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Group similarity transformation of a non‐Newtonian laminar flow past a vertical plate
Author(s) -
Kassem M.M.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700062
Subject(s) - laminar flow , prandtl number , boundary layer , matrix similarity , mathematics , partial differential equation , ordinary differential equation , flow (mathematics) , similarity solution , blasius boundary layer , newtonian fluid , mechanics , reynolds number , mathematical analysis , heat transfer , boundary layer thickness , physics , differential equation , geometry , turbulence
The heat and mass transfer of a non‐Newtonian fluid past a continuous moving vertical sheet subjected to constant heat flux is analyzed using the group similarity transformation method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. Two cases for the external flow are analytically obtained during the transformation process. One is new; u w = x / t , while the other corresponds to Falkner–Skan case. For both cases the ordinary differential equations are solved numerically using the shooting method. The effect of Prandtl and Reynolds numbers as well as the fluid flow index n on the velocity and temperature of the boundary‐layer, is investigated. A comparison with previous numerical work is then presented.