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L. S. Goruleva, I. I.Obabkov, E. Yu. Prosviryakov

EXACT SOLUTIONS TO THERMAL DIFFUSION EQUATIONS FOR STOKES SLOW FLOWS

DOI: 10.17804/2410-9908.2024.6.241-267

The article considers a class of exact solutions for describing Stokes slow flows of binary fluids. The family of exact solutions is constructed on the basis of the Lin–Sidrov–Aristov ansatz for the velocity field. The velocity field has a wide functional arbitrariness. It depends linearly on two coordinates (horizontal or longitudinal). The coefficients of the linear forms are functions of two variables from the third (vertical or transverse) coordinate and time. The pressure field, the temperature field, and the field of dissolved substance concentration are quadratic forms. In other words, the study takes into account not only horizontal gradients, but also the curvature of the hydrodynamic fields. The constructed exact solution describes thermal diffusion with both Soret and Dufour cross dissipative effects. A system of equations for describing unsteady flows is derived, which consists of heat conduction equations and gradient equations. Formulas of hydrodynamic fields are given to describe the Stokes slow steady-state flow of a binary fluid.

Keywords: exact solution, binary fluid, convection, diffusion, thermal diffusion, Stokes approximation, Lin–Sidorov–Aristov class

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Л. С. Горулева, И. И. Обабков, Е. Ю. Просвиряков

ТОЧНЫЕ РЕШЕНИЯ УРАВНЕНИЙ ТЕРМОДИФФУЗИИ ДЛЯ МЕДЛЕННЫХ ТЕЧЕНИЙ ТИПА СТОКСА

В статье рассматривается класс точных решений для описания медленных течений Стокса бинарных жидкостей. Семейство точных решений построено на основе анзаца Линя – Сидорова – Аристова для поля скорости. Поле скорости обладает широким функциональным произволом. Оно зависит линейно от двух координат (горизонтальных или продольных). Коэффициенты линейных форм являются функциями двух переменных от третьей (вертикальной или поперечной) координаты и времени. Поле давления, поле температуры и поле концентрации растворенного вещества являются квадратичными формами. Иными словами, учитываются не только горизонтальные градиенты, но и кривизна гидродинамических полей. Построенное точное решение описывает термодиффузию с обоими перекрестными диссипативными эффектами Соре и Дюфура. Выведена система уравнений для описания неустановившихся потоков, состоящая из уравнений типа теплопроводности и градиентных уравнений. Приведены формулы гидродинамических полей для описания установившегося медленного течения Стокса бинарной жидкости.

Ключевые слова: точное решение, бинарная жидкость, конвекция, диффузия, термодиффузия, приближение Стокса, класс Линя – Сидорова – Аристова

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  15. The effect of abrasive additives on the tribotechnical properties of lubricants for the wheel–rail system / L. F. Koroleva, R. A. Savrai, E. Yu. Prosviryakov, V. A. Kostarev, S. V. Pavlyshko, P. V. Kostarev // Diagnostics, Resource and Mechanics of materials and structures. – 2023. – Iss. 1. – P. 54–64. – DOI: 10.17804/2410-9908.2023.1.054-064. – URL: http://dream-journal.org/issues/2023-1/2023-1_390.html
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Библиографическая ссылка на статью

Goruleva L. S., I.Obabkov I., Prosviryakov E. Yu. Exact Solutions to Thermal Diffusion Equations for Stokes Slow Flows // Diagnostics, Resource and Mechanics of materials and structures. - 2024. - Iss. 6. - P. 241-267. -
DOI: 10.17804/2410-9908.2024.6.241-267. -
URL: http://dream-journal.org/issues/content/article_481.html
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