Open Access Open Access  Restricted Access Subscription or Fee Access

Numerical Solution and Scale Analysis Method of Nusselt Numbers for Vertical Flat Plate and Closed Cavity


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/ireme.v11i12.11881

Abstract


This research aims at creating the Nusselt number formula of heat transfer convection in the vertical flat plate and in the closed cavity containing fluids by using scale analysis and numerical solution. This research was theoretically conducted employing thermodynamics, heat transfer and also referring to some previous studies. The new formula created included Nusselt numbers and was used for calculating heat transfer convection on the vertical flat plate and in a closed rectangular gap with heating coming from one side of the upright. Making the formula is based on the shape of the boundary layer, such as quarter elliptic, half parabola and triangle shape. It seems that researchers never used this method. After being simulated, the results showed that the new formula is not much different from the results of other researchers. The formula was not tested to calculate the influence of width and height of the cavity on transferred heat.
Copyright © 2017 Praise Worthy Prize - All rights reserved.

Keywords


Scale Method; Numerical; Nusselt Number; Convection; Vertical Plate; Closed Cavity

Full Text:

PDF


References


Achemlal Driss, Mohammed Sriti, Mohamed El Haroui, Mohammed Guedda, Free convection modeling over a vertical flat plate embedded in saturated porous medium with a variable heat source and radiation flux, World Journal of Modelling and Simulation Vol. 9 No. 3, pp. 163-172, 2013

Ahmadi Mehran, Mohammad Fakoor Pakdaman, and Majid Bahrami, Natural Convection from Vertical Parallel Plates: An Integral Method Solution, Journal of Thermophysics and Heat Transfer, Vol. 29, No. 1, 2015.
http://dx.doi.org/10.2514/1.t4308

Alam M. S., M. M. Haque, M. J. Uddin, Unsteady MHD free convective heat transfer flow along a vertical porous flat plate with internal heat generation, Int. J. Adv. Appl. Math. and Mech. (ISSN: 2347-2529), 2(2) 52 – 61, 2014.

Andre Maripia, Sharifpur M. and Meyer J.P., Investigation Into Cavity flow Natural Convection fo Al2O3 Water Nano Fluids Numerically, 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 14–16 July 2014

Ali S. Alzwayi and Manosh C., Paul an analytical investigation of the physical dimensions of natural convection flow on a vertical heated plat, proceedings of the World Congress on Engineering Vol II WCE 2010, June 30 - July 2, 2010, London, U.K. ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966. 2010

Alina Adriana Minea, 2A Review on Analytical Techniques for Natural Convection Investigation in a Heated Closed Enclosure Case Study, Thermal Science: Vol. 19, No. 3, pp. 1077-1095, 2015.
http://dx.doi.org/10.2298/tsci131027021m

Amine Zoubir, Christophe Daverat, Shihe Xin, Stephanie Giroux-Julien, Herve Pabiou, Christophe Menezo, Natural Convection in a Vertical Open-Ended Channel: Comparison between Experimental and Numerical Results. Journal of Energy and Power Engineering, 7, pp.1265-1276, 2013.

Amir Faghri, Yuwen Zhang, John Howell, Advanced Heat and Mass Transfer, Global digital press, Columbia, copyright 2010.

Bambang Irawan, ING. Wardana, Slamet W. and Bambang D. W, Numerical Method for Prediction of Material’s Properties Effect on Temperature Difference in the Gap of Contact Surface During Conduction Heat Transfer, Applied Mathematical Sciences, Vol. 7, , no. 19, 923 – 932, 2013.
http://dx.doi.org/10.12988/ams.2013.13083

Bambang Irawan, ING. Wardana, Slamet W. and Bambang D.W, Numerical Methods for Predicting Melting through the Gap Applied to the One-Dimensional Stefan Problem Using Taylor Series, Applied Mathematical Sciences, Vol. 7, no. 91, 4509 – 4519, 2013.
http://dx.doi.org/10.12988/ams.2013.36313

Barakos G., E. Mitsoulis and D. Assimacopoulos, Natural Convection Flow in a Square Cavity Revisited Laminar and Turbulent Models with Wall Functions, International Journal for Numerical Methods in Fluids, Vol. 18, 695-719, 1994.
http://dx.doi.org/10.1002/fld.1650180705

Berkovsky B. M., V.K. Polevikov, Numerical study of problems on high intensive free convection, in: D.B. Spalding, H. Afgan (Eds.), Heat Transfer and Turbulent Buoyant Convection, Hemisphere, Washington, pp. DC,443–455, 1977.

