Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer

ali belhocine, Wan Zaidi Wan Omar

Resumen

In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.


DOI: http://dx.doi.org/10.18272/aci.v11i2.968

Palabras clave

Lévêque approximation, Thermal entrance region, Thermal boundary layer, Dimensionless variables, Temperature, Nusselt number, Runge-Kutta method

Texto completo:

Referencias

References

Hamad ,M. A. A.,and Ferdows , M., Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet, Applied Mathematics and Mechanics (English Edition) ,33(7), 923-930 (2012)

Wei, D. M.,and Al-ashhab, S., Similarity solutions for non-Newtonian power-law fluid flow, Applied Mathematics and Mechanics (English Edition) ,35(9), 1155-1166 (2014)

Trîmbijas, R., Grosan, T.,and Pop, I., Mixed convection boundary layer flow past vertical flat plate in nanofluid: case of prescribed wall heat flux, Applied Mathematics and Mechanics (English Edition) ,36(8), 1091-1104 (2015)

Ahmed ,S. E., Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature, Applied Mathematics and Mechanics (English Edition) ,38(8) ,1171-1180 (2017)

Shen,L., and Lu,C., Mechanism of three-dimensional boundary-layer receptivity, Applied Mathematics and Mechanics (English Edition) , 38(9) ,1213-1224 (2017)

Mahanthesh ,B., Gireesha ,B. J., Shehzad ,S. A., Abbasi ,F. M. , and Gorla ,R. S. R. ,Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection. Applied Mathematics and Mechanics (English Edition) .,., 38(7), 969-980(2017)

Eldesoky ,I. M., Abdelsalam ,S. I., Abumandour ,R. M., Kamel ,M. H. ,, and Vafai ,K. Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel. Applied Mathematics and Mechanics (English Edition) ., 38(1), 137-154(2017)

Baehr, H., and Stephan, K.,Heat Transfer, Springer-Verlag,(1998)

Stephan, K., Warmeubergang und Druckabfall bei Nicht Ausgebildeter Laminar Stromung in Rohren und in Ebenen Spalten,’Chemie-Ingenieur-Technik,31(12), 773-778 (1959)

Asako, Y., Nakamura, H., and Faghri, M ,Developing Laminar Flow and Heat Transfer in the Entrance Region of Regular Polygonal Ducts, International Journal of Heat Mass Transfer,31(12), 2590–2593(1988)

Shah, R. K., and London, A. L., Laminar Flow Forced Convection in Ducts, Academic Press, New York, NY,(1978)

Kakac, S., Shah, R. K., and Aung, W., Handbook of Single Phase Convective Heat Transfer, Wiley, New York,(1987)

Ebadian, M.A. and Dong, Z.F., Forced convection internal flows in ducts, In: Handbook of heat transfer,3rd Edition, McGraw-Hill, New York, 5.1-5.137(1998)

Kakac, S., and Yener, Y.,‘‘Laminar Forced Convection in the Combined Entrance Region of Ducts,’’ in Low Reynolds Number Heat Exchangers,S.Kakac, R. K. Shah and A. E. Bergles, eds., Hemisphere Publishing, Washington, 165–204 (1983)

Hausen, H. “Darstellung des Wärmeübergangs in Rohren durch verallgemeinerte Potenzbezie-hungen”, VDI-Zeitung, Suppl. “Verfahrenstechnik”, 4, 91-98(1943)

Churchill, S. W., and Ozoe, H., ‘‘Correlations for Laminar Forced Con-vection with Uniform Heating in Flow Over a Plate and in Developing and Fully Developed Flow in a Tube,’’ ASME J. Heat Transfer,95, 78 – 84(1973)

Churchill, S. W., and Ozoe, H., ‘‘Correlations for Laminar Forced Con-vection in Flow Over an Isothermal Flat Plate and in Developing and Fully Developed Flow in an Isothermal Tube,’’ ASME J. Heat Transfer,95, 416 – 419 (1973)

Yilmaz.T and Cihan.E. ‘’General equation for heat transfer for laminar flow in ducts of arbitrary cross-sections’’, International Journal of Heat and Mass Transfer,36(13), 1993, 3265-3270 (1993)

Yilmaz.T and Cihan.E. ‘’An Equation for Laminar Flow Heat Transfer for Constant Heat Flux Boundary Condition in Ducts of Arbitrary Cross-Sectional Area’’,J. Heat Transfer 117(3), 765-766 (1995)

Belhocine, A. and Wan Omar, W. Z, ‘’Numerical study of heat convective mass transfer in a fully developed laminar flow with constant wall temperature’’, Case Studies in Thermal Engineering, 6 , 116-127(2016)

Belhocine A. ‘’Numerical study of heat transfer in fully developed laminar flow inside a circular tube’’. International Journal of Advanced Manufacturing Technology Int J AdvManuf Tech. 85(9):2681–2692 (2016)

Belhocine.A , and Wan Omar,W.Z. An analytical method for solving exact solutions of the convective heat transfer in fully developed laminar flow through a circular tube,,Heat Transfer—Asian Research, 1–12 (2017)

Bird, R.B., Stewart, W.E.,and Lightfoot, E.N. ‘’Transport Phenomena’’, John Wiley and Sons, New York,(1960)

Lévêque, M.A. ‘’Les lois de la transmission de chaleur par convection’’, Annales des Mines, Memoires, Series 12, 13, 201-299, 305-362, 381-415 (1928) {as cited by J. Newman, Trans. ASME J. Heat Transfer, 91, 177 (1969)

Abramowitz, M. and Stegun, I., Handbook of Mathematical Functions, Dover, New York (1965).

Enlaces refback

  • No hay ningún enlace refback.


Copyright (c) 2019 ali belhocine, Wan Zaidi Wan Omar

Licencia de Creative Commons
Este obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial 4.0 Internacional.