Effects of Viscous Dissipation on MHD Natural Convection Flow along a Vertical Wavy Surface with Heat Generation

K. H. Kabir, M. A. Alim, L. S. Andallah

Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.
Department of Mathematics, Jahangirnagar University, Savar, Bangladesh.
Department of Mathematics, Mohammadpur Kendriya University College, Dhaka, Bangladesh.

DOI: 10.4236/ajcm.2013.32015                

Abstract

The effect of external magnetic field and internal heat generation or absorption on a steady two-dimensional natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a non-dimensional form using suitable set of dimensionless variables. The transformed boundary layer equations are solved numerically using the implicit finite difference method, known as Keller-box scheme. Numerical results for velocity, temperature, skin friction, the rate of heat transfer are obtained for different values of the selected parameters, such as viscous dissipation parameter (Vd), heat generation parameter (Q), magnetic parameter (M) and presented graphically and discussed. Streamlines and isotherms are presented for selected values of heat generation parameter and explained.

Keywords

Natural Convection; Wavy Surface; Magnetohydrodynamics; Viscous Dissipation; Prandtl Number; Heat Generation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. S. Yao, “Natural Convection along a Vertical Wavy Surface,” ASME Journal of Heat Transfer, Vol. 105, No. 3, 1983, pp. 465-468. doi:10.1115/1.3245608
[2]	S. G. Moulic and L. S. Yao, “Mixed Convection along Wavy Surface,” ASME Journal of Heat Transfer, Vol. 111, No. 4, 1989, pp. 974-979. doi:10.1115/1.3250813
[3]	M. A. Alim, S. Alam and M. Miraj, “Effects of Temperature Dependent Thermal Conductivity on Natural Convection Flow along a Vertical Wavy Surface with Heat Generation,” International Journal of Engineering & Technology, Vol. 11, No. 6, 2011, pp. 60-69.
[4]	M. A. Hossain and D. A. S. Rees, “Combined Heat and Mass Transfer in Natural Convection Flow from a Vertical Wavy Surface,” Acta Mechanica, Vol. 136, No. 3-4, 1999, pp. 133-141. doi:10.1007/BF01179253
[5]	C. C. Wang and C. K. Chen, “Transient Force and Free Convection along a Vertical Wavy Surface in Micropolar Fluid,” International Journal of Heat and Mass Transfer, Vol. 44, No. 17, 2001, pp. 3241-3251. doi:10.1016/S0017-9310(00)00329-X
[6]	K. C. A. Alam, M. A. Hossain and D. A. S. Rees, “Magnetohydrodynamic Free Convection along a Vertical Wavy Surface,” Journal of Applied Mechanical Engineering, Vol. 1, 1997, pp. 555-566.
[7]	J. H. Jang, W. M. Yan and H. C. Liu, “Natural Convection Heat and Mass Transfer along a Vertical Wavy Surface,” International Journal of Heat Mass Transfer, Vol. 46, No. 6, 2003, pp. 1075-1083. doi:10.1016/S0017-9310(02)00361-7
[8]	J. H. Jang and W. M. Yan, “Mixed Convection Heat and Mass Transfer along a Vertical Wavy Surface,” International Journal of Heat Mass Transfer, Vol. 47, No. 3, 2004, pp. 419-428. doi:10.1016/j.ijheatmasstransfer.2003.07.020
[9]	M. M. Molla, M. A. Hossain and L. S. Yao, “Natural Convection Flow along a Vertical Wavy Surface with Uniform Surface Temperature in Presence of Heat Generation/Absorption,” International Journal of Thermal Sciences, Vol. 43, No. 2, 2004, pp. 157-163. doi:10.1016/j.ijthermalsci.2003.04.001
[10]	B. Tashtoush and M. Al-Odat, “Magnetic Field Effect on Heat and Fluid flow over a Wavy Surface with a Variable Heat Flux,” Journal of Magnetism and Magnetic Materials, Vol. 268, No. 3, 2004, pp. 357-363. doi:10.1016/S0304-8853(03)00547-X
[11]	M. A. Hossain, S. Kabir and D. S. A. Rees, “Natural Convection of Fluid with Temperature Dependent Viscosity from Heated Vertical Wavy Surface,” Zeitschrift für angewandte Mathematik und Physik, Vol. 53, No. 1, 2002, pp. 48-57. doi:10.1007/s00033-002-8141-z
[12]	N. Parveen and M. A. Alim, “Joule Heating Effect on Magnetohydrodynamic Natural Convection flow along a Vertical Wavy Surface with Viscosity Dependent on Temperature,” International Journal of Energy & Technology, Vol. 3, 2011, pp. 1-10.