SOLVING PROBLEM OF THERMAL CONDUCTION FOR PROVIDING STRENGTH OF ELECTRONIC UNITS ON THERMAL IMPACTS

Paper represents new approach to physical and mathematical modeling of thermal fields distribution in sealed electronic units on the base of introducing “effective parameters” of the system. Effectiveness of developed mathematical model and its computer implementing are demonstrated on the example of standard unit sealed by compound.


Introduction
Modern development of cutting-edge electronic components and units by applying new composite materials and aimed at providing reliability and resource is impossible without applying mathematical modeling of thermal and mechanical processes, which run inside these components during their operation.
Developing technologies for manufacturing sealed electronic systems demands considering impacts which are produced on their strength by as physical and mechanical so thermal factors.

Solution
The paper [1] represents physical and mathematical models, which were obtained and researched, for radial and tangential stress calculation in material of electronic component where 1 2 , P P -Poisson's ratios of component and compound materials correspondingly; , present in formulas of thermal integrals (and stresses , where W , r t temperature of cylindrical surface of radius r in the moment of time W, which is counted from the moment to transfer item from the constant temperature 0 t into the temperature 1 t .For calculations 0 t is assumed to be the initial temperature of the body. Using obtained formulas 1-5 for calculations required solving non-stationary problem of thermal conduction in compounded sealed unit, i.e. finding temperature distribution law over the volume of sealed unit from the moment as it is transferred from its highest temperature t 0 and to the lowest one t 1 (in our case from +70 deg С to -60 deg С) and until the whole volume receives the environmental (lowest) temperature.Solving this problem was offered by developing mathematical model for thermal fields calculation over the sealed unit volume on the base of introducing "effective parameters" [2], which consider inhomogeneity of the unit's material, since sealed unit has a complex structure and consists of many heterogeneous components: various electronic components and compound.
Effective parameters represent average physical and mechanical characteristics of all materials compiling the sealed unit.So temperature conductivity of the whole unit is defined as effective parameter by the formula: Using effective parameter F allows assuming sealed unit as homogeneous body made from mixture of compound and electronic components materials.
Compounded sealed unit having box shape with coordinate origin in the cross point of its diagonals and axes along its principal axes of inertia and sizes a 1) has the following solution for the problem of thermal conduction: where 0 t -initial body temperature, 1 t -environmental temperature, Ф 1 , Ф 2 , Ф 3 -Laplace functions [3], Wtime.Obtained law of temperature distribution allows estimating temperature in any moment of time and in any point of the solid body.Moreover, this law makes possible to estimate the time of the complete cooling or heating a sealed unit.
The applied calculations of thermal fields in sealed units were to perform by using originally developed software on the base of MATHCAD.The developed software outputs on a display the two-and three-dimensional graphs of isotherms, which demonstrate thermal field in the selected section of a sealed unit in the specified moment of time, and also estimates time of complete cooling or heating sealed unit.
The temperature calculation conducted in the set time interval resulted that actual cooling a sealed unit occurs in 1366 sec (22.7 min).
For experimental estimation of the complete cooling time the sealed unit ZU5.760.001 had been prepared by attaching microthermocouple ХК 68 before it was sealed by compound ESK-25.After compound had polymerized the unit was subjected to the range of thermal impacts (thermal cycling) in the temperature range from +70 deg С to -60 deg С. Indications of microthermocouple were recorded on the tape of light-beam oscillograph Н071.4М.As result of conducting 10 thermal cycles the average time of cooling sealed unit -1160 seconds (19.33 min) has been measured, which deviation from estimated one is negligible.Noteworthy is that in manufacturing process when such units are subjected to technological testing, which is conducted in order to improve reliability of the product, the cooling (heating) time makes 1 hour: product is first placed in a heat chamber; then it is transferred to a cooling chamber (the transfer time is limited to few seconds); exposure period in chambers lasts until the thermal balance (1 hour).The total amount of thermal cycles equals three.Such testing is supposed to detect hidden design defects and reject potentially unreliable products.
Thus, modeling and estimating thermal field in sealed units and its time rate allows optimizing technological time for conducting thermal impacts in the process of their manufacturing.So for the case given above the exposure time for thermal impacts in temperature range from +70 deg С to -60 deg С is recommended to optimize and shorten down to 23-24 min as longest.After the problem of thermal conduction has been solved for thermal impacts in the volume of the whole sealed unit whose material was considered as a composite one and the shape of its individual components was not considered at all the further research of temperature distribution near the estimated electronic component and surrounding layer of compound appears to be reasonable.Therefore the problem of non-stationary radial distribution of temperature in electronic component and compound has been posed and solved; these results will be represented in the further papers.

Conclusion
The paper represents mathematical models for thermal fields calculation over the volume of the sealed unit on the base of introducing "effective parameters" which represent average physical and mechanical characteristics of all materials compiling the sealed unit.The developed model allows estimating thermal field distribution in time and over the volume of the solid body and also optimizing technological time for conducting thermal impacts in the process of manufacturing sealed units.

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elasticity modulus of component and compound materials; D 1 , D 2coefficient of linear expansion of component and compound materials; R 1 , R 2internal and external radius of electronic component; R 2 , R 3internal and external radius of compound; r -