Mathematic / 5 Mathematical modeling

Birtaeva Z.B.

Kostanay poly technical college, Kostanay

Iterative method of calculation of coefficient of heat conductivity of soil taking into account moisture convection

This work studies the inverse problem of the propagation of heat in a homogeneous medium.

Convective transfer of heat in soil is carried out by water or air. Movement of moisture can be carried out in undergrad or as a result of a filtration (i.e. under the influence of gravitational forces), or as a result of migration (i.e. under the influence of the "internal" forces arising in the soil on the water - a mineral skeleton undressