# температурне поле

## MATHEMATICAL SPATIAL MODELS OF DETERMINATION OF TEMPERATURE FIELD FROM LOCALLY CONCENTRATED THERMAL HEATING

Linear and nonlinear mathematical models for determining the temperature field, and later the analysis of temperature regimes in isotropic spatial inhomogeneous media exposed to internal and external thermal loads have been developed. To do this, the thermal conductivity for such structures is described as a whole using symmetric unit functions, which allows us to consider boundary thermal conductivity problems with one linear and nonlinear differential equation of thermal conductivity with discontinuous coefficients and linear and nonlinear boundary conditions on boundary surfaces.

## Temperature modes in a heat-sensitive plate with local heating

Nonlinear mathematical models for the analysis of temperature regimes in a thermosensitive isotropic plate heated by locally concentrated heat sources have been developed. For this purpose, the heat-active zones of the plate are described using the theory of generalized functions. Given this, the equation of thermal conductivity and boundary conditions contain discontinuous and singular right parts. The original nonlinear equations of thermal conductivity and nonlinear boundary conditions are linearized by Kirchhoff transformation.

## MATHEMATICAL MODEL OF HEAT EXCHANGE IN ELEMENTS OF DIGITAL DEVICES

A mathematical model of heat exchange analysis between an isotropic two-layer plate heated ba point heat source concentrated on the conjugation surfaces of layers and the environment has been developed.

## MATHEMATICAL MODELS OF HEAT TRANSFER IN ELEMENTS OF TURBO GENERATORS (CONTINUED)

Previously developed [8] and presented new mathematical models for the analysis of temperature regimes in individual elements of turbo generators, which are geometrically described by isotropic half-space and space with an internal heat source of cylindrical shape. Cases are also considered for half-space, when the fuel-releasing cylinder is thin, and for space, when it is heat-sensitive. For this purpose, using the theory of generalized functions, the initial differential equations of thermal conductivity with boundary conditions are written in a convenient form.

## Optimization of technology of sealing of the output capillary pillar of the ionization chamber

Goal. Investigation of the conditions of formation of operational tightness of the end of the output capillary - the rod of the ionization chamber with simultaneous provision of the temperature regime in the process of formation of the welded joint.

## Calculation of strength of heated curvilinear bar structural elements of tubular cross-sections

Practical importance. The analytical and numerical results obtained can be used in the study of the stress state and, respectively, to evaluate the strength and stiffness of curvilinear tubular structural elements, in particular, the pipeline bends and pipes of economizers.

## MATHEMATICAL MODELS OF HEAT TRANSFER IN ELEMENTS OF TURBOGENERATORS

Se­pa­ra­te mat­he­ma­ti­cal mo­dels for de­ter­mi­ning the tem­pe­ra­tu­re distri­bu­ti­on in the ele­ments of tur­bo­ge­ne­ra­tors ha­ve be­en de­ve­lo­ped, which are descri­bed ge­omet­ri­cally by an isot­ro­pic half-spa­ce and a he­at-sen­si­ti­ve spa­ce with lo­cally con­centra­ted so­ur­ces of he­ating. For this pur­po­se, using the the­ory of ge­ne­ra­li­zed functi­ons in a con­ve­ni­ent form, we wri­te the ini­ti­al dif­fe­ren­ti­al eq­ua­ti­ons of ther­mal con­duc­ti­vity with bo­un­dary con­di­ti­ons.

## ANALYTICAL MODEL OF THE MEASURER OF THERMOANEMOMETRIC TYPE OF KINEMATIC PARAMETERS OF THE BIPHASIC PULSING FLOW

The  structural  and  functional  diagrams  of  the  thermoanemometric  type  sensor  for measuring  the mono-  and biphasic  (liquid  +  gas) medium  by  the  pulsating  nature  of  the  flow  are  presented.  The  temperature  distribution  in  the  sensor environment is considered and the sensing elements are not in contact with the inner surface of the sensor body.

## The influence of local transformations on the temperature field of the tourbogenerator’s rotor

The method of determining the integral characteristics of the temperature field of a turbine generator rotor in the case of local overheating is proposed in relation to the study of its deflections and the level of vibration; Influence of thermophysical and geometrical parameters of rotor ТГВ-500-4 on its temperature field is investigated.