Analytical solutions of magnetohydrodynamical problems on a flow of conducting fluid in the entrance region of channels in a strong magnetic field šķidruma plūsmu kanāla ieejas apgabalā stiprā magnētiskā laukā
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Latvijas Universitāte
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eng
Abstract
Darbā iegūti analītiskie atrisinājumi magnetohidrodinamiskiem (MHD) uzdevumiem par
elektrovadoša šķidruma plūsmu plakanā un cilindriskā kanālā stiprā magnētiskā laukā
gadījumiem, kad šķidrums ietek kanālos caur galīga platuma spraugu vai caur galīga rādiusa
atveri kanāla sānu malā. Pamatojoties uz iegūtajiem atrisinājumiem, veikta plūsmas ātruma lauka
skaitliskā analīze. Iegūti uzdevumu asimptotiskie atrisinājumi lieliem Hartmana skaitļiem.
Turklāt darbā pētīta pilna spiediena spēka šķidruma ieplūdes apgabalā atkarība no funkcijas
veida, ar kuru ir uzdots ātruma robežnosacījums. Pētījums veikts analītiski, risinot divas
hidrodinamiskas problēmas un divas MHD problēmas par viskoza šķidruma ietecēšanu pustelpā
caur galīga platuma spraugu vai caur galīga rādiusa atveri. Gadījumā, kad uz ieejas pustelpā
uzdots parabolisks ātruma profils, MHD uzdevumam iegūti jauni asimptotiskie atrisinājumi pie
lieliem Hartmana skaitļiem. Visi uzdevumi promocijas darbā atrisināti Stoksa vai Ozeena
tuvinājumā, izmantojot integrālo transformāciju metodi.
The PhD thesis is concerned with theoretical study of new magnetohydrodynamic (MHD) problems on a flow of a conducting fluid in an initial part of a plane or circular channel at the condition that fluid flows into the channel through a split of finite width or through a hole of finite radius on the channel’s lateral side. On the basis of the obtained solutions the velocity field of the flow is analysed numerically and asymptotic solutions at large Hartmann numbers are obtained. Moreover, in the thesis the dependence of the full pressure force in the entrance region on the profile of the inlet velocity in this region is studied analytically by means of analytical solution of two hydrodynamic problems and two MHD problems on an inflow of a viscous fluid into a half-space through a plane split of finite width or through a round hole of finite radius. Both the case of a uniform inlet velocity profile and the case of a parabolic velocity profile are considered. New asymptotic solutions for MHD problems are obtained at large Hartmann numbers for the case of parabolic inlet velocity profile. All problems in the thesis are solved in Stokes or Oseen approximation by using integral transforms.
The PhD thesis is concerned with theoretical study of new magnetohydrodynamic (MHD) problems on a flow of a conducting fluid in an initial part of a plane or circular channel at the condition that fluid flows into the channel through a split of finite width or through a hole of finite radius on the channel’s lateral side. On the basis of the obtained solutions the velocity field of the flow is analysed numerically and asymptotic solutions at large Hartmann numbers are obtained. Moreover, in the thesis the dependence of the full pressure force in the entrance region on the profile of the inlet velocity in this region is studied analytically by means of analytical solution of two hydrodynamic problems and two MHD problems on an inflow of a viscous fluid into a half-space through a plane split of finite width or through a round hole of finite radius. Both the case of a uniform inlet velocity profile and the case of a parabolic velocity profile are considered. New asymptotic solutions for MHD problems are obtained at large Hartmann numbers for the case of parabolic inlet velocity profile. All problems in the thesis are solved in Stokes or Oseen approximation by using integral transforms.