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Abstract
Experiments were performed to investigate the conjugate forced convection–conduction cooling of a protruding heater mounted on the lower wall (substrate plate) of a rectangular duct. The heater was an aluminum rectangular block heated by means of electric power dissipation in an embedded resistance. Airflow was forced in the duct with a hydraulic diameter Reynolds number in the range from 2,000 to 6,000. Effects of the substrate plate thermal conductivity on the heater conjugate cooling were obtained from measurements with two distinct substrates: a Plexiglas plate and an aluminum plate. The experimental results for the heater conjugate cooling were described by a single dimensionless conjugate coefficient expressed as a function of the Reynolds number. The results also indicated that the conjugate coefficient is invariant with the heater power dissipation. In addition, the heater direct convective loss to the airflow was also evaluated and described by another invariant descriptor, the adiabatic Nusselt number, as a function of the duct Reynolds number.
NOMENCLATURE
| A | = | area, m2 |
| cp | = | constant pressure specific heat, J/kg-K |
| g+ij | = | dimensionless conjugate coefficient |
| g+11 | = | conjugate coefficient of the single heater |
| H | = | height, m |
| had | = | adiabatic heat transfer coefficient, W/m2-K |
| k | = | thermal conductivity, W/m-K |
| L | = | length, m |
| = | mass flow rate, kg/s | |
| Nuad | = | adiabatic Nusselt number |
| pw | = | duct cross section perimeter, m |
| qcav | = | cavity losses, W |
| qcc | = | conduction losses, W |
| qcj | = | conjugate heat transfer rate, W |
| qcv | = | convective heat transfer rate, W |
| qdp | = | electric power dissipation, W |
| qp | = | power wires losses, W |
| qrd | = | radiation losses, W |
| qsl | = | silicone film losses, W |
| qt | = | thermocouples losses, W |
| qti | = | thermal insulation losses, W |
| qw | = | wires losses, W |
| ReD | = | duct flow Reynolds number |
| T | = | temperature, °C |
Greek Symbols
| ϵ | = | heater emissivity |
| ϵsb | = | substrate emissivity |
| μ | = | air dynamic viscosity, N-s/m2 |
| σ | = | Stefan-Boltzmann constant, W/m2-K4 |
Subscripts
| 0 | = | referring to the duct flow inlet |
| a | = | alumel |
| ad | = | adiabatic |
| air | = | air |
| c | = | chromel |
| cav | = | cavity |
| cu | = | cupper |
| ex | = | external |
| h | = | heater |
| s | = | heater surface |
| sb | = | substrate |
| sl | = | silicone film |
| ti | = | thermal insulation |
| w | = | wires |
Additional information
Notes on contributors
Bruna R. Loiola
Bruna R. Loiola received her B.Sc. degree in mechanical engineering in 2012 from the State University of Campinas, Brazil and also from the Ecole des Arts et Métiers ParisTech, France. She received her M.Sc. in mechanical engineering with emphasis in thermal and fluids engineering from the State University of Campinas in 2013. The focus of her research was the conjugate cooling of protruding heaters in a rectangular duct. She is currently a doctoral student at the Federal University of Rio de Janeiro (UFRJ).
Carlos A. C. Altemani
Carlos A. C. Altemani is a professor of mechanical engineering (Energy Department) at the State University of Campinas (UNICAMP), Brazil. He received his PhD in 1980 from the University of Minnesota. His main research interests are in convective heat transfer, including the thermal cooling of electronics, heat exchangers, and the numerical simulation of fluid flow and heat transfer. He is a senior member of the Brazilian Society of Mechanical Sciences and Engineering (ABCM).