Journal of Naval Architecture and Marine Engineering · 2014 · 13 citations · 35 references
EngineeringMechanical EngineeringPhysicsDifferential EquationsFluid DynamicsHeat TransferHeat ConductionHeat FlowHeat Transfer AnalysisHeat Transfer In FluidsMass TransferMass TransportConvectionCoupled Reaction-diffusion EquationsMass Transfer EffectsNusselt NumberSecond-order Differential EquationsSherwood NumberSimilarity TransformationsSteady Flow
This paper concerns with a steady two-dimensional flow of an electrically conducting incompressible dissipating fluid over an inclined semi-infinite porous surface with heat and mass transfer in presence of chemical reaction. The flow is permeated by a uniform transverse magnetic field. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The coupled ordinary differential equations along with the boundary conditions are solved numerically. The effects of various parameters on velocity, temperature and concentration fields as well as skin-friction, Nusselt number and Sherwood number are presented graphically and in tabulated form. DOI: http://dx.doi.org/10.3329/jname.v11i2.18313
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Applications of lie groups to differential equations
Acta Applicandae Mathematicae · 1990 · 6.1K citations
Group Analysis of Differential Equations.
Willard Miller · American Mathematical Monthly · 1985 · 2.5K citations