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Effective cooling of vertical heat-generating stacks in a cavity with openings

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Abstract

Passive (natural convection) and mixed-convection cooling of vertical stacks of heat-generating bodies located inside a cavity with openings for inlet and outlet coolant flow have been investigated numerically. The applicable equations for the conservation of mass, momentum, and energy were applied under laminar, steady-state two-dimensional flow conditions. The solution was obtained using a finite-control-volume approach. Results were obtained for three different stack geometries using different locations of the stack within the cavity and various locations of the inlet and outlet ports. It is demonstrated that passive cooling can be more effective than mixed-convection cooling for certain conditions and that the locations of the inlet and outlet ports relative to the stack position within the cavity have significant influences on the cooling effectiveness for all three geometries.

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Abbreviations

a 1 to a 10 :

geometrical parameters

C p :

specific heat, J/kg·K

g :

gravitational acceleration, m/s2

Gr :

Grashof number defined by Eq. 11c

k :

thermal conductivity, W/m·K

L :

dimension of cavity, m

P :

dimensionless pressure defined by Eq. 11b

p :

pressure, Pa

p * :

dynamic pressure defined by Eq. 6, Pa

Pr :

Prandtl number defined by Eq. 11c

q′′:

heat flux at block walls, W/m2

Re in :

inlet Reynolds number defined by Eq. 11c

T :

temperature, K

U :

dimensionless velocity component in the x direction defined by Eq. 11b

u :

velocity component in the x direction, m/s

V :

dimensionless velocity component in the y direction defined by Eq. 11b

v :

velocity component in the y direction, m/s

V in :

average inlet velocity of air, m/s

x,y :

Cartesian coordinates, m

X,Y :

dimensionless coordinates defined by Eq. 11a

α:

ratio of the total mass flow rate through the channels formed by the blocks in the stack to the inlet mass flow rate

β:

coefficient of thermal expansion, 1/K

μ:

viscosity, N·s/m2

θ:

dimensionless temperature defined by Eq. 11b

ρ:

density, kg/m3

ave:

average

in:

inlet

max:

maximum

out:

outlet

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Acknowledgments

This research has been funded by grants from Manitoba Hydro and the Natural Sciences and Engineering Research Council of Canada. This funding is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, Canada, R3T 5V6

    O. A. Ramirez-Iraheta, H. M. Soliman & S. J. Ormiston

Authors
  1. O. A. Ramirez-Iraheta
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  2. H. M. Soliman
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  3. S. J. Ormiston
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Corresponding author

Correspondence to H. M. Soliman.

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Ramirez-Iraheta, O.A., Soliman, H.M. & Ormiston, S.J. Effective cooling of vertical heat-generating stacks in a cavity with openings. Heat Mass Transfer 42, 398–410 (2006). https://doi.org/10.1007/s00231-005-0030-5

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  • DOI: https://doi.org/10.1007/s00231-005-0030-5

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