## Abstract

Prandtl velocity boundary layer has conceptualized the mathematical description of boundary layers that led to wide applications in engineering processes. In coupled dissipative boundary layer, the surface tension gradient play an important role at the interface in determining the characteristics of the boundary layer flow. In this study, the surface tension is assumed to depend linearly or quadratically on temperature and/or concentration gradients. Four mathematical models are formulated for the steady dissipative boundary layer flows. The systems of the steady boundary layer equations in form of system of partial differential equations (PDE) are transformed to system of ordinary differential equations (ODE) by similarity transformation. The ODE systems are solved numerically by using the Runge-Kutta-Fehlberg with shooting technique. The first problem considered the linear dependence of surface tension on temperature and solute concentration on the momentum and heat and mass transfer of MHD mixed convection boundary layers with suction or injection. The results show that as thermal and solutal Marangoni parameters increase the velocity, thermal and concentration boundary layer thickness for buoyancy-opposed flow increases but their thickness reduce for buoyancyassisted flow. In the second problem, the combined effects of power law temperature and solute concentration on the surface tension, species concentration and pressure gradient are considered. The results shows thermosolutal surface tension ratio increases the velocity boundary layer thickness but decrease the temperature and concentration boundary layer thickness. The effect of porosity is considered in the third problem and significant effect of porosity can be observed in the momentum boundary layer but less impact on the rate of heat and mass transfer. In the fourth problem, the flow and temperature patterns on thermal Marangoni convection are studied. The effect of magnetic field, porous medium and permeable surface with the quadratic temperature dependence surface tension are considered. The results show the increase of thermocapillary or Marangoni effects and weaker magnetic field strength lead to stronger reverse flow.

## Metadata

Divisions: | Faculty of Computer and Mathematical Sciences |
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Item ID: | 16382 |

Uncontrolled Keywords: | Thermosolutal marangoni; Convective boundary layer equations |

Last Modified: | 27 Mar 2017 09:32 |