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ABSTRACT
Experimental investigation is reported on natural convection heat transfer from the outer surface of a vertical array of horizontal square tubes in air. Five tubes equally spaced are used with cross section 0.02 × 0.02 m2. The tubes are subject to constant heat flux boundary condition using internal constant heat flux heating elements in the range 46–510 W/m2. Experiment is done for arrays of 2–5 square tubes and for four center-to-center separation distance to hydraulic diameter ratios. Study is concentrated on the effect of tube location in the array and on the geometry of the array. Results show that the downstream tubes exhibit reduced Nusselt numbers than that of a single tube for small center-to-center separation ratio of 2.5. This reduction depends on the location of the tube in the array and the number of tubes in each array. Results also show that as the ratio increases, enhancement in heat transfer over that of a single tube is observed and critical ratio is obtained at a specified value of the modified Rayleigh number for the upper (downward) tubes in each array. Local circumference averaged correlations are proposed for the upper tubes in each array and for any other individual tube in each array geometry. An overall general averaged correlation is also reported for each tube in the array.
Acknowledgments
The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through the research group project No RGP-080.
Nomenclature
| As | = | tube surface area, m2 |
| Abk | = | end plate cross section area, m2 |
| D | = | diameter of circular cylinder as a characteristic length (m) |
| Dh | = | hydraulic diameter equal to the square of cross section side length, m |
| EIP | = | electrical input power, W |
| F12 | = | shape factor between two long parallel cylinders |
| F1∞ | = | shape factor between any tube and the ambient |
| g | = | acceleration due to gravity, m/s2 |
| H | = | heating element |
| h | = | convection heat transfer coefficient, W m-2 K-1 |
| k | = | thermal conductivity, W m-1 K-1 |
| L | = | tube length, (= 1m) |
| M | = | ordinal number of the ith tube in the array, 1 ≤ M ≤ 4 |
| N | = | number of tubes in the array, 2 ≤ N ≤ 5 |
| Nu | = | Nusselt number, h Dh / k or h x / k |
| q″ | = | convection heat flux, W/m2 |
| qr | = | radiation heat flux, W/m2 |
| qbk | = | heat lost by conduction through the Bakelite end plates, W/m2 |
| Qc | = | averaged convection heat transfer rate, W |
| R2 | = | coefficient of determination (correlation coefficient) |
| Ra* | = | modified Rayleigh number, gβ q″x4 ν− 1α− 1 k− 1 or g β q″D4h − 1− 1k− 1 |
| Ra | = | Rayleigh number, gβ ΔTD3 ν− 1α− 1 |
| S | = | distance of tube enter to the next tube center, m |
| S/Dh | = | distance ratio |
| T | = | temperature, K |
| TiB | = | inside surface temperature of the Bakelite end plate, K |
| ToB | = | outside surface temperature of the Bakelite end plate, K |
| x | = | axial or axial distance, m |
| Y/Dh | = | non-dimensional coordinate |
Greek symbols
| α | = | thermal diffusivity, m2 s− 1 |
| β | = | coefficient for thermal expansion, K-1 |
| δ | = | Bakelite thickness, m |
| ϵ | = | emissivity |
| θ | = | arithmetic mean temperature defined by Eq. (Equation7 |
| ν | = | kinematics viscosity, m2 s− 1 |
| σ | = | Stefan- Boltzmann constant, (= 5.67 × 10−8, W m−2 K−4) |
Subscripts
| bk | = | Bakelite |
| Dh | = | characteristic length, m |
| j | = | indices in the perimeter direction ranging from 1 to 3 |
| x | = | indices in the axial direction ranging from 1 to 9 |
| x | = | characteristic length, m |
| ∞ | = | ambient condition |
Superscripts
| − | = | averaged value |
Additional information
Notes on contributors
Mohamed Ali
Mohamed Ali is a professor of mechanical engineering department at King Saud University, Riyadh, Saudi Arabia. He received his Ph.D. from the University of Colorado at Boulder in 1988. His research interests include natural and forced convection heat transfer, nanofluid heat transfer, and stability of fluids. He has published more than 80 articles in well-recognized journals and 38 in conference proceedings. He is currently on the editorial boards of King Saud University (Engineering Sciences Journal) and Journal of Mechanics Engineering and Automation. He has collaborated research with professors at University of Colorado at Boulder, Northwestern University at Evanston, IL, and Swiss Federal Institute of Technology, Zürich, Switzerland. His new invention of natural insulating material has been recognized by the Asia Research News 2012 and by Physics Today Magazine, July 2014 Daily edition, Enterprise. This invention was awarded the gold medal at the British Invention Show 2011 and at the International Exhibition of Inventions of Geneva 2012. It also awarded the TechConnect Innovation Award by the TechConnect World Innovation Summit & Showcase, in 2014, Washington, DC, USA. He was also awarded the Distinguished Research and Publication Award for the year 2010, the Best Research Award for the year 2011 and the second prize winner on his Distinguished Research published in ISI journals for the year 2014 by the College of Engineering at King Saud University.
Abdullah Nuhait
Abdullah Nuhait received his B.S. degree in mechanical engineering from California State University at Sacramento, M.S. degree in mechanical engineering from University of Michigan (Ann Arbor, Michigan), and Ph.D. from Virginia Tech (Blacksburg, Virginia) in engineering mechanics. He was the chairman of Mechanical Engineering Department at King Saud University for two years 1992-1994. He (with others) has a granted USA patent in desalination and recently, has applied with others for a USA patent in desalination and in cooling of gas turbines. He is an HVAC consultant to several Saudi ministries and developed and implemented standards of Saudi made AC units and supervised performance tests by Intertech Testing Services in Cortland, NY, USA.
Redhwan Almuzaiqer
Redhwan Almuzaiqer is a Ph.D. student in the Mechanical Engineering Department at King Suad University, Riyadh, Saudi Arabia. He received his B.S. degree from King Khaled University, Abha, Saudi Arabia, in 2011 and his M.S. degree from King Suad University, Riyadh, Saudi Arabia, in 2016.