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 numerically. The general governing partial differential equations 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 temperature 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 surface 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.

Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects

Exact analytical results for the thermosolutal MHD Marangoni boundary layers

Thermal and solutal Marangoni convection in In–Ga–Sb system

Analysis of MHD thermosolutal Marangoni convection with the heat generation and a first-order chemical reaction

Prandtl number effects for Marangoni convection over a flat surface

The natural and Marangoni convections formed spontaneously in the melt inside a two-dimensional rectangular open boat were investigated by means of an order-of-magnitude evaluation and a numerical analysis according to the finite difference method. A quantitative evaluation was made of the Grashof number, Marangoni number, Prandtl number and melt depth, all of which affect the interfacial velocity and the velocity distribution of the melt convection. It was concluded that Marangoni convection as well as natural convection is important when the melt is shallow.

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Masayasu Itoh

Papers

Natural and Marangoni convections in a two-dimensional rectangular open boat