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Lie group analysis of natural convection heat and mass transfer in an inclined surface. (English) Zbl 1125.93330
Summary: Natural convection heat transfer fluid flow past an inclined semi-infinite surface in the presence of solute concentration is investigated by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations by the translation and scaling symmetries. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. It is found that the velocity increases and temperature and concentration of the fluid decrease with an increase in the thermal and solutal Grashof numbers. The velocity and concentration of the fluid decrease and temperature increases with increase in the Schmidt number.
MSC:
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)
76R10Free convection (fluid mechanics)
80A20Heat and mass transfer, heat flow