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Run-Up of Linear Long Waves on Uniform Slope in Lagrangian Description

100%

Chybicki W.

Archives of Hydro-Engineering and Environmental Mechanics

2006

tom Vol. 53, nr 2

97-104

The case of linear, two-dimensional long waves on a uniform slope is considered. It is assumed that the fluid is nonviscous and incompressible. In the present paper the description of the long wave proposed by Wilde (Wilde, Chybicki 2004) is based on the fundamental assumption that the vertical material lines of fluid remain vertical during the entire motion. The equations of motion are derived with the help of a variational formulation of the problem. The Lagrangian is the difference between the kinetic and potential energy of the fluid. In the paper a correction followed from dispersion to the results obtained by Shuto is presented.

On a class of multivalent functions

100%

Patel J. , Mohanty A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

1999

tom z. 23 [175]

85-91

In the paper some special class of multivalent functions connected with the hypergeometric series are investigated.

On Kaluza’s sign criterion for reciprocal power series

100%

Baricz A. , Vesti J. , Vuorinen M.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 2

T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.

Non-isothermal hydromagnetic convection in a porous medium with heat sink: hypergeometric function solutions

51%

Beg O. A. , Takhar H. S. , Beg T. A. , Singh A. K.

International Journal of Applied Mechanics and Engineering

2007

tom Vol. 12, no 2

337-351

The present paper deals with the free convection laminar boundary layer flow and heat transfer of an incompressible, electrically conducting, viscous fluid through a porous medium caused by stretching a porous wall in the presence of a heat source and under the influence of uniform magnetic field. Exact solutions of the basic equations of momentu m and energy ar e obtained after reducing them i n to non-linear ordinary differential equations and using confluent hypergeometric functions. The variations in the velocity field and temperature distribution with the Prandtl number (Pr), hydromagnetic parameter (M), permeability param eter (K), suction parameter (N), wall temperature parameler (S), and the heat sink parameter (Q) are obtained and depicted graphically. The skin-friction at the wall is also derived, and the numerical values for various physical parameters are also tabulaled. Magnetic field (M) is seen to reduce both longitudinal and translational velocities and also lower temperalures, aiding in controlling momentum and heat transfer during materiaIs processing. Suction (N) posivitely influences the transverse velocity but depresses the longitudinal velocity magnitudes as we II as decreasing tempcratures. Suction therefore also assists in controlling heat transfer in Ihe boundary layer. Increasing permeability parameter (K) depresses the longitudinal velocity but elevates transverse velocities and increases the skin friction at the wall. Both rising temperature (non-isothermal wall) parameter (S) and heat sink parameter (Q) decrease temperature values. The model finds applications in nucIear engineering control systems and MHD energy systems.