An invariant descriptor for conjugate forced convection-conduction cooling of 3D protruding heaters in channel flow

Thiago ANTONINI ALVES, Paulo H. D. SANTOS, Murilo A. BARBUR

Front. Mech. Eng. ›› 2015, Vol. 10 ›› Issue (3) : 263-276.

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Front. Mech. Eng. ›› 2015, Vol. 10 ›› Issue (3) : 263-276. DOI: 10.1007/s11465-015-0345-y
RESEARCH ARTICLE
RESEARCH ARTICLE

An invariant descriptor for conjugate forced convection-conduction cooling of 3D protruding heaters in channel flow

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Abstract

In this research, the temperatures of three-dimensional (3D) protruding heaters mounted on a conductive substrate in a horizontal rectangular channel with laminar airflow are related to the independent power dissipation in each heater by using a matrix G+ with invariant coefficients, which are dimensionless. These coefficients are defined in this study as the conjugate influence coefficients (g+) caused by the forced convection-conduction nature of the heaters’ cooling process. The temperature increase of each heater in the channel is quantified to clearly identify the contributions attributed to the self-heating and power dissipation in the other heaters (both upstream and downstream). The conjugate coefficients are invariant with the heat generation rate in the array of heaters when assuming a defined geometry, invariable fluid and flow rate, and constant substrate and heater conductivities. The results are numerically obtained by considering three 3D protruding heaters on a two-dimensional (2D) array by ANSYS/FluentTM 15.0 software. The conservation equations are solved by a coupled procedure within a single calculation domain comprising of solid and fluid regions and by considering a steady state laminar airflow with constant properties. Some examples are shown, indicating the effects of substrate thermal conductivity and Reynolds number on conjugate influence coefficients.

Keywords

channel flow / conjugate forced convection-conduction cooling / conjugate influence coefficients / discrete heating / invariant descriptor / thermal management

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Thiago ANTONINI ALVES, Paulo H. D. SANTOS, Murilo A. BARBUR. An invariant descriptor for conjugate forced convection-conduction cooling of 3D protruding heaters in channel flow. Front. Mech. Eng., 2015, 10(3): 263‒276 https://doi.org/10.1007/s11465-015-0345-y

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Acknowledgements

The authors thank the National Council for Scientific and Technological Development (CNPq), a foundation linked to the Ministry of Science and Technology and Innovation (MCTI), and the Federal University of Technology-Paraná (UTFPR) for the financial support.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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