Exact analytical results for the thermosolutal MHD Marangoni boundary layers

Stability analysis of MHD thermosolutal Marangoni convection boundary layer flow

“…Figure 1 depicts the values of the surface velocity, (0) f when r is varies with the effect of the magnetic field. We also manage to get the same figure as Figure 4 in [6]. Hence, we are confident that our present method produces the same results with [6].…”

“…We also manage to get the same figure as Figure 4 in [6]. Hence, we are confident that our present method produces the same results with [6]. Moreover, Figure 2 represents the variations of the Nusselt number with r. We can see from both figures that the second solution exists within a certain range.…”

“…The mathematical formulation for this problem follows closely to the problem by Magyari and Chamkha [6]. We consider the steady two-dimensional thermosolutal Marangoni boundary layer flow with the effects of the magnetic field.…”

“…Al-Mudhaf and Chamkha [5] investigated the magnetohydrodynamic (MHD) Marangoni convection boundary layer flow and obtained the same results. Magyari and Chamkha [6] also studied the Marangoni convection under the effects of the magnetic field. They obtained the exact analytical solution for the problem and concluded that the flow solutions depend solely on the thermosolutal surface tension ratio and the magnetic field parameters.…”

“…In this present problem, we extended the problem by Magyari and Chamkha [6] by employing the stability analysis on the dual solutions found in the problem. The stability analysis is computed using the bvp4c function in Matlab.…”