Meccanica (2009) 44: 573–586 DOI 10.1007/s11012-009-9197-z The effects of variable properties on MHD unsteady natural convection heat and mass transfer over a vertical wavy surface Nasser S. Elgazery · Nader Y. Abd Elazem Received: 9 March 2008 / Accepted: 16 January 2009 / Published online: 6 March 2009 © Springer Science+Business Media B.V. 2009 Abstract A mathematical model will be analyzed in order to study the effects of variables viscosity and thermal conductivity on unsteady heat and mass trans- fer over a vertical wavy surface in the presence of magnetic field numerically by using a simple coor- dinate transformation to transform the complex wavy surface into a flat plate. The fluid viscosity is as- sumed to vary as a exponential function of tempera- ture and thermal conductivity is assumed to vary lin- early with temperature. An implicit marching Cheby- shev collocation scheme is employed for the analy- sis. Numerical solutions are obtained for different val- ues of variable viscosity, variable thermal conductivity and MHD variation parameter. Numerical results show that, variable viscosity, variable thermal conductivity and MHD variation parameter have significant influ- ences on the velocity, temperature and concentration profiles as well as for the local skin friction, Nusselt number and Sherwood number. N.S. Elgazery · N.Y. Abd Elazem Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Heliopolis, Cairo, Egypt Present address: N.S. Elgazery ( ) Deanship of Educatonail Services, Preparatory Year Unit, Al-Qassim University, P.O. Box 6595, Al-Qassim, Buraidah 51452, Saudi Arabia e-mail: nasser_522000@yahoo.com Keywords Wavy surface · Variable properties · Chebyshev collocation method PACS 47.11.-j · 47.11.kb 1 Introduction Our concern is with the effects of variables viscos- ity and thermal conductivity on MHD unsteady nat- ural convection heat and mass transfer along a ver- tical wavy surface. The most common type of body force, which acts on a fluid, is due to gravity, so that the body force can be defined as in magnitude and di- rection by the acceleration due to gravity. Sometimes, electromagnetic effects are important. The electric and magnetic fields themselves must obey a set of phys- ical laws, which are expressed by Maxwell’s equa- tions. The solution to such problems requires the si- multaneous solution of the equations of fluid mechan- ics and of electromagnetism. One special case of this type of coupling is the field known as magnetohydro- dynamic (MHD). Many works on heat and mass trans- fer have focused mainly on regular geometries, the re- cent studies of them such as heat and mass transfer along a vertical plate with variable surface temper- ature and concentration in the presence of the mag- netic field studied by Elbashbeshy [1]. Similarity so- lutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption studied by