Abstract
In this venture, the challenge to study the mathematical model and its approximate solution for boundary layer thermosolutal Marangoni convection on a permeable flat surface with thermophoretic velocity and aligned magnetic field has been undertaken. Using a special type of transformation, governing PDEs are converted into ODEs. A semi-analytical method known as optimal homotopy analysis method(OHAM) has been used to develop solutions for proposed mathematical model. The novelty of the study is in the exploration of simultaneous impacts of thermophoretic velocity and inclined magnetic field on flow and heat-mass transport while mass suction/injection is using OHAM. Solutions obtained by OHAM are compared with other published literature and it is revealed that our numerical values are improved by approximately up to 7%. The obtained solutions for various important parameters are displayed in the form of graphs and tables. The study explores the variable behaviors of velocity, temperature, and concentration for growths of Marangoni number, magnetic parameter, and thermophoretic parameter, while there exists mass suction or injection. It reveals that in both cases, i.e. suction and injection cases, velocity grows and temperature and concentration reduce with increasing magnetic parameters and inclination angle of aligned magnetic field and these variations are more prominent in case injection. If the magnetic field is orthogonal to the flat surface, then corresponding Lorentz force produces maximum resistance for the transport phenomenon. The spreading effect of induced surface velocity due to Marangoni convection is observed in the entire boundary layer region in case of mass suction, while for injection case it is witnessed only near the surface. Whereas, for higher value of thermophoretic velocity, the concentration exhibits a reducing trend. For rising values of Marangoni number, wall velocity, Nusselt number, and Sherwood number significantly grow, while magnetic field has contrary impacts.
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