In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we ...In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.展开更多
The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,D...The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,Dufour and Soret effects are also considered in the model.The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs)by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method(RKF-45)with shooting process.The impacts of pertinent parameters on thermal,mass and velocity curves are deliberated graphically.Skin friction,rate of heat and mass transfer are also discussed graphically.Results reveal that,the increase in values of Brownian motion,thermophoresis,Dufour number,heating and radiative parameters improves the heat transfer.The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number.Finally,the escalating values of the radiative parameter decays the rate of heat transfer.展开更多
文摘In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.
文摘The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,Dufour and Soret effects are also considered in the model.The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs)by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method(RKF-45)with shooting process.The impacts of pertinent parameters on thermal,mass and velocity curves are deliberated graphically.Skin friction,rate of heat and mass transfer are also discussed graphically.Results reveal that,the increase in values of Brownian motion,thermophoresis,Dufour number,heating and radiative parameters improves the heat transfer.The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number.Finally,the escalating values of the radiative parameter decays the rate of heat transfer.