Bejan Andrian, Method of Scale Analysis Natural Convection in Porous Media, Research Gate, upload by Andrian Bejan on December 2015.

Bejan Andrian, The Basic Scales of Natural Convection Heat and Mass Transfer in Fluids and Fluid-Saturated Porous Media, Int. CCMM. Heat Mass Transfer, vol. 14, 107-123, 1987.
http://dx.doi.org/10.1016/s0735-1933(87)81002-3

Bejan Andrian, A synthesis of analytical results for natural convection heat transfer across rectangular enclosures, Int. J. Heat Mass Transfer 23, 723–726, 1980.
http://dx.doi.org/10.1016/0017-9310(80)90017-4

Bejan Andrian, A. A. Al-Homoud, J. Imberger, Experimental study of high Rayleigh number convection in a horizontal cavity with different end temperatures, J. Fluid Mech. 109, 283–299, 1981.
http://dx.doi.org/10.1017/s0022112081001079

Bejan Andrian, C. L. Tien, Laminar natural convection heat transfer in a horizontal cavity with different end temperatures, J. Heat Transfer 100C, 641–647, 1978.
http://dx.doi.org/10.1115/1.3450870

Bejan Andrian, Note on Gill’s solution for free convection in a vertical enclosure, J. Fluid Mech. 90, 561–568, 1979.
http://dx.doi.org/10.1017/s0022112079002391

Carrijo Rodrigo Lino, Douglas M. R., Jose Luiz AFR, Natural Convection on Vertical Flats Plates a Numerical and Experimental Study, Proceedings of COBEM 2003, 17th International Congress of Mechanical Engireering, November 2003.
http://dx.doi.org/10.26678/abcm.cobem2017.cob17-1955

Churchill SW, Chu HHS, Correlating equations for laminar and turbulent free convection from a vertical plate, Int. J. Heat Mass Transf 18 (11):1323–1329, 1975.
http://dx.doi.org/10.1016/0017-9310(75)90243-4

Cormack D. E., L. G. Leal, J. H. Seinfeld, Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solution, J. Fluid Mech. 65 (1974) 231–246.
http://dx.doi.org/10.1017/s0022112074001364

Eckert, E. R. G., Jackson, T. W., Analysis of turbulent free-convection boundary layer on a flat plate, NACA TR 1015, 1951.
http://dx.doi.org/10.1007/978-3-662-03997-7_50

Franco A. T., Ganzarolli M.M., Combined Force and Natural Convection in a Square Cavity-Numerical Solution and Scale Analysis, Transactions on Engineering Sciences vol. 12, 1996.
http://dx.doi.org/10.6028/nbs.ir.84-2830

Fischenden, M., Saunders, O. A., The calculation of heat transmission, his Majesty's Stationary Office, London, 1932.
http://dx.doi.org/10.1177/0032258x5102400215

Frank B. Lipps and Richard S Hemler, A Scale Analysis of Deep Moist Convection and some Related Numerical Calculations, Journal of the Atmospheric Sciences, volume 39, p 2192-2210, 1982
http://dx.doi.org/10.1175/1520-0469(1982)039%3C2192:asaodm%3E2.0.co;2

Haghighi A. and K. Vafai, Optimal Positioning of Strips for Heat Transfer Reduction Within an Enclosure, Numerical Heat Transfer, Part A, 66: 17–40, 2014,
http://dx.doi.org/10.1080/10407782.2013.869081

Jashim Udin MD., M.A.A. Hamad and A.I. MD. Ismail, Investigation of Heat Mass Transfer for Combined Convective Slips Flow, Sains Malaysiana 41(9): 1139–1148, 2012.
http://dx.doi.org/10.1063/1.4724137

Kakac S, Yener Y, Convective heat transfer, 2nd edn. CRC Press LLC, Boca Raton, 1995

Kays, W. M. and M. E. Crawford, Convection heat and mass transfer, 2nd Ed, the McGraw Hill Companies, 1980.

