Natural convection arising from a heat generating substrate-mounted protrusion in a liquid-filled two-dimensional enclosure

doi:10.1016/0017-9310(91)90224-3

International Journal of Heat and Mass Transfer

Volume 34, Issue 8, August 1991, Pages 2149-2163

https://doi.org/10.1016/0017-9310(91)90224-3 Get rights and content

Abstract

An investigation of natural convection flow and heat transfer arising from a substrate-mounted protruding heat source immersed in a liquid-filled square enclosure is reported. The model considers heat transfer within the protrusion and substrate and the coupled natural convection in the fluid. Numerical predictions are obtained for a wide range of appropriate Rayleigh and Prandtl numbers and substrate to fluid thermal conductivity ratios that may be encountered in liquid-immersion cooling of electronic components. For many situations of interest prescribing simplistic heat transfer conditions at the solid surfaces is found inappropriate. Increasing the Rayleigh number beyond 10⁶ and the substrate thermal conductivity beyond 100 times that of the liquid produces only a marginal decrease in the maximum temperatures. Computed protrusion surface temperatures compare favorably with available experimental results for a similar configuration.

Résumé

On étudie l'écoulement et le transfert thermique de convection naturelle autour d'une source de chaleur protubérante montée sur substrat et immergée dans un liquide à l'intérieur d'une cavité. Le modèle considère le transfert thermique dans la protubérance et le substrat ainsi que la convection naturelle couplée dans le fluide. Des prédictions numériques sont obtenues pour un large domaine de nombres de Rayleigh et de Prandtl et de rapports des conductivités thermiques du substrat et du fluide qui peuvent être rencontrés dans le refroidissement par immersion des composants électroniques. Beaucoup de situations réelles prescrites par des conditions thermiques simplistes à la surface solide sont trouvées inappropriées. L'accroissement du nombre de Rayleigh au delà de 10⁶ et de la conductivité thermique du substrat au delà de 100 fois celle du liquide produit seulement une décroissance marginale des températures maximales. Les températures calculées de la surface de la protubérance se comparent favorablement aux valeurs expérimentales pour une configuration semblable.

Zusammenfassung

Strömung und Wärmeübergang bei natürlicher Konvektion an einem wärmeerzeugenden Vorsprung in einem flüssigkeitsgefüllten quadratischen Hohlraum werden untersucht. Das Modell berücksichtigt den Wärmetransport innerhalb des Vorsprungs und des darunterliegenden Substrats sowie bei der gekoppelten natürlichen Konvektion im Fluid. Für einen weiten Bereich von Rayleigh- und Prandtl-Zahlen sowie von Verhältnissen der Wärmeleitfähigkeit des Substrats zu derjenigen der Flüssigkeit—wie sie zum Beispiel bei Flüssigkeitskühlung elektronischer Bauelemente vorkommen—werden numerische Berechnungen ausgeführt. Für viele praktisch interessierende Situationen ist die Annahme der üblichen einfachen Randbedingungen für den Wärmeübergang an festen Oberflächen ungenügend. Eine Vergrößerung der Rayleigh-Zahl über 10⁶ und der Wärmeleitfähigkeit des Substrats über das Hundertfache der Flüssigkeit führt nur zu einer geringfügigen Verringerung der maximalen Temperaturen. Die berechneten Temperaturen des Vorsprungs stimmen recht gut mit verfügbaren Versuchsergebnissen für ähnliche Konfigurationen überein.

Реферат

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References (20)

E. Baker
Liquid cooling of microelectronic devices by free and forced convection
Microelectron. Reliability
(1972)
E. Baker
Liquid immersion cooling of small electronic devices
Microelectron. Reliability
(1973)
J.J. Lee et al.
Laminar natural convection in a rectangular enclosure due to a heated protrusion on one vertical wall—Part II: numerical simulation
Y. Jaluria et al.
Buoyancy-induced flow arising from a line thermal source on an adiabatic vertical surface
Int. J. Heat Mass Transfer
(1977)
R.C. Chu
Heal transfer in electronic systems
W. Nakayama
Thermal management of electronic equipment: a review of technology and research topics
F.P. Incropera
Convection heat transfer in electronic equipment cooling
ASME J. Heat Transfer
(1988)
Y. Jaluria
Interaction of natural convection wakes arising from thermal sources on a vertical surface
ASME J. Heat Transfer
(1985)
S. Lee et al.
Conjugate heat transfer from a vertical plate with discrete heat sources under natural convection
ASME Paper No. 89-WA/EEP-9
(1989)
M. Afrid et al.
Natural convection air cooling of heated components mounted on a vertical wall
Numer. Heat Transfer
(1989)

There are more references available in the full text version of this article.

