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Abstract
Analysis of natural convection with heating source protruding from the nonheated lower surface of a rectangular enclosure has been performed using experimental apparatus of a two-dimensional particle image velocimetry system. Results obtained from the experiments are used to validate the numerical simulations. Extensive numerical simulation is carried out using in-house code based on the finite-volume method and the SIMPLE algorithm. Heat transfer and entropy generation are estimated numerically for a protruding heater of different perimeters and aspect ratios, Rayleigh number, and Prandtl number. It is found that the Rayleigh number, Prandtl number, and heater sizes have strong influence on the flow fields, thermal mixing, heat transfer characteristics, and entropy production rate in the enclosure. The analysis indicates that a high thermal mixing may not be the most favorable situation for achieving higher degree of temperature uniformity. The effect of Bejan number is discussed.
NOMENCLATURE
| ARH | = | aspect ratio of heater, (e/w) |
| Be | = | Bejan number, (NScond./NS) |
| CCD | = | charge coupled device (type of camera) |
| Cp | = | specific heat capacity (kJ/kg-K) |
| d | = | location of the heater (m) |
| D | = | dimensionless location of the heater,(d/H) |
| e | = | height of the heater (m) |
| E | = | dimensionless heater height, (e/H) |
| Ec | = | Eckert number, (α2/(H2Cp(TH − TC))) |
| g | = | acceleration due to gravity (m/s2) |
| Ge | = | Gebhart number, (gβL/Cp) |
| H | = | enclosure height (m) |
| k | = | thermal conductivity (W/m-K) |
| L | = | enclosure length (m) |
| N | = | number of nodes |
| Nu | = | local Nusselt number |
| Nuavg | = | average Nusselt number |
| Nul | = | local Nusselt number of left wall of the heater |
| Nur | = | local Nusselt number of right wall of the heater |
| Nut | = | local Nusselt number of top wall of the heater |
| NS | = | dimensionless total entropy generation |
| NScond | = | dimensionless entropy generation due to heat transfer |
| NSloc | = | dimensionless local entropy generation |
| NSvisc | = | dimensionless entropy generation due to viscous effects |
| p | = | pressure (Pa) |
| P | = | dimensionless pressure |
| PIV | = | particle image velocimetry |
| Pr | = | Prandtl number, ( |
| Ra | = | Rayleigh number, ( |
| RMSD | = | root-mean-square deviation |
| S | = | dimensionless heater perimeter, (((2e + w)/H)) |
| T | = | temperature (K) |
| TC | = | cold wall temperature (K) |
| TH | = | hot wall temperature (K) |
| Tref | = | nondimensional reference temperature |
| u, v | = | velocity (m/s) |
| U, V | = | dimensionless velocities |
| x, y | = | Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates |
| w | = | width of the heater (m) |
| W | = | dimensionless width of the heater( = w/H) |
Greek Symbols
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (K−1) |
| ψ | = | dimensionless stream function |
| θ | = | nondimensional temperature |
| θcup | = | nondimensional cup-mixing temperature |
| v | = | kinematic viscosity (m2/s) |
| ρ | = | fluid density (kg/m3) |
Additional information
Notes on contributors
Nirmalendu Biswas
Nirmalendu Biswas is a Ph.D. student in the Department of Mechanical Engineering, Jadavpur University, Kolkata, in India. He received his bachelor's degree in 2004 and master's in mechanical engineering degree in 2008 from Jadavpur University. His research interests include heat transfer, and numerical and experimental analysis of single-phase flow.
Pallab S. Mahapatra
Pallab S. Mahapatra is currently pursuing a Ph.D. in the Mechanical Engineering Department, Jadavpur University, Kolkata, in India. He completed a bachelor's degree in mechanical engineering from Jadavpur University in 2007. His research interests include heat transfer, multiphase flow, spray and atomization, and boiling.
Nirmal K. Manna
Nirmal K. Manna completed his P.h.D (mechanical engineering) from Jadavpur University in 2005, master's (heat power) from Bengal Engineering & Science University in 1996, has 4 years of industrial experience, and has been working as an assistant professor in the Mechanical Engineering Department of Jadavpur University in India since 2007. His research interests are development of CFD code on single- and multiphase flows, biofluid mechanics, free and forced convection, spool valve of HCS, FCI, and premixing.
Prokash C. Roy
Prokash C. Roy graduated from Jadavpur University and did an M.S. degree in mechanical engineering from Indian Institute of Technology Kharagpur. He did a PhD in engineering from Jadavpur University in 2010. Presently he is an assistant professor in the Department of Mechanical Engineering, Jadavpur University, Kolkata, India. Formerly he served as a faculty member of FIEM Kolkata and NIT Silchar, Assam. He has published a good number of research papers in international journals and conference proceedings. He is a life member of the ISHMT.