STUDY OF NATURAL CONVECTION ALONG A VERTICAL SINUSOIDAL WAVY SURFACE: COMBINED HEAT AND MASS TRANSFER

Jamaleddin O. Esalah

doi:10.66411/jer.v11i.183

Authors

Jamaleddin O. Esalah Faculty of Engineering Department of Materials & Metallurgical Engineering Al-Fatah University, Tripoli – Libya Author

DOI:

https://doi.org/10.66411/jer.v11i.183

Keywords:

Combined (coupled) heat and mass transfer, Natural (free) convection, vertical plate, Wavy surface

Abstract

The problem of natural convection along a vertical wavy surface has been studied numerically when mass transfer is combined with heat transfer and the buoyancy force is due to temperature and concentration differences. The wavy surface is transformed to a flat surface for which the obtained governing equations are solved using an implicit finite difference scheme. the derivations are carried out for a vertical surface of arbitrary shape, and the numerical results are provided for a sinusoidal wavy surface. The sinusoidal wavy surface is used as example because it can be considered as an approximation to practical geometry for which natural convection heat and mass transfer are of interest. the effects of Prandtl number, Schmidt number, mass transfer number, and the amplitude of the sinusoidal wavy surface on the heat transfer and mass transfer rates are investigated. increasing the Prandtl number is found to increase the heat transfer rate. For a given Prandtl number, Increasing Schmidt number decreases the heat transfer rate and increases the mass transfer rate. increasing the amplitude of the wavy surface tends to decrease the heat and mass transfer rates and to increase the magnitudes of the local Nusselt number and local Sherwood number. The average Nusselt number and average Sherwood number for sinusoidal wavy surface are found to be smaller than those for the corresponding flat plate

References

[1] Yao, L., Natural Convection Along a Vertical Wavy Surface, J. Heat Transfer, (1983), vol.105, pp.465-468 DOI: https://doi.org/10.1115/1.3245608

[2] Khair, K., and A. Bejan, Mass transfer to natural convection boundary layer flow driven by heat transfer, Int. J. Heat Mass Transfer, (1985), 30, 369 – 376 DOI: https://doi.org/10.1115/1.3247535

[3] Moulic, S. and L. Yao, Natural convection along a wavy surface with uniform heat flux, J. Heat Transfer, (1989), 111, 1106 -1108 DOI: https://doi.org/10.1115/1.3250780

[4] Chin, C. and H. Chou, Transient analysis of natural convection along a vertical wavy surface in micro-polar fluids, Int. J. Eng. Sci., (1994), 32, 19-33 DOI: https://doi.org/10.1016/0020-7225(94)90146-5

[5] Rees, D. and I. Pop, A note on free convection along a vertical wavy surface in a porous medium, ASME J. Heat Transfer, (1994), 116, 505-508 DOI: https://doi.org/10.1115/1.2911430

[6] Rees, D. and I. Pop, Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium, ASME J. Heat Transfer (1995), 117, 545- 550 DOI: https://doi.org/10.1115/1.2822565

[7] Yang, Y., Chen. Ch., and M. Lin, Natural convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect, Int. J. Heat Mass Transfer, (1996), 39, 2831 - 2842 DOI: https://doi.org/10.1016/0017-9310(95)00354-1

[8] Alam, K., Hossain, M. and D. Rees, Magnetohydrodynamic free convection along a vertical wavy surface, Internat. J. Appl. Mech. Eng., (1997), 1, 555-566

[9] Kim, E., Natural convection along a wavy vertical plate to non-Newtonian fluids, Int. J. Heat Mass Transfer, (1997), 40, no. 13, 3069 – 3078 DOI: https://doi.org/10.1016/S0017-9310(96)00357-2

[10] Rahman, S., Natural convection along vertical wavy surface: an experimental study, Chemical Engineering Journal, (2000), 84, 587 – 591 DOI: https://doi.org/10.1016/S1385-8947(01)00174-7

[11] Wang, Ch., and Ch. Chen, Transient force and free convection along a vertical wavy surface in micro-polar fluids, Int. J. Heat Mass Transfer, (2001), 44, 3241 -3251 DOI: https://doi.org/10.1016/S0017-9310(00)00329-X

[12] Jang, J. and W.Yan, Transient analysis of heat and mass transfer by natural convection over a vertical wavy surface, Int. J. Heat Mass Transfer, (2004), 47, 3695 – 3705. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2004.03.010

[13] Molla, M., Hossain, M., and L. Yao, Natural convection flow along a vertical wavy surface with uniform surface temperature in presence of heat generation / absorption, Internat. J. Thermal Sci., (2004), 43, 157 – 163 DOI: https://doi.org/10.1016/j.ijthermalsci.2003.04.001

[14] Yao, L., Natural convection along a vertical complex wavy surface, Int. J. Heat Mass Transfer, (2006), 49, 281 – 286 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2005.06.026

[15] Somers, E., Theoretical considerations of combined thermal and mass transfer from a flat plate, J. Applied Mechanics, (1956), 23, 295 – 301 DOI: https://doi.org/10.1115/1.4011304

[16] Mather, W., Madden, A., and E. Piret, Simultaneous heat and mass transfer in free convection, Ind. Eng. Chem., (1957), 49, 961 – 968 DOI: https://doi.org/10.1021/ie50570a025

[17] Adams, J. and P. Mcfaddem, Simultaneous Heat and Mass Transfer in Free Convection with Opposing Body Forces, A. I. Ch. E. J., 1966, vol.12, pp.642 DOI: https://doi.org/10.1002/aic.690120407

[18] Saville, D. and S. Churchill, Simultaneous Heat and Mass Transfer in Free Convection Boundary Layer, A. I. Ch. E. J.,1970, vol. 16, pp. 268 DOI: https://doi.org/10.1002/aic.690160220

[19] Bottemanne, F., Theoretical solution of simultaneous heat and mass transfer by free convection about a vertical flat plate, Appl. Scient. Res., (1971), 25, 137 – 149 DOI: https://doi.org/10.1007/BF00382290

[20] Gebhart, B., and L. Pera, the nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. heat and mass transfer, (1971), 14, 2025 – 2050 DOI: https://doi.org/10.1016/0017-9310(71)90026-3

[21] Srinivasan, J., and D. Augirasa, Numerical study on double diffusion free convection from a vertical surface, Int. J. heat and mass transfer, (1988), 31, 2033 - 2038 DOI: https://doi.org/10.1016/0017-9310(88)90114-7

[22] Lin, H., and C. Wu, Combined heat and mass transfer by laminar natural convection from a vertical plate, Heat Mass transfer, (1995), 30, 369 - 376 DOI: https://doi.org/10.1007/BF01647440

[23] Lin, H., and C. Wu, Combined heat and mass transfer by laminar natural convection from a vertical plate with uniform heat flux and concentration, Heat Mass transfer, (1997), 32, 293- 299 DOI: https://doi.org/10.1007/s002310050124