The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite...The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropyI this dissipation coefficient and the magnetic field in each period are smaller than those of sound Waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.展开更多
It is increasingly apparent that the inclusion of mass transfer aspects,together with certain thermal conditions,in the momentum and energy equations governing MHD flows leads to a numbers of real life applications.Ke...It is increasingly apparent that the inclusion of mass transfer aspects,together with certain thermal conditions,in the momentum and energy equations governing MHD flows leads to a numbers of real life applications.Keeping this in view,we have attempted an exact analysis of heat and mass transfer aspects in transient hydromagnetic free convective flow of an incompressible viscous fluid through a vertical pipe under an externally applied magnetic field,assuming presence of chemical reaction and heat source/sink.The governing PDEs,which simplify to a set of 3 linear ODEs in the physical set up considered here,have been solved using Laplace transform technique,with solutions for key physical variables presented in the term of Bessel and modified Bessel functions.The influence of governing non-dimensional parameters,namely,Hartmann number,Schmidt number,source/sink parameter,Prandtl number and chemical reaction parameter,has been illustrated on the developing velocity and some concentration profiles.Some important quantities of engineering interest-surface skin friction and volumetric flow rates-have been computed too and analysed.Some notable finding worth mentioning are:(a)heat source presence causes higher fluid velocity as compared to the heat sink;(b)all important surface shear stress can be suitably controlled,among others,by chemical reaction parameter and Schmidt number.The key challenge of this study has been to obtain exact closed-form solutions of the field equations,including cumbersome Laplace inverses.This study finds innovative applications in the emerging fields such as magnetic materials processing,chemical processes,solar energy systems,etc.展开更多
基金Project supported by the National Natural Science Foundation of China(No. 10571024)the Natural Science Foundation of Henan Province of China (No.200510078005)the Science Foundation of Educational Department of Henan Province of China (No.200511051700)
文摘The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropyI this dissipation coefficient and the magnetic field in each period are smaller than those of sound Waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.
基金The author,Naveen Dwivedi,is thankful to the University Grant Commission,New Delhi for financial support(UGC Ref.No.1274/PWD).
文摘It is increasingly apparent that the inclusion of mass transfer aspects,together with certain thermal conditions,in the momentum and energy equations governing MHD flows leads to a numbers of real life applications.Keeping this in view,we have attempted an exact analysis of heat and mass transfer aspects in transient hydromagnetic free convective flow of an incompressible viscous fluid through a vertical pipe under an externally applied magnetic field,assuming presence of chemical reaction and heat source/sink.The governing PDEs,which simplify to a set of 3 linear ODEs in the physical set up considered here,have been solved using Laplace transform technique,with solutions for key physical variables presented in the term of Bessel and modified Bessel functions.The influence of governing non-dimensional parameters,namely,Hartmann number,Schmidt number,source/sink parameter,Prandtl number and chemical reaction parameter,has been illustrated on the developing velocity and some concentration profiles.Some important quantities of engineering interest-surface skin friction and volumetric flow rates-have been computed too and analysed.Some notable finding worth mentioning are:(a)heat source presence causes higher fluid velocity as compared to the heat sink;(b)all important surface shear stress can be suitably controlled,among others,by chemical reaction parameter and Schmidt number.The key challenge of this study has been to obtain exact closed-form solutions of the field equations,including cumbersome Laplace inverses.This study finds innovative applications in the emerging fields such as magnetic materials processing,chemical processes,solar energy systems,etc.
