Thermodynamic second law analysis for a gravitydriven variable viscosity liquid film along an inclined heated plate with convective cooling
 O. D. Makinde
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The inherent irreversibility and thermal stability in a gravitydriven temperaturedependent variable viscosity thin liquid film along an inclined heated plate with convective cooling is investigated. In this study, both the isothermal and isoflux heating of the plate are considered. The free surface of the liquid film is assumed to exchange heat with the surroundings following Newton’s cooling law and the fluid viscosity model varies as an inverse linear function of the temperature. Analytical solutions are constructed for the governing boundaryvalue problem, and important properties of velocity and temperature fields such as thermal stability criterion are obtained. Expressions for volumetric entropy generation numbers, irreversibility distribution ratio, and the Bejan number in the flow field are also obtained and discussed quantitatively.
 Anderson, H. I. (1987) The momentum integral approach to laminar thin film flow, Proc. ASME Symp. on Thin Fluid Films. Cincinatti, OH, FED. 48: pp. 713
 Astarita, G., Marrucci, G., Palumbo, G. (1964) NonNewtonian gravity flow along inclined plane surfaces. Ind. Eng. Chem. Fundam. 3: pp. 333339 CrossRef
 Cebeci, T., Bradshaw, P. (1984) Physical and computational aspects of convective heat transfer. SpringerVerlag, New York, USA
 Schlichting, H. (2000) Boundary layer theory. SpringerVerlag, New York, USA
 Rahman, M. M., Faghri, A., Hankey, W. L., Swanson, T. D. (1990) Computation of the free surface flow of a thin liquid film at zero and normal gravity. Numer.Heat Transf., Part A Appl. 17: pp. 5371 CrossRef
 Therien, N., Coupal, B., Corneille, J. L. (1970) Verification experimentale de l’epaisseur du film pour des liquides nonNewtonien s’ecoulant pargravite sur un plan incline. Can. J. Chem. Eng. 48: pp. 1720 CrossRef
 Sylvester, N. D., Tyler, J. S., Skelland, A. H. P. (1973) NonNewtonian thin films: theory and experiment. Can. J. Chem. Eng. 51: pp. 418429 CrossRef
 Makinde, O. D. (2001) Heat and mass transfer in a pipe with moving surfaceeffect of viscosity variation and energy dissipation. Quaestiones Mathematicae 24: pp. 93104
 Makinde, O. D. (2007) HermitePadé approximation approach to steady flow of a liquid film with adiabatic free surface along an inclined heat plate. Physica A 381: pp. 17 CrossRef
 Makinde, O. D. (2006) Laminar falling liquid film with variable viscosity along an inclined heated plate. Applied Mathematics and Computation 175: pp. 8088 CrossRef
 Makinde, O. D. (2009) Thermal criticality for a reactive gravity driven thin film flow of a third grade fluid with adiabatic free surface down an inclined plane. Applied Mathematics and Mechanics 30: pp. 373380 CrossRef
 Narusawa, U. (2001) The second law analysis of mixed convection in rectangular ducts. Heat and Mass Transfer 37: pp. 197203 CrossRef
 Ibanez, G., Cuevas, S., Lopez de Haro, M. (2003) Minimization of entropy generation by asymmetric convective cooling. Int. J. Heat Mass Transfer 46: pp. 13211328 CrossRef
 Bejan, A. (1994) Entropy generation through heat and fluid Flow. John Wiley & Sons. Inc., Canada
 Bejan, A. (1996) Entropy generation minimization. CRC Press, Boca Raton, Florida
 Makinde, O. D. (2006) Irreversibility analysis for gravity driven nonNewtonian liquid film along an inclined isothermal plate. Physica Scripta 74: pp. 642645 CrossRef
 Saouli, S., AiboudSaouli, S. (2004) Second law analysis of laminar falling liquid film along an inclined heated plate. Inter. Comm. Heat Mass Transfer 31: pp. 879886 CrossRef
 Reddy Gorla, R. S., Byrd, L. W., Pratt, D. M. (2007) Second law analysis for microscale flow and heat transfer. Applied Thermal Engineering 27: pp. 14141423 CrossRef
 Taufiq, B. N., Masjuki, H. H., Mahlia, T. M. I., Saidur, R., Faizul, M. S., Niza Mohamad, E. (2007) Second law analysis for optimal thermal design of radial fin geometry by convection. Applied Thermal Engineering 27: pp. 13631370 CrossRef
 Tasnim, S. H., Mahmud, S. (2002) Entropy generation in a vertical concentric channel with temperature dependent viscosity. Int. Comm. Heat Mass Transfer 29: pp. 907918 CrossRef
 Sahin, A. Z. (1999) Effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux. Heat Mass Transfer 35: pp. 499506 CrossRef
 Makinde, O. D. (2008) Entropygeneration analysis for variableviscosity channel flow with nonuniform wall temperature. Applied Energy 85: pp. 384393 CrossRef
 Makinde, O. D. (2008) Irreversibility analysis of variable viscosity channel flow with convective cooling at the walls. Canadian Journal of Physics 86: pp. 383389 CrossRef
 Elbashbeshy, E. M. A., Bazid, M. A. A. (2000) The effect of temperature dependent viscosity on heat transfer over a continuous moving surface. Journal of Applied Phys. 33: pp. 27162721
 W. Squire, A mathematical analysis of selfignition, Applications of Undergraduate Mathematics in Engineering, Ed. Noble, B. MacMillan, New York, USA, (1967).
 http://maplesoft.com/products/maple/technical.aspx
 Title
 Thermodynamic second law analysis for a gravitydriven variable viscosity liquid film along an inclined heated plate with convective cooling
 Journal

Journal of Mechanical Science and Technology
Volume 24, Issue 4 , pp 899908
 Cover Date
 20100401
 DOI
 10.1007/s1220601002159
 Print ISSN
 1738494X
 Online ISSN
 19763824
 Publisher
 Korean Society of Mechanical Engineers
 Additional Links
 Topics
 Keywords

 Inclined plate
 Liquid film
 Variable viscosity
 Thermal stability
 Convective cooling
 Entropy analysis
 Industry Sectors
 Authors

 O. D. Makinde ^{(1)}
 Author Affiliations

 1. Faculty of Engineering, Cape Peninsula University of Technology, P. O. Box 1906, Bellville, 7535, South Africa