Математика/5. Математическое моделирование

Baimankulov A.

Kostanay State University named after A.Baitursynov, Kazakhstan.

Definition of a generalized heat exchange coefficient

The following problem is

, , (1)

, , (2)

. (3)

The problem is solved by iterative method. Suppose that – iteration parameter.

The initial value , and the following values determined from the monotony of the functional

. (4)

Previously, we obtained dual problem to (1)-(3)

, , (5)

, . (6)

Thus for the calculation of the generalized heat transfer coefficient is taken iterative formula.

(7)

Consider when . In this case, the differential problem can be written as

, (8)

(9)

. (10)

A conjugate differential problem has the form

(11)

, (12)

Recall that – measured soil temperature at the earth's surface. Variation of the functional has the form

(13)

At the same time the following generalized heat transfer coefficient is determined by the formula

(14)

That is, further controlled parameter is chosen so that the sequence converges.

References

1.Нерпин С.В., Юзефович Г.И. О расчете нестационарного движения влаги в почве// Доклады ВАСХНИЛ, № 6, 1966.

2.Юзефович Г.И., Янгарбер В.А. Исследование нелинейного уравнения влагопереноса. // Л.: Колос. Сб. трудов по агрофизике, вып. № 14, 1967.

3.Байманкулов А.Т. Определение коэффициента капиллярной диффузии.// Материали за VIII международна научна практична конференция «Бъдещето въпроси от света на науката -2012», т.36, 17-25 декември, 2012, София.