Summary
A study is made of the unsteady motion of an electrically conducting two-phase fluid in the presence of a uniform magnetic field using the slip boundary condition and modified initial conditions so as to satisfy the free molecular flow condition at the beginning of the motion. An asymptotic analysis is carried out to determine the solutions of the flow field for small mass concentration, small and large times. The principal features of the boundary layer solutions are discussed with physical implications. It is shown that the asymptotic solutions for large time are modified by the external magnetic field and the mass concentration of the particles. Several limiting situations of physical interest are also investigated.
Riassunto
Si è fatto uno studio del moto non stazionario di un fluido a due fasi elettricamente conduttore in presenza di un campo magnetico uniforme usando la condizione del limite di scorrimento e le condizioni iniziali modificate in modo da soddisfare la condizione del libero flusso molecolare all'inizio del moto. Si è effettuata un'analisi asintotica per determinare le soluzioni del campo di flusso per piccole concentrazioni di massa e per piccoli e grandi tempi. Si sono discusse con implicazioni fisiche le caratteristiche principali delle soluzioni dello strato limite. Si dimostra che le soluzioni asintotiche per grandi tempi si modificano per mezzo del campo magnetico esterno e per la concentrazione della massa delle particelle. Si sono anche studiate alcune situazioni limite di interesse fisico.
Резюме
Проводится исследование нестационарного движения электрически проводящей двухфазовой жидкости в присутствии однородного магнитного поля, используя граничные условия скольжения и модифицированные начальные условия, чтобы удовлетворить условию свободиого молекулярного течения в начале движения. Проводится асимптотический анализ, чтобы определить решения для поля потока в случае малой концентрации массы, малых и больших времен. Обсуждаются основные особенности решений для пограничного слоя и рассматриваются физические следствия. Показывается, что асимптотические решения для больших времен изменяются во внешнем магнитном поле и при наличии массовой концентрции частиц. Также исследуются некоторые предельные ситуации, представляющие физический интерес.
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Debnath, L., Basu, U. Unsteady slip flow in an electrically conducting two-phase fluid under transverse magnetic fields. Nuovo Cim B 28, 349–362 (1975). https://doi.org/10.1007/BF02726662
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DOI: https://doi.org/10.1007/BF02726662