Lienhard John H IV and Lienhard John H V, A Heat transfer textbook, Third Edition, Phlogiston Press, Cambridge Massachusetts USA, 2011.

MacGregor, R.K, and Emery, A.P, Free Convection through Vertical plane layers Moderate and high prandtl Number Fluid, ASME, Journal Heat Transfer Vol 91, pp 391 – 403, 1969.
http://dx.doi.org/10.1115/1.3580194

Mahdi Fahiminia, Mohammad Mahdi Naserian, Hamid Reza Goshayeshi, Davood Majidian, Investigation of Natural Convection Heat Transfer Coefficient on Extended Vertical Base Plates, Energy and Power Engineering, 2011, 3, 174-180. 2011.
http://dx.doi.org/10.4236/epe.2011.32022

Mamun A. A., Z. R. Chowdhury, M. A. Azim, M. A. Maleque, Conjugate Heat Transfer for a Vertical Flat Plate with Heat Generation Effect, Nonlinear Analysis: Modelling and Control, Vol. 13, No. 2, 213–223, 2008.
http://dx.doi.org/10.1016/j.icheatmasstransfer.2008.06.007

McAdams, W. H., Heat Transmission, 3rd ed., McGraw-Hill, New York, USA, 1954.
http://dx.doi.org/10.1126/science.120.3128.984

Mulolani I. and M. Rahman, Similarity Analysis for Natural Convection from a Vertical Plat with Distributed Wall Concentration, Internat. J. Math. & Math. Sci. Vol. 23, No. 5 2000.
http://dx.doi.org/10.1155/s0161171200001745

Meraj Mustafa, Ammar Mushtaq, Tasawar Hayat, Bashir Ahmad, Nonlinear Radiation Heat Transfer Effects in the Natural Convective Boundary Layer Flow of Nano fluid Past a Vertical Plate: A Numerical Study, PLOS ONE, September 2014 | Volume 9 | Issue 9 | e103946, 2014.
http://dx.doi.org/10.1371/journal.pone.0103946

Newell M. E., F. W. Schmid, Heat Transfer If Laminar Natural Convection Within Rectangular Enclosures, Journal of Heat Transfer february 1970 / 159. 1970.
http://dx.doi.org/10.1115/1.3449616

Osman Turan, Anuj Sachdeva, Nilanjan Chakraborty and Robert J. Poole, Laminar Natural Convection of Bingham Fluids in a square Enclosure with Vertical walls Subjected to Constant Heat Flux, Numerical Heat Transfer, Part A, 60: 381–409, 2011.
http://dx.doi.org/10.1080/10407782.2011.594417

Ostrach, S., Natural convection in enclosures, in: Advances in Heat Transfer (Ed. J. P. Hartnett, T. F. Ervine), Vol. 8, academic Press, New York, USA, pp. 161-227, 1972.
http://dx.doi.org/10.1016/s0065-2717(08)70039-x

Ostrach, S., Natural convection in enclosures, J. Heat Transfer , 110, 48, pp. 1175-1190, 1988.
http://dx.doi.org/10.1115/1.3250619

Paul Ashish, Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium, International Journal of Engineering Mathematics, Volume 2017, Article ID 2981071, 9 pages, 2017.
http://dx.doi.org/10.1155/2017/2981071

Patrick H. Oosthuizen, Jane T. Paul, Natural Convection heat transfer from a narrow vertical flat plate with a uniform surface heat flux and with different plate edge conditions, Frontiers in Heat and Mass Transfer (FHMT), 1, 013006 (2010), Global Digital Central, ISSN: 2151-8629, 2010.
http://dx.doi.org/10.5098/hmt.v1.1.3006

Rana Puneet and R. Bhargava, Flow and Heat Transfer Analysis of a Nanofluid Along a Vertical Flat Plate with Non-Uniform Heating Using Fem: Effect of Nanoparticle Diameter, International Journal of Applied Physics and Mathematics, Vol. 1, No. 3, November 2011.
http://dx.doi.org/10.7763/ijapm.2011.v1.33

