Effects of wall waviness and temperature variations on the fluid flow and natural convection in an inclined corrugated channel

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    A parametric study involving the effects of some combinations of parameters, in particular, different combinations of the Rayleigh number, amplitude, temperature, and inclination angle of a two-dimensional long wavy-walled channel on a laminar incompressible fluid flow and natural convection within the channel is performed. The considered channel has an undulated wall as one side of the channel, and a parallel flat wall at a differentially different temperature as its counterpart. The channel sustains variable inclination angle, variable wavy wall amplitude, and variable temperature-difference between its two walls. A perturbation technique in terms of the small waviness of the undulated wall is performed to obtain a set of non-linear ordinary differential equations for the main flow and its perturbations. Solving this set of equations determines the streamline and temperature profiles for the imposed varying parameters. The results reveal that the fluid velocity along the channel axis increases with increasing the Rayleigh number, but decreases with increasing the channel inclination angle. The results also show that eddies appeared due to the steep undulations intensify as the temperature-difference between the two channel walls increases. The veracity of the present work is demonstrated through comparing the obtained results with those available in the literature.


  • Keywords


    Natural Convection; Inclined Channel; Wavy Wall; Perturbation Technique.

  • References


      [1] Lekoudis, S. G., Nayfeh, A. H., & Saric, W. S. (1976). Compressible boundary layers over wavy walls. Physics of Fluids, 19, 514–519. http://dx.doi.org/10.1063/1.861507.

      [2] Shankar, P. N., & Sinha, U. N. (1976). The Rayleigh problem for a wavy wall. Journal of Fluid Mechanics, 77, 243–256. http://dx.doi.org/10.1017/S0022112076002097.

      [3] Lessen, M., & Gangwani, S. T. (1976). Effects of small amplitude wall waviness upon the stability of the laminar boundary layer. Physics of Fluids, 19, 510–513. http://dx.doi.org/10.1063/1.861515.

      [4] Rees, D. A. S., & Pop, I. (1994). Free convection induced by a horizontal wavy surface in a porous medium. Fluid Dynamics Research, 14, 151–66. http://dx.doi.org/10.1016/0169-5983(94)90026-4.

      [5] Vajravelu, K., & Sastri, K. S. (1978). Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall. Journal of Fluid Mechanics, 86, 365–383. http://dx.doi.org/10.1017/S0022112078001172.

      [6] Vajravelu, K. (1980). Fluid flow and heat transfer in horizontal wavy channels. Acta Mechanica, 35, 245–258. http://dx.doi.org/10.1007/BF01190400.

      [7] Das, U. N., & Ahmed, N. (1992). Free convective MHD flow and heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall. Indian Journal of Pure and Applied Mathematics, 23, 295–204.

      [8] Das, U. N., & Deka, R. (1992). Free convection in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall: A numerical approach. Journal of Assam Science Society, 34(4), 33–43

      [9] Patidar, R. P., & Purohit G. N. (1998). Free convection flow of a viscous incompressible fluid in a porous medium between two long vertical wavy walls. Indian Journal of Mathematics, 40, 76–86.

      [10] Rao, D. R. V. P., Krishna, D. V., & Sivaprasad, R. (1987). MHD convection flow in a vertical wavy channel with temperature-dependent heat sources. Proceedings of the Indian National Science Academy, 53, 63–74.

      [11] Vajravelu, K. (1989). Combined free and forced convection in hydro magnetic flows in vertical wavy channels with traveling thermal waves. International Journal of Engineering Science, 27(3), 289–300. http://dx.doi.org/10.1016/0020-7225(89)90117-1.

      [12] Choudhury, R., & Das, A. (2000). Free convection flow of a non-newtonian fluid in a vertical channel. Defence Science Journal, 50(1), 37–44. http://dx.doi.org/10.14429/dsj.50.3322.

      [13] Rajeev, T., & Jain, N. C. (2004). MHD flow with slip effects and temperature-dependent heat source in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall. Defence Science Journal, 54(1), 21–29. http://dx.doi.org/10.14429/dsj.54.2018.

      [14] Guria, M., & Jana, R. N. (2006). Hydrodynamic flows through vertical wavy channel with travelling thermal waves embedded in porous medium. International Journal of Applied Mechanics and Engineering, 11(3), 609–621.

      [15] Muthuraj, R., & Srinivas, S. (2010). Mixed convective heat and mass transfer in a vertical wavy channel with traveling thermal waves and porous medium. Computers & Mathematics with Applications, 59, 3516–3528. http://dx.doi.org/10.1016/j.camwa.2010.03.045.

      [16] Umavathi, J. C., & Shekar, M. (2011). Mixed convection flow and heat transfer in a vertical wavy channel containing porous and fluid layer with traveling thermal waves. International Journal of Engineering, Science and Technology, 197(3), 196-219.

      [17] Gireesha B. J., & Mahanthesh, B. (2013). Perturbation solution for radiating viscoelastic fluid flow and heat transfer with convective boundary condition in nonuniform channel with hall current and chemical reaction. ISRN Thermodynamics, Article ID 935481, 14. http://dx.doi.org/10.1155/2013/935481.

      [18] Kumar, J. P., & Umavathi, J. C. (2013). Free convective flow in an open-ended vertical porous wavy channel with a perfectly conductive thin baffle. Heat Transfer—Asian Research, DOI: 10.1002/htj.21118. http://dx.doi.org/10.1002/htj.21118.

      [19] Umavathi, J. C., & Shekar, M. (2014). Mixed convective flow of immiscible fluids in a vertical corrugated channel with traveling thermal waves. Journal of King Saud University – Engineering Sciences, 26, 49–68. http://dx.doi.org/10.1016/j.jksues.2012.11.002.

      [20] Bejan, A. (2004). Convective heat transfer. (3rd Ed.). New York: Wiley, (140–142).


 

View

Download

Article ID: 4155
 
DOI: 10.14419/ijamr.v4i1.4155




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.