# High power electronic devices cooling at minimum ventilation power

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## 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## List of symbols

*A*_{a},*A*_{b},*A*_{f}*heat transfer matrices for the dissipator lower part in system of Eqs.*(6), (7*), and*(8)*, respectively (W/K)**A*_{m}parameter of the dissipator simplified model (K/W)

*B*_{a},*B*_{b},*B*_{f}*heat transfer matrices for the dissipator lower part in system of Eqs.*(6), (7)*, and*(8)*, respectively (W/K)**B*_{m}parameter of the dissipator simplified model (s/kg)

*C*_{a},*C*_{b},*C*_{f}*heat transfer matrices for the fluid in system of Eqs.*(6), (7)*, and*(8)*, respectively (W/K)**c*_{f}specific heat of the fluid (J/K kg)

*C*_{m}parameter of the dissipator simplified model (s)

*C*_{ta},*C*_{tb}thermal capacity of a portion of the dissipator upper and lower part (J/K)

*C*_{Ta},*C*_{Tb}diagonal matrices containing the thermal capacity of the dissipator upper and lower part elements (J/K)

*C*_{tf}thermal capacity of the fluid in a portion of one channel (J/K)

*C*_{Tf}diagonal matrix containing the thermal capacity of the fluid elements (J/K)

*D*_{a}*vector containing the ratio of the heat flux entering in each node**D*_{f}*vector containing specific heat of the fluid elements (J/K kg)**D*_{m}parameter of the dissipator simplified model (s/kg)

*g*_{a},*g*_{b}*thermal conductance between nodes in the dissipator upper and lower part, respectively (W/K)**g*_{c}*thermal conductance between nodes in the upper part and nodes in the lower part of the dissipator (W/K)**I*_{m},*I*_{d}*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)

*N*_{c}number of channels

*P*_{c}proportional control parameter (K

^{−1})*P*_{e}electric power absorbed by the fan (W)

*P*_{f}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)

*t*_{a},*t*_{b}temperature of the dissipator upper and lower part (K)

*T*_{a},*T*_{b}vectors containing the temperature of the dissipator upper part nodes (K)

*t*_{f}temperature of the fluid (K)

*T*_{f}vector containing the temperature of the fluid nodes (K)

*t*_{fa}fan air temperature (K)

*t*_{max}maximum temperature on the surface where the heat generating component is located

*t*_{saf}maximum limit for

*t*_{max}ensuring the safety of the electronic component*U*_{M}ratio between \({\dot{M}}\) and \({\dot{M}_{{\rm max}}}\)

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

- \({\dot{V}}\)
total air volume flow rate of the fan (m

^{3}/s)

## Greek symbols

- α
*ratio between power transferred from the fan to the fluid and the square of the air volume flow rate*(W s^{2}/m^{6})- β
*ratio between the ventilation power and the square of the air mass flow rate*(W s^{2}/kg^{2})- Δ
*p* pressure drop in the air before and after crossing the dissipator (Pa)

- η
fan effectiveness

- θ
_{max} model prediction of

*t*_{max}(K)- Π
normalized ventilation power

- ρ
density of the air (kg/m

^{3})- 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*

## References

- 1.Bagley JD (1967) The behavior of adaptive systems which employ genetic and correlation algorithms. In: Dissertation Abstracts International 28Google Scholar
- 2.Bar-Cohen V (1987) Thermal management of air and liquid cooled multichip modules. IEEE Trans Compon Hybrid Manuf Technol 2:159–75CrossRefGoogle Scholar
- 3.Bar-Cohen A, Kraus AD (1990) Advances in thermal modeling of electronic components and systems, vol 2. ASME Press Series, New York, pp 41–107Google Scholar
- 4.Cesini G, Ricci R, Ruggeri B (1992) Ottimizzazione di dissipatori di calore alettati per applicazioni elettroniche. Modello numerico e verifica sperimentale. In: Proceedings of the 10th UIT National Congress, pp 201–212Google Scholar
- 5.Fabbri G (1998) Heat transfer optimization in internally finned tubes under laminar flow conditions. Int J Heat Mass Transf 41:1243–1253zbMATHCrossRefGoogle Scholar
- 6.Fabbri G (1999) Optimum profiles for asymmetrical longitudinal fins in cylindrical ducts. Int J Heat Mass Transf 42:511–523zbMATHCrossRefGoogle Scholar
- 7.Fabbri G (2000) Heat transfer optimization in corrugated wall channels. Int J Heat Mass Transf 43:4299–4310zbMATHCrossRefGoogle Scholar
- 8.Fabbri G, Lorenzini M, Salvigni S (2004) A study on industrial heat sinks for power electronics. In: Proceedings of the 22nd UIT National Congress, pp 201–212Google Scholar
- 9.Jeevan K, Quadir GA, Seetharamu KN, Azid IA (2005) Thermal management of multi-chip module and printed circuit board using FEM and genetic algorithms. Microelectron Int 22:3–15CrossRefGoogle Scholar
- 10.Kandasamy R, Subramanyam S (2005) Application of computational fluid dynamics simulation tools for thermal characterization of electronic packages. Int J Numer Methods Heat Fluid Flow 15:61–72zbMATHCrossRefGoogle Scholar
- 11.Ong KE, Lee KO, Seetharamu KN, Azid IA, Quadir GA, Zainal ZA, Goh TJ (2005) Optimization of fins used in electronic packaging. Microelectron Int 22:10–15CrossRefGoogle Scholar
- 12.Parker J, Boggs J, Blick E (1969) Introduction to fluid mechanics and heat transfer, chap 4. Addison–Wesley, ReadingGoogle Scholar
- 13.Queipo N, Devarakonda R, Humphrey JAC (1994) Genetic algorithms for thermosciences research: application to the optimized cooling of electronic components. Int J Heat Mass Transf 37:893–908CrossRefGoogle Scholar
- 14.Shah RK, Bhatti MS (1987) Laminar convective heat transfer in ducts. In: Kakac S, Shah RK, Aung W (eds) Handbook of single-phase convective heat transfer. Wiley, New York, pp 3–12Google Scholar
- 15.Shah RK, London AL (1974) Thermal Boundary Conditions for Laminar Duct Flow Forced Convection. ASME J Heat Transf 96:159–165Google Scholar
- 16.Yeo MF, Agyei EO (1998) Optimising engineering problems using genetic algorithms. Eng Comput 15:268–280zbMATHCrossRefGoogle Scholar