![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
Micro-scale cooling is an efficient and effective cooling technique to achieve the goal of higher heat removal capabilities. The present research focuses to find the physical effects of fluid property variations on flow and thermal development in micro-channel. The effects of temperature-dependent density, viscosity, and thermal conductivity variations on single-phase laminar forced convection are numerically investigated. The problem is especially simulated for hydrodynamically and thermally developing water flow in micro-channel with no-slip, no-temperature jump, and constant wall heat flux boundary conditions. It is observed that the density variation induces radially inward flow due to continuity, which sharpens the axial velocity profile and decreases Nusselt number compared to constant property solution. The axial velocity profile significantly alters due to viscosity variation. This alteration varies along the micro-flow and it induces radially flow due to flow continuity. The reducing rate of Nusselt number for viscosity variation is substantially lower than constant property solution due to a significant flattening effect of the axial velocity profile, which augments the Nusselt number. Thermal-conductivity variation across the flow induces radial conduction, which enhances convection compared to constant property solution. Additionally, the effects of thermophysical fluid property variations on static gauge pressure drop are also investigated.
Funding
The authors thank the seed grant research project no. IITM/SG/SPM/28 of Indian Institute of Technology (IIT) Mandi, Himachal Province.
Acknowledgments
The authors are grateful to IIT Bombay for granting deputation (in public interest) to Prof. Shripad P. Mahulikar at IIT Mandi from 1 June 2013 to 31 December 2014, vide office Order no. Admn-I/246/2013. The authors would like to thank Dr. Syed Abbas, Assistant Professor, School of Basic Sciences, IIT Mandi, India, for the administrative support.
Nomenclature
| A | = | micro-channel cross-sectional area [m2] |
| cp(T) | = | temperature-dependent specific heat at constant pressure [J·(kg·K)−1] |
| D | = | diameter of micro-tube [m] |
| fD | = | Darcy friction factor |
| ff | = | Fanning friction factor |
| L | = | length of micro-tube [m] |
| h | = | heat transfer coefficient [W·m−2·K−1] |
| k(T) | = | temperature-dependent thermal conductivity [W·(m·K)−1] |
| Nu | = | Nusselt number (h·D/k) |
| p | = | pressure [Pa] |
| Po | = | Poiseuille number (fD·Re) |
| Pr | = | Prandtl number (cp·µm/k) |
| q′′w | = | heat flux at wall [W·m−2] |
| r | = | radial cylindrical coordinate [m] |
| R | = | radius of micro-tube [m] |
| Re | = | Reynolds number (ρ·um·D/µm) |
| SkT | = | thermal conductivity-temperature sensitivity (∂k/∂T) [W·m−1·K−2] |
| SµT | = | viscosity temperature sensitivity (∂µ/∂T) [kg(m·s·K)−1] |
| SρT | = | density temperature sensitivity (∂ρ/∂T) [kg·m−3·K−1] |
| Tm | = | bulk mean temperature [K] |
| Tw | = | wall temperature [K] |
| T(r) | = | temperature profile in radial direction (K) |
| u(r) | = | axial velocity profile in radial direction [m·s−1] |
| v | = | radial velocity [m·s−1] |
| z | = | axial cylindrical coordinate [m] |
| Greek symbols | ||
| Δps | = | static gauge pressure drop [Pa] |
| (∂u/∂r)w | = | wall velocity gradient [s−1] |
| (∂ū/∂ | = | dimensionless wall velocity gradient |
| ρ(T) | = | temperature-dependent density [kg·m−3] |
| µ(T) | = | temperature-dependent viscosity [kg(m·s)−1] |
| τw | = | shear stress at wall [N·m−2] |
| Subscripts | ||
| 0 | = | value at axis |
| atm | = | atmospheric value |
| CP | = | constant properties |
| ex | = | value at outlet |
| in | = | value at inlet |
| m | = | mean value of properties calculated at bulk mean temperature, Tm |
| ref | = | reference value |
| VP | = | variable properties |
| w | = | condition at wall |
Additional information
Notes on contributors
Rajan Kumar
Rajan Kumar is a Ph.D. student in the School of Engineering at Indian Institute of Technology, Mandi (India). He is currently working on laminar micro-convection of gas and liquid with variation in fluid properties. His research interest includes micro-convective flow, micro-electronic cooling, and heat exchanger, numerical investigation of variation in thermophysical properties, and computational fluid dynamics.
Shripad P. Mahulikar
Shripad P. Mahulikar is a professor in the Department of Aerospace Engineering, Indian Institute of Technology Bombay (IIT-B). He obtained his B.Tech. and M.Tech. (by research) in aerospace engineering from IIT-B in 1990 and 1992, respectively, and earned his Ph.D. from Nanyang Technological University, Singapore, in 1999. He received the A. von Humboldt Fellowship in the Federal Republic of Germany (in 2003, 2007, 2009), Outstanding Reviewer Award from the ASME Journal of Heat Transfer in 2007, and DFG-Mercator Professorship in Hamburg University of Technology, Federal Republic of Germany (December 2011 onward).