Rebhi A. Damseh, Tariq A. Al-Azab, Benbella A. Shannak, Mahmoud Al Husein, Unsteady Natural Convection Heat Transfer of Micropolar Fluid over a Vertical Surface with Constant Heat Flux, Turki sh J. Eng. Env. Sci . 225-233, 31 2007
http://dx.doi.org/10.1016/j.ijthermalsci.2008.12.018

Reda I. El-Ghnam, Numerical Investigation of Natural Convection Heat Transfer between Two Vertical Plates with Symmetric Heating, International Journal of Thermal Technologies, E-ISSN 2277 – 4114, ©2015.
http://dx.doi.org/10.14741/ijcet/22774106/spl.5.6.2016.43

Saitoh, T. K. Hirose, high-accuracy bench mark solutions to natural convection in a square cavity, Computational Mechanics (1989) 4, 4 I7 – 427, 1989.
http://dx.doi.org/10.1007/bf00293047

Plankovskyy Sergiy, Olga Shypul, Yevgen Tsegelnyk, Oleg Tryfonov, Ivan Golovin, Simulation of surface heating for arbritary shape moving bodies sources by using R-function, Acta Polytechnica 56(6):472–477, 2016.
http://dx.doi.org/10.14311/ap.2016.56.0472

Terekhov V. I. and A. L. Ekaid, Three Dimensional Laminar Convection in a Parallelepiped with Heating of Two Side Walls, ISSN 0018_151X, High Temperature, 2011, Vol. 49, No. 6, pp. 874–880. © Pleiades Publishing, Ltd., 2011.
http://dx.doi.org/10.1134/s0018151x11060228

Tieszen S., A. Ooi, P. Durbin and M. Behnia, Modeling of natural convection heat transfer, Center for Turbulence Research, Proceedings of the Summer Program 1998.
http://dx.doi.org/10.1016/s0142-727x(02)00181-9

Togni Riccardo, Andrea Cimarelli and Elisabetta D A., Physical and Scale-by-Scale Analysis of Rayleigh-Benard Convection, Journal Fluid Mechanic 2015 vol. 782, 2015.
http://dx.doi.org/10.1017/jfm.2015.547

Tsuji T., Y. Nagano, Velocity and temperature measurements in a natural convection boundary layer along a vertical flat plate, experimental thermal and fluid sciences 2; 208-215, 1989.
http://dx.doi.org/10.1016/0894-1777(89)90035-6

Turan O, N. Chakraborty, R.J. Poole, Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls, J. Non-Newtonian, Fluid Mech. 165, 2010.
http://dx.doi.org/10.1016/j.jnnfm.2010.04.013

Xiaoxing Yuan, Wall functions numerical simulation of natural convection along vertical surface, A dissertation, Swiss Federal Institute of Technology, 1995.
http://dx.doi.org/10.1016/0017-9310(93)90132-p

Yanhu Guo and Klaus- Jurgen Bathe, A numerical study of a natural convection flow in a cavity, International Journal for Numerical Methods in Fluids, 2002; 40:1045–1057, 2002.
http://dx.doi.org/10.1002/fld.391

Zeyghami Mehdi, and Muhammad M. Rahman, Analysis of Combined Natural Convection and Radiation Heat Transfer Using a Similarity Solution, Energy Research Journal 2015, 6 (2): 64.73,
http://dx.doi.org/10.3844/erjsp.2015.64.73

El Khaoudi, F., Gueraoui, K., Driouich, M., Sammouda, M., Numerical and Theoretical Modeling of Natural Convection of Nanofluids in a Vertical Rectangular Cavity, (2014) International Review on Modelling and Simulations (IREMOS), 7 (2), pp. 350-355.
http://dx.doi.org/10.15866/iremos.v7i2.585

Sene, M., Dia, S., Thiam, O., Sow, M., Numerical Study of the Steady Natural Convection Inside an Enclosure delimited by a Cylindrical Parabolas and a Plane Surface: Influence of the Slope Angle, (2015) International Journal on Engineering Applications (IREA), 3 (2), pp. 36-42.

Oukaira, A., Pal, N., Ettahri, O., Kengne, E., Lakhssassi, A., Simulation and FPGA Implementation of Thermal Convection Equation for Complex System Design, (2016) International Journal on Engineering Applications (IREA), 4 (6), pp. 169-177.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize