Краевые задачи теплопроводности при переменном во времени коэффициенте теплоотдачи

The practically important problem of unsteady heat conduction with time-varying relative coefficient of heat transfer is considered. Systematization of different approaches for finding the analytical solution of the problem is shown: the method of splitting the generalized Fourier integral; expanding the desired temperature function in a power series; reduction of the problem to an integral Voltaire equation of the second kind. It is shown that in all cases the solution is reduced to an infinite series of successive approximations of various functional forms, and the main goal of each approach is to find the more successful of the first approximations. Particular cases of the time dependence of the relative heat transfer coefficient are considered: linear, exponential, degree, root. The analytical solutions and numerical experiments, the peculiarities of the temperature curves for a number of specified dependencies are given. It was established that in case of the time-linear heat transfer coefficient the temperature curve changes significantly differ in comparison with the classical case of constant coefficient, while exponential dependence makes no substantive difference.Рассмотрены практически важные задачи нестационарной теплопроводности с переменным во времени относительным коэффициентом теплообмена. Приведена систематизация различных подходов при нахождении аналитического решения задачи: метод расщепления обобщенного интегрального преобразования Фурье; разложение искомой температурной функции в степенной ряд; сведение задачи к интегральному уравнению Вольтера второго рода. Показано, что во всех случаях решение сводится к бесконечному ряду последовательных приближений различной функциональной формы и главной целью каждого из подходов является отыскание наиболее удачного первого приближения. Рассмотрены частные случаи временной зависимости относительного коэффициента теплообмена: линейная, экспоненциальная, степенная, корневая. Приведены аналитические решения и численные эксперименты, выявлены особенности температурных кривых для ряда указанных зависимостей. Установлено, что для линейного закона во времени коэффициента теплоотдачи картина изменения температурной кривой по сравнению с классическим случаем для постоянного коэффициента существенно изменяется, в то время как экспоненциальная зависимость не вносит существенных изменений

Тепловой нагрев диска с внутренним круговым вырезом

The thermal reaction of infinite disc with internal round neck was studied. The law of thermal elastic stresses with thermal heating was established on surface neck.Исследована термическая реакция бесконечного диска с внутренним круговым вырезом. Установлены закономерности термоупругих напряжений, возникающих при тепловом нагреве поверхности выреза

Термоупругая реакция двухслойного кругового диска с центральным круговым вырезом

The thermal response of a two-layer disc with an inner circular indention was studied. The regularities of the thermoelastic stresses upon thermal heating of the boundary circular surfaces of the disk were determined.Исследована термическая реакция двухслойного диска с внутренним круговым вырезом. Установлены закономерности термоупругих напряжений при температурном нагреве граничных круговых поверхностей диска

Термовязкоупругость в динамических моделях теории теплового удара

While researching the thermal reaction of viscoelastic bodies under heatstroke conditions, the quasi-static HiltonLee-Sternberg theory of viscoelastic analogy generalization to dynamic models given inertial effects in the equations of motion was considered. The thermal reaction to heatstroke of a massive body (area with internal spherical cavity) with a sudden increase of its surface from initial To to Tc > 0 was researched. Numerical experiments were done, which revealed the qualitative difference of modeling results for the elastic body and viscoelastic body from rheological Maxwell and Kelvin models. It was found that the sudden heat of the surface of the viscoelastic body due to inertia force results in short-time stress close enough to the stress of the elastic, medium. Moreover, the difference of these stresses is decreased with increasing viscosity. The addition to this duration of action of inertial effects is about microseconds. During this time stress reaches its thermoelastic value before the growth of significant viscous flow. The qualitative behavior difference of viscoelastic Maxwell and Kelvin mediums on the body surface under conditions of sudden cooling within the quasi-static model of thermoviscoelasticity was described. The beginning of viscous flow in Maxwell medium which results in continuous stress decrease after discontinuous change tending to elastic medium stress was shown. On the contrary, in Kelvin medium jump of stress exceeds the value for the elastic medium, to which these stresses are tending.Р ассмотрена теория теплового удара вязкоупругих тел на основе динамической модели. Описана термическая реакция на тепловой удар массивного тела (полупространство). Указано качественное отличие результатов моделирования для динамических и квазистатических случаев

Тепловой удар массивного тела с внутренней сферообразной трещиной

The role of inertial effects in the problem of heat stroke with a massive body having an internal spherical crack as an example was studied. An interrelationship for the calculation of the maximum dynamic stress, which is of great practical importance, is suggested.Исследована роль инерционных эффектов в проблеме теплового удара на примере массивного тела с внутренней сферообразной трещиной. Предложено соотношение по расчету максимума динамических напряжений, имеющее важное практическое значение

Changes in the reactivity of the vertebrobasilar arteries when using glucose-electrolyte drink with antioxidant plant extracts during submaximal exercise test

The aim. To assess the effect of glucose-electrolyte composition with plant extracts having antioxidant activity on the hemodynamic parameters of vertebrobasilar system during the incrementally increasing submaximal exercise test.Materials and methods. The study included 12 athletes (6 candidates for master of sports and 6 masters of sports) aged 18–22, who have been engaged in orienteering for 10 years and more. Time of aerobic exercise – 2 hours a day, five days a week. The study subjects performed an incrementally increasing submaximal exercise test and also submaximal exercise test with the preventive intake of a glucose-electrolyte composition with plant extracts having antioxidant properties. To assess the hemodynamic parameters in all study subjects we used Doppler ultrasound of the cerebral vessels, evaluating vertebrobasilar system blood flow, exercise gas test in the modification of hypo- and hyperventilation, and also positional test.Results. A single intake of glucose-electrolyte drink under conditions of incrementally increasing exercise test contributed to the manifestation of a homeostatic effect in hemodynamic parameters of the vertebrobasilar arteries. It is evidenced by the approximation to the pre-exercise level of maximum systolic velocity and average blood velocity in the breath-holding test, of the diastolic blood velocity in the hyperventilation test, and of the pulsatility index in the torsion test, as compared to the isolated submaximal exercise test which caused the change in both velocity indicators and calculated indices during the functional tests.The article considers the main mechanisms underlying the change in arterial hemodynamic parameters caused by incrementally increasing load, as well as describes the proposed mechanisms arising from the combined effect of an incrementally increasing load and the intake of a glucose-electrolyte composition with plant extracts having antioxidant activity.Conclusion. It was shown that using glucose-electrolyte drink contributed to the restoration of hemodynamic parameters of the vertebrobasilar arteries after an incrementally increasing submaximal exercise test

Обобщенная модель термовязкоупругости в теории теплового удара

The theory of heat stress for viscoelastic bodies based on linear rheological models of Maxwell and Kelvin for infinite domain bounded from inside by surfaces of either flat or cylindrical, or spherical shape together was examined. The influence of the geometrical factor and features of viscoelastic substances were found.Предложена обобщенная теория теплового удара вязкоупругих тел на основе линейных реологических моделей Максвелла и Кельвина одновременно для бесконечной области, ограниченной изнутри поверхностями: либо плоской, либо цилиндрической, либо сферической. Выяснено влияние геометрического фактора и особенности вязкоупругих сред

Tнеrmal heating of dick with internal round neck

The thermal reaction of infinite disc with internal round neck was studied. The law of thermal elastic stresses with thermal heating was established on surface neck

Thermoelastic reaction of a two-layer circular disk with a central circular indention

The thermal response of a two-layer disc with an inner circular indention was studied. The regularities of the thermoelastic stresses upon thermal heating of the boundary circular surfaces of the disk were determined

Thermoviscoelasticity theory in the dynamic models of thermal shock

While researching the thermal reaction of viscoelastic bodies under heatstroke conditions, the quasi-static HiltonLee-Sternberg theory of viscoelastic analogy generalization to dynamic models given inertial effects in the equations of motion was considered. The thermal reaction to heatstroke of a massive body (area with internal spherical cavity) with a sudden increase of its surface from initial To to Tc > 0 was researched. Numerical experiments were done, which revealed the qualitative difference of modeling results for the elastic body and viscoelastic body from rheological Maxwell and Kelvin models. It was found that the sudden heat of the surface of the viscoelastic body due to inertia force results in short-time stress close enough to the stress of the elastic, medium. Moreover, the difference of these stresses is decreased with increasing viscosity. The addition to this duration of action of inertial effects is about microseconds. During this time stress reaches its thermoelastic value before the growth of significant viscous flow. The qualitative behavior difference of viscoelastic Maxwell and Kelvin mediums on the body surface under conditions of sudden cooling within the quasi-static model of thermoviscoelasticity was described. The beginning of viscous flow in Maxwell medium which results in continuous stress decrease after discontinuous change tending to elastic medium stress was shown. On the contrary, in Kelvin medium jump of stress exceeds the value for the elastic medium, to which these stresses are tending