Se proporcionan algunas desigualdades tipo Grüss para la integral de Riemann-Stieltjes de integra... more Se proporcionan algunas desigualdades tipo Grüss para la integral de Riemann-Stieltjes de integrandos de valores continuos complejos definidos sobre el circulo unitario complejo C(0, 1) y varias subclases de integradores son dados. Aplicaciones naturales para funciones de operadores unitarios en espacios de Hilbert son proporcionadas.
Abstract This paper presents a numerical investigation on steady triple diffusive mixed convectio... more Abstract This paper presents a numerical investigation on steady triple diffusive mixed convection boundary layer flow past a vertical plate moving parallel to the free stream in the upward direction. The temperature of the plate is assumed to be hotter compared to the surrounded fluid temperature. Sodium chloride and Sucrose are chosen as solutal components which are added in the flow stream from below with various concentration levels. The concentrations of NaCl-Water and Sucrose-Water are considered to be higher near the wall compared to the concentrations of NaCl-Water and Sucrose-Water within the free stream. The coupled nonlinear partial differential equations are transformed using the non-similarity variables and solved numerically by an implicit finite difference scheme with quasi-linearization technique. The effects of Richardson numbers, velocity ratio parameters, ratio of buoyancy parameters and Schmidt numbers of both the solutal components on the fluid flow, thermal and species concentration fields are investigated. Results indicate that the species concentration boundary layer thickness decreases with the increase of Schmidt numbers and that increases with the ratio of buoyancy parameters for both the species components. Overall, the mass transfer rate is found to increase with Schmidt numbers approximately 4.36% and 64.56% for NaCl and Sucrose, respectively.
International Journal of Non-Linear Mechanics, 1998
... 1.2)can be expressed in terms of the ratio of the characteristic thickness of the thin film t... more ... 1.2)can be expressed in terms of the ratio of the characteristic thickness of the thin film to the thickness of the Ekman boundary layer in a ... In Section 2the thin-film equations for an incompressible viscous fluid with respect to a frame of reference attached to the rotating disk ...
Zeitschrift für angewandte Mathematik und Physik, 2014
An energy method is used to analyze the stability of solutions of a mixed space-time diffusion eq... more An energy method is used to analyze the stability of solutions of a mixed space-time diffusion equation that has application in the unidirectional flow of a second-grade fluid and the distribution of a compound Poisson process. Solutions to the model equation satisfying Dirichlet boundary conditions are proven to dissipate total energy and are hence stable. The stability of asymptotic solutions satisfying Neumann boundary conditions coincides with the condition for the positivity of numerical solutions of the model equation from a Crank–Nicolson scheme. The Crank–Nicolson scheme is proven to yield stable numerical solutions for both Dirichlet and Neumann boundary conditions for positive values of the critical parameter. Numerical solutions are compared to analytical solutions that are valid on a finite domain.
An energy method is used to analyze the stability of solutions of a mixed space-time diffusion eq... more An energy method is used to analyze the stability of solutions of a mixed space-time diffusion equation that has application in the unidirectional flow of a second-grade fluid and the distribution of a compound Poisson process. Solutions to the model equation satisfying Dirichlet boundary conditions are proven to dissipate total energy and are hence stable. The stability of asymptotic solutions satisfying Neumann boundary conditions coincides with the condition for the positivity of numerical solutions of the model equation from a Crank–Nicolson scheme. The Crank–Nicolson scheme is proven to yield stable numerical solutions for both Dirichlet and Neumann boundary conditions for positive values of the critical parameter. Numerical solutions are compared to analytical solutions that are valid on a finite domain.
ABSTRACT The third-order ODE yny‴=1 obtained by investigating travelling-wave solutions or steady... more ABSTRACT The third-order ODE yny‴=1 obtained by investigating travelling-wave solutions or steady-state solutions of the lubrication equation is considered. The third-order ODE yny‴=1 admits two generators of Lie point symmetries. These generators of Lie point symmetries effect a reduction of the third-order ODE to first order. The problem is to determine the initial values of the second derivative, when the initial height and gradient are specified, for which a solution to yny‴=1 touches the contact line y=0. Phase planes corresponding to different representations of the first-order ODE for the cases n2, n=2 and n>2 are analyzed. For the case n2 we are able to determine the initial values of the second derivative for which the solution touches the contact line. For n≥2 no values of the initial second derivative are obtained for which a solution touches the contact line. A symmetry reduction of autonomous first integrals of the third-order ODE yny‴=1 is then investigated. For the cases n=0, n=5/4 and n=5/2 the third-order ODE admits second-order autonomous first integrals. The case n=5/4 is special because the second-order autonomous first integral admits the same two generators of Lie point symmetries as the original third-order ODE and can hence be reduced to an algebraic equation. Investigations of the phase plane for the case n=5/4 shows that the original third-order ODE satisfies the contact line condition y=0 for initial values of the second derivative y″(0)≤−3.
Fourier and Bessel function solutions of two mixed derivative equations are investigated. For the... more Fourier and Bessel function solutions of two mixed derivative equations are investigated. For the appropriate sign of the material constants in the derivation of the mixed derivative equation, we obtain both Fourier and Bessel function solutions that tend to the corresponding solutions of the phenomenological diffusion equation. For the opposite sign of the material constants, the solutions diverge.
