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Heat and Mass Transfer

, Volume 44, Issue 3, pp 305–314 | Cite as

High power electronic devices cooling at minimum ventilation power

  • Giampietro FabbriEmail author
Original

Abstract

In the present work, the cooling of a high power electronic device is studied. The device is in contact with a heat dissipator crossed by air. The air motion through the dissipator is forced by a fan whose supplied power is to be minimized. A finite element dynamic model of the dissipator is firstly created, taking geometrical and physical properties into account as well as steady state experimental data. A simplified model is then obtained, which reproduces the time pattern of the maximum dissipator temperature as a response of the thermal flux removed from the electronic device and the mass flow rate of the air. Afterwards, the simplified model is utilized to build a control system which allows the electronic device to be correctly cooled at minimum air ventilation power during transition to steady states. Genetic algorithms are used to find the parameters of the finite element model and of the control system. Some functioning conditions of the electronic device are lastly considered and discussed.

Keywords

Mass Flow Rate Time Pattern Corrugate Plate Steady State Temperature Distribution Apparent Thermal Conductivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Aa, Ab, Af

heat transfer matrices for the dissipator lower part in system of Eqs. (6), (7 ), and (8), respectively (W/K)

Am

parameter of the dissipator simplified model (K/W)

Ba, Bb, Bf

heat transfer matrices for the dissipator lower part in system of Eqs. (6), (7), and (8), respectively (W/K)

Bm

parameter of the dissipator simplified model (s/kg)

Ca, Cb, Cf

heat transfer matrices for the fluid in system of Eqs. (6), (7), and (8), respectively (W/K)

cf

specific heat of the fluid (J/K kg)

Cm

parameter of the dissipator simplified model (s)

Cta, Ctb

thermal capacity of a portion of the dissipator upper and lower part (J/K)

CTa, CTb

diagonal matrices containing the thermal capacity of the dissipator upper and lower part elements (J/K)

Ctf

thermal capacity of the fluid in a portion of one channel (J/K)

CTf

diagonal matrix containing the thermal capacity of the fluid elements (J/K)

Da

vector containing the ratio of the heat flux entering in each node

Df

vector containing specific heat of the fluid elements (J/K kg)

Dm

parameter of the dissipator simplified model (s/kg)

ga, gb

thermal conductance between nodes in the dissipator upper and lower part, respectively (W/K)

gc

thermal conductance between nodes in the upper part and nodes in the lower part of the dissipator (W/K)

Im, Id

matrices giving the mean and the difference between the temperature of every two adjacent nodes in the fluid

\({\dot{M}}\)

total air mass flow rate of the fan (kg/s)

\({\dot{M}_{{\rm max}}}\)

maximum total air mass flow rate of the fan (kg/s)

Nc

number of channels

Pc

proportional control parameter (K−1)

Pe

electric power absorbed by the fan (W)

Pf

power transferred from the fan to the fluid (W)

\({\dot{Q}}\)

heat flux generated by the component (W)

\({\dot{Q}_a}\)

heat flux entering a portion of the dissipator upper part (W)

\({\dot{Q}_f}\)

heat flux entering in the channel portion between two subsequent nodes in the fluid (W)

\({\dot{Q}_{{\rm max}}}\)

maximum heat flux generated by the component (W)

ta, tb

temperature of the dissipator upper and lower part (K)

Ta, Tb

vectors containing the temperature of the dissipator upper part nodes (K)

tf

temperature of the fluid (K)

Tf

vector containing the temperature of the fluid nodes (K)

tfa

fan air temperature (K)

tmax

maximum temperature on the surface where the heat generating component is located

tsaf

maximum limit for t max ensuring the safety of the electronic component

UM

ratio between \({\dot{M}}\) and \({\dot{M}_{{\rm max}}}\)

UQ

ratio between \({\dot{Q}}\) and \({\dot{Q}_{{\rm max}}}\)

\({\dot{V}}\)

total air volume flow rate of the fan (m3/s)

Greek symbols

α

ratio between power transferred from the fan to the fluid and the square of the air volume flow rate (W s2/m6)

β

ratio between the ventilation power and the square of the air mass flow rate (W s2/kg2)

Δp

pressure drop in the air before and after crossing the dissipator (Pa)

η

fan effectiveness

θmax

model prediction of t max (K)

Π

normalized ventilation power

ρ

density of the air (kg/m3)

τ

time (s)

Subscripts

i

refers to the considered element or node

j, m, n

refer to elements or nodes adjacent to the considered one

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Energetic, Nuclear, and Environmental Control EngineeringUniversity of BolognaBolognaItaly

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