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Abstract
This paper reports the results of numerical and experimental investigations of conjugate mixed convection from a vertical channel with sets of protruding heat sources. The goal of this study is to investigate the possibility of obtaining reasonably accurate results with a simpler or compact thermal model that replaces a set of protruding heat sources with a heat source of appropriate thickness that occupies the whole of the channel wall. Commercially available FLUENT 6.3 was used for the simulations. In order to validate the numerical results, a low-speed vertical wind tunnel has been employed. These are followed by three-dimensional simulations for various heat transfer coefficients on the back side of the printed circuit board (PCB). The differences between the computational fluid dynamics (CFD) predicted and experimentally measured temperatures were minimized using least squares and the optimum value of heat transfer coefficient was obtained for use in the simple model. The effect of Reynolds number on heat transfer has been analyzed for both the full CFD and simpler thermal models. The variation of error in the maximum temperature between the full CFD model and the simpler thermal model under different conditions, as the number of chips changes from three to eight, is studied.
NOMENCLATURE
| a | = | absorption coefficient, m−1 |
| A | = | area of heat source, m2 |
| b | = | thickness of the substrate, m |
| B | = | distance between edge of substrate and nearest chip edge, m |
| c | = | thickness of cork, m |
| CFD | = | computational fluid dynamics |
| D | = | thickness of heat source, m |
| DC | = | direct current |
| DO | = | discrete ordinates method |
| d | = | thickness of simpler thermal model, m |
| g | = | acceleration due to gravity, m s−2 |
| Gr | = | Grashof number |
| h | = | heat transfer coefficient, W m−2 K−1 |
| H | = | height of the duct/channel, m |
| I | = | total radiation intensity, W m−2 |
| IC | = | integrated circuit |
| J | = | height of the heat source, m |
| k | = | thermal conductivity, W m−1 K−1 |
| L | = | spacing between the walls of the channel, m |
| N | = | number of chips |
| n | = | refractive index |
| p | = | pressure, N m−2 |
| PCB | = | printed circuit board |
| q | = | power supply, W |
| Q | = | volumetric heat generation, W m−3 |
| r | = | position vector |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| RPM | = | revolutions per minute |
| RTE | = | radiative transfer equation |
| s | = | direction vector |
| S | = | some of residues, K2 |
| t | = | heat source thickness, m |
| T | = | temperature, K |
| ΔT | = | temperature difference, K |
| U | = | velocity in Y direction, m s−1 |
| V | = | velocity in X direction, m s−1 |
| v | = | volume, m3 |
| W | = | velocity in Z direction, m s−1 |
| w | = | thickness of wood, m |
| X | = | x direction coordinate |
| Y | = | y direction coordinate |
| Z | = | z direction coordinate |
Greek Symbols
| α | = | thermal diffusivity of the fluid, m2 s−1 |
| β | = | coefficient of expansion, K−1 |
| γ | = | kinematic viscosity of the fluid, m2 s−1 |
| ρ | = | density, kg m−3 |
| σ | = | Stefan–Boltzmann constant, 5.67 × 10−8 W m−2 K−4 |
| ∞ | = | ambient |
| Δ | = | difference in value |
Subscripts
| CFD | = | temperature value corresponding to FLUENT |
| equi | = | equivalent model data |
| EXPT | = | experimental temperature value |
| g | = | generation |
| max | = | maximum value |
| s | = | solid |
Additional information
Notes on contributors
Shaik Imran Ahamad
Shaik Imran Ahamad is a assistant manager in an automobile air-conditioning manufacturing company in Chennai. He obtained his B.E. degree in mechanical engineering from VITS college and he completed his M.S. degree (2012) at Indian Institute of Technology Madras, Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Chennai, India, under the supervision of Prof C. Balaji. His research interests include experimental and numerical studies on conjugate mixed convection from protruding heat sources, artificial neural networks, inverse methods, and CFD simulations.
C. Balaji
C. Balaji is a professor in the Department of Mechanical Engineering at the Indian Institute of Technology (IIT) Madras. He graduated in mechanical engineering from Guindy Engineering College, Chennai (1990), and obtained his M.Tech. (1992) and Ph.D. (1995) both from IIT Madras. His research interests include computational and experimental heat transfer, optimization in thermal sciences, inverse heat transfer, satellite meteorology, and numerical weather prediction.