Se proporcionan algunas desigualdades tipo Grüss para la integral de Riemann-Stieltjes de integra... more Se proporcionan algunas desigualdades tipo Grüss para la integral de Riemann-Stieltjes de integrandos de valores continuos complejos definidos sobre el circulo unitario complejo C(0, 1) y varias subclases de integradores son dados. Aplicaciones naturales para funciones de operadores unitarios en espacios de Hilbert son proporcionadas.
Abstract This paper presents a numerical investigation on steady triple diffusive mixed convectio... more Abstract This paper presents a numerical investigation on steady triple diffusive mixed convection boundary layer flow past a vertical plate moving parallel to the free stream in the upward direction. The temperature of the plate is assumed to be hotter compared to the surrounded fluid temperature. Sodium chloride and Sucrose are chosen as solutal components which are added in the flow stream from below with various concentration levels. The concentrations of NaCl-Water and Sucrose-Water are considered to be higher near the wall compared to the concentrations of NaCl-Water and Sucrose-Water within the free stream. The coupled nonlinear partial differential equations are transformed using the non-similarity variables and solved numerically by an implicit finite difference scheme with quasi-linearization technique. The effects of Richardson numbers, velocity ratio parameters, ratio of buoyancy parameters and Schmidt numbers of both the solutal components on the fluid flow, thermal and species concentration fields are investigated. Results indicate that the species concentration boundary layer thickness decreases with the increase of Schmidt numbers and that increases with the ratio of buoyancy parameters for both the species components. Overall, the mass transfer rate is found to increase with Schmidt numbers approximately 4.36% and 64.56% for NaCl and Sucrose, respectively.
International Journal of Non-Linear Mechanics, 1998
... 1.2)can be expressed in terms of the ratio of the characteristic thickness of the thin film t... more ... 1.2)can be expressed in terms of the ratio of the characteristic thickness of the thin film to the thickness of the Ekman boundary layer in a ... In Section 2the thin-film equations for an incompressible viscous fluid with respect to a frame of reference attached to the rotating disk ...
Zeitschrift für angewandte Mathematik und Physik, 2014
An energy method is used to analyze the stability of solutions of a mixed space-time diffusion eq... more An energy method is used to analyze the stability of solutions of a mixed space-time diffusion equation that has application in the unidirectional flow of a second-grade fluid and the distribution of a compound Poisson process. Solutions to the model equation satisfying Dirichlet boundary conditions are proven to dissipate total energy and are hence stable. The stability of asymptotic solutions satisfying Neumann boundary conditions coincides with the condition for the positivity of numerical solutions of the model equation from a Crank–Nicolson scheme. The Crank–Nicolson scheme is proven to yield stable numerical solutions for both Dirichlet and Neumann boundary conditions for positive values of the critical parameter. Numerical solutions are compared to analytical solutions that are valid on a finite domain.
An energy method is used to analyze the stability of solutions of a mixed space-time diffusion eq... more An energy method is used to analyze the stability of solutions of a mixed space-time diffusion equation that has application in the unidirectional flow of a second-grade fluid and the distribution of a compound Poisson process. Solutions to the model equation satisfying Dirichlet boundary conditions are proven to dissipate total energy and are hence stable. The stability of asymptotic solutions satisfying Neumann boundary conditions coincides with the condition for the positivity of numerical solutions of the model equation from a Crank–Nicolson scheme. The Crank–Nicolson scheme is proven to yield stable numerical solutions for both Dirichlet and Neumann boundary conditions for positive values of the critical parameter. Numerical solutions are compared to analytical solutions that are valid on a finite domain.
ABSTRACT The third-order ODE yny‴=1 obtained by investigating travelling-wave solutions or steady... more ABSTRACT The third-order ODE yny‴=1 obtained by investigating travelling-wave solutions or steady-state solutions of the lubrication equation is considered. The third-order ODE yny‴=1 admits two generators of Lie point symmetries. These generators of Lie point symmetries effect a reduction of the third-order ODE to first order. The problem is to determine the initial values of the second derivative, when the initial height and gradient are specified, for which a solution to yny‴=1 touches the contact line y=0. Phase planes corresponding to different representations of the first-order ODE for the cases n2, n=2 and n>2 are analyzed. For the case n2 we are able to determine the initial values of the second derivative for which the solution touches the contact line. For n≥2 no values of the initial second derivative are obtained for which a solution touches the contact line. A symmetry reduction of autonomous first integrals of the third-order ODE yny‴=1 is then investigated. For the cases n=0, n=5/4 and n=5/2 the third-order ODE admits second-order autonomous first integrals. The case n=5/4 is special because the second-order autonomous first integral admits the same two generators of Lie point symmetries as the original third-order ODE and can hence be reduced to an algebraic equation. Investigations of the phase plane for the case n=5/4 shows that the original third-order ODE satisfies the contact line condition y=0 for initial values of the second derivative y″(0)≤−3.
Fourier and Bessel function solutions of two mixed derivative equations are investigated. For the... more Fourier and Bessel function solutions of two mixed derivative equations are investigated. For the appropriate sign of the material constants in the derivation of the mixed derivative equation, we obtain both Fourier and Bessel function solutions that tend to the corresponding solutions of the phenomenological diffusion equation. For the opposite sign of the material constants, the solutions diverge.
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Papers by E. Momoniat