ORIGINAL Ali Al-Mudhaf Æ Ali J. Chamkha Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects Received: 12 May 2004 / Accepted: 19 November 2004 / Published online: 11 October 2005 Ó Springer-Verlag 2005 Abstract The problem of steady, laminar, thermosolutal Marangoni convection flow of an electrically-conducting fluid along a vertical permeable surface in the presence of a magnetic field, heat generation or absorption and a first-order chemical reaction effects is studied numeri- cally. The general governing partial differential equa- tions are converted into a set of self-similar equations using unique similarity transformations. Numerical solution of the similarity equations is performed using an implicit, iterative, tri-diagonal finite-difference method. Comparisons with previously published work is performed and the results are found to be in excellent agreement. Approximate analytical results for the tem- perature and concentration profiles as well as the local Nusselt and sherwood numbers are obtained for the conditions of small and large Prandtl and Schmidt numbers are obtained and favorably compared with the numerical solutions. The effects of Hartmann number, heat generation or absorption coefficient, the suction or injection parameter, the thermo-solutal surface tension ratio and the chemical reaction coefficient on the velocity, temperature and concentration profiles as well as quantitites related to the wall velocity, boundary- layer mass flow rate and the Nusselt and Sherwood numbers are presented in graphical and tabular form and discussed. It is found that a first-order chemical reaction increases all of the wall velocity, Nusselt and Sherwood numbers while it decreases the mass flow rate in the boundary layer. Also, as the thermo-solutal sur- face tension ratio is increased, all of the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are predicted to increase. However, the exact opposite behavior is predicted as the magnetic field strength is increased. Keywords Marangoni convection Æ Magnetic field Æ Heat generation or absorption Æ Chemical reaction Æ Similarity solutions Æ Permeable surface Nomenclature A temperature gradient coefficient A * concentration gradient coefficient B 0 magnetic induction c dimensional concentration C dimensionless concentration c¢¢ mass flux c p specific heat at constant pressure C 1 similarity transformation coefficient C 2 similarity transformation coefficient D mass Diffusivity f 0 dimensionless suction or injection velocity f(g) stream function similarity variable K dimensionless chemical reaction coefficient m Mass flow rate per unit width M Hartmann number Ma marangoni number, Eq. 16 Nu Nusselt number, Eq. 34 Pr Prandtl number Q 0 dimensional heat generation or absorption coefficient q¢¢ heat flux r thermo-solutal surface tension ratio R dimensionl chemical reaction parameter Re Reynolds number, Eq. 18 Sc Schmidt number Sh Sherwood number, Eq. 35 T temperature u, v xcomponent and y-component of velocity, respectively v 0 dimensional suction or injection velocity x, y coordinates Greek symbols a thermal diffusivity d boundary layer thickness A. Al-Mudhaf Æ A. J. Chamkha (&) Manufacturing Engineering Department, The Public Authority for Applied Education and Training, 42325, Shuweikh, 70654, Kuwait Heat Mass Transfer (2005) 42: 112–121 DOI 10.1007/s00231-004-0611-8