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The maximum relative temperature drop in the optimum configuration can be as much as 20 percent of the equi-spaced arrangement. Sathe and Joshi [11,12] numerically investigated the coupled conduction and natural convection transport from a substrate-mounted heat generating protrusion in a liquid-filled square enclosure. The effects of different thermal boundary conditions at the enclosure walls on the transfer characteristics were examined.
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Natural convection in porous triangular enclosure with a centered conducting body
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All of these were given in literature on porous media [1–4]. Natural convection in a triangular shaped enclosure was mostly studied for a pure fluid filled enclosure due to its wide application for roof-building, electronic equipment and some solar applications [5–9]. Porous media filled attic shaped building was firstly proposed by Poulikakos and Bejan [10].
A numerical work was performed to examine the heat transfer and fluid flow due to natural convection in a porous triangular enclosure with a centered conducting body. The center of the body was located onto the gravity center of the right-angle triangular cavity. The Darcy law model was used to write the governing equations and they were solved using a finite difference method. Results are presented by streamlines, isotherms, mean and local Nusselt numbers for the different parameters such as the Rayleigh number, thermal conductivity ratio, and height and width of the body. It was observed that both height and width of the body and thermal conductivity ratio play an important role on heat and fluid flow inside the cavity.
Natural convective characteristics of a heat source module at different angles in the closed and ventilated cabinets
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The maximum relative temperature drop in the optimum configuration can be as much as 20% of the equi-spaced arrangement. Sathe and Joshi [9,10] numerically investigated the coupled conduction and natural convection transport from a substrate-mounted heat-generating protrusion in a liquid-filled square enclosure. The effects of different thermal boundary conditions at the enclosure walls on the transfer characteristics were examined.
A numerical analysis is performed to study the characteristics of heat transfer from a block heat source module at different angles in two-dimensional cabinets. Great efforts are carried out to conduct the effects of thermal interaction between the air steams inside and outside the cabinet on the conjugate conduction–natural convection phenomena. Moreover, the enhancement of cooling performance of the heat source module through the construction of air vents on cabinet wall is rigorously examined. The computation domain covers the cabinet and the surrounding area, and the temperature and velocity fields of the cabinet and surrounding area are solved simultaneously. Comparing the results for cases with and without the consideration of thermal interaction between the air streams, the difference in hot spot temperature of module can be up to 26% for Pr = 0.7, K_bf = K_wf = 100, 0 ≦ K_pf ≦ 100, 10⁵ ≦ Ra ≦ 10⁷ and φ = 0°, 90°, 270°. The maximum reduction in hot spot temperature is about 41% when two air vents are constructed on the cabinet wall. The variation of module angle results in the maximum difference of the hot spot temperature is 17% for closed cabinet, and 10% for ventilated cabinet. In addition, the hot spot temperatures for cases with K_pf = 10 are about two times of that for K_pf = 100.
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The present work is concerned with computation of natural convection flow in a square enclosure with a centered internal conducting square block both of which are given an inclination angle. Finite volume method through the concepts of staggered grid and SIMPLE algorithm have been applied. Deferred QUICK scheme has been used to discretize the convective fluxes and central difference for diffusive fluxes. The problem of conjugate natural convection has been taken up for validating the code. The abrupt variation in the properties at the solid/fluid interface are taken care of with the harmonic mean formulation. Solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been performed for Ra = 10³–10⁶, angle of inclination varying from 15° to 90° in steps of 15° and ratio of solid to fluid thermal conductivities of 0.2 and 5.0. Results are presented in terms of streamlines, isotherms, local and average Nusselt number.
Internal heat generation in a discrete heat source: Conjugate heat transfer analysis
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In the present work, we conduct an asymptotic and numerical analysis for the cooling process of a discrete heat source, which is placed in a rectangular-channel laminar cooling flow. In our physical model, the heated strip is embedded in a substrate, generating continuously a uniform volumetric heat rate. We assume that this heat-generation mechanism is due to an electrical current in the heat source. Hence, heat losses to the cooling fluid and to the substrate material during this process are presented. The governing equations of the cooling flow and the participating solid are reduced to an integro-differential equation that predicts the temperature variations of the heat source. We show that the conjugate heat transfer process is controlled by a conjugate nondimensional parameter, here denoted by α, which determines the basic heat transfer regimes between the cooling flow and the discrete heat source.
Natural convection heat transfer in a enclosure with a heated backward step
2001, International Journal of Heat and Mass Transfer
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Abstract

Résumé

Zusammenfassung

Реферат

Microelectron. Reliability

Microelectron. Reliability

Int. J. Heat Mass Transfer

Heal transfer in electronic systems

Thermal management of electronic equipment: a review of technology and research topics

Convection heat transfer in electronic equipment cooling

ASME J. Heat Transfer

Interaction of natural convection wakes arising from thermal sources on a vertical surface

ASME J. Heat Transfer

Conjugate heat transfer from a vertical plate with discrete heat sources under natural convection

ASME Paper No. 89-WA/EEP-9

Natural convection air cooling of heated components mounted on a vertical wall

Numer. Heat Transfer