## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Entropy generation of aiding mixed thermal convection, between two nonparallel vertical plates with uniform temperature

**ABSTRACT**

In the aim to optimize the flow systems, a numerical simulation is carried out to investigate the entropy generation of the aiding mixed convection within two nonparallel vertical plates. The computational procedure is made by solving the laminar, steady and bi-dimensional continuity, momentum and energy equations with the finite volume method. The plates are symmetrically heated with uniform temperature. The mixed convection flow in the heated vertical channel is studied for two aiding buoyancy conditions (upstream flow between hot plates and downstream flow between cold plates). The calculations are performed for several parameters such as Richardson number or buoyancy parameter (Gr/Re2), Reynolds and Bejan numbers. The results showed that the velocity, temperature and entropy generation profiles within the channel are significantly affected by the later parameters..

**KEYWORDS**

PAPER SUBMITTED: 2016-08-26

PAPER REVISED: 2017-08-11

PAPER ACCEPTED: 2017-08-15

PUBLISHED ONLINE: 2017-09-09

- MILLSAPS, K., POHLHAUSEN, K., Thermal distributions in Jeffery-Hamel flows between nonparallel plane walls, The Aeronautical Sciences, (1953), pp.187-196.
- SPARROW, E. M., et. al., Combined forced and free convection in boundary layer flow, The Physics of Fluids, (1959), 2, pp.319-328.
- KATKOV, V. L., Exact solutions of certain convection problems, PMM, 32 (1968), 3, pp. 482-487
- Chen, T.H., Jeffery-Hamel flow with free convection, Phd thesis, University of Nebraska, Lincolin, USA, 1973
- SPARROW, E.M., et. al., Experimental and numerical investigation of natural convection in convergent vertical channel, Thermal Sciences, 31 (1988), pp. 907-915
- HUANG, T. M., et. al., Mixed convection flow and heat transfer in heated vertical convergent channel. Heat and mass transfer. 38 (1995), pp. 2445-2456.
- BIANCO, N., et. al., Experimental investigation on natural convection in convergent channel with uniformly heated plates, Heat and Mass Transfer, 50 (2007), pp. 2772-2786
- KAISER, A. S., et. al., Correlation for Nusselt number in natural convection in vertical convergent channel at uniform wall temperature by a numerical investigation, Heat and Fluid Flow, 2004, 25: 671-682
- PREMACHANDRAN, B., BALAJI, C., A correlation for mixed convection heat transfer from converging, parallel and diverging channels with uniform volumetric heat generating plates, Thermal Sciences, 33 (2006), pp. 350-356
- BIANCO, N., et. al., Thermal design and optimization of vertical convergent channels in natural convection, Applied Thermal Engineering, 26 (2006), pp. 170-177
- R. K. SHAH et al, Laminar Flow Forced Convection in Ducts, Academic Press, New York, 1978
- A. BEJAN, Astudy of Entropy generation in fundamental convective heat transfer, Heat Transfer, 101 (1979), pp. 718-725
- A. BEJAN, Second-law analysis in heat transfer and thermal design , Heat Transfer, 15 (1982), pp. 1-58
- A. BEJAN, Entropy Generation Minimization, CRC, Boca Raton, NY, 1996
- BEN MANSOUR, R., et al., Dissipation and entropy generation in fully developed forced and mixed laminar convection, Thermal Sciences, 45 (2006), pp. 998-1007
- YANG, G., et. al., Flow reversal and entropy generation due to buoyancy assisted mixed convection in the entrance region of a three dimensional vertical rectangular duct, Thermal Sciences, 67 (2013), pp. 741-751
- C. PADET et al, Analysis of the developed mixed thermal convection by use of 2nd law, Bulletin of the Transilvania University of Brasov, 2-51 (2009), pp. 227-234
- M. SALARI et al, Effects of circular corners and aspect-ratio on entropy generation due to natural convection of nanofluid flows in rectangular cavities, Thermal Science, 19 (2015), pp. 1621-1632
- E. SOURTIJI, S. F. HOSSEINIZADEH, Heat transfer augmentation of magnetohydrodynamics Natural convection in l-shaped cavities utilizing nanofluids, Thermal Science, 16 (2012), pp. 489-501
- M. NOUROLLAHI et al, Numerical study of mixed convection and entropy generation in the poiseulle-benard channel in different angles, Thermal Science, 14 (2010), pp. 329-340
- ϚENGEL, Y. A., Heat transfer: a practical approach, McGRAW-HILL, New York, USA, 2003
- FEIDT, M., Thermodynamique et optimisation énergétique des systèmes et des procédés (Thermodynamic and energetic optimisation of system and methods), 2ème Edition(2nd Edition), frensh, TECDOC, Paris, France 1996
- PATANKAR, S. V., Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, USA, 1980
- P. H. Oosthuizen, D. Naylor, An Introduction to Convective Heat Transfer Analysis, WCB/McGraw Hill, 1999
- LAURIAT, G., et al.,Convection naturelle - cas particuliers (Natural convection - particular cases) French, af4081, Techniques de l'ingénieur (Technics of engineer) French, Paris, France, 2014.
- GAU, C., et al. Reversed flow structure and heat transfer mesurments for Buoyancy-assisted convection in a heated vertical duct, Heat Transfer, ASME, 114 (1992), pp. 928-935
- IQBAL, M., et al. Viscous dissipation effects on combined free and forced convection through vertical circular tubes, Applied Mechanics, ASME, (1970), pp. 931-935
- AUNG, W., WORKU, G., Theory of fully developed, combined convection including flow reversal, Heat Transfer, ASME, 108 (1986), pp. 485-488
- SHOHEL, M., et al., Second law analysis of heat transfer and fluid flow inside a cylindrical annular space, Exergy, 2002, 2, pp.322-329