A. Florio.

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Florio, L.A., Harnoy, A. Natural convection enhancement by a discrete vibrating plate and a cross-flow opening: a numerical investigation. Heat Mass Transfer 47, 655–677 (2011). https://doi.org/10.1007/s00231-010-0755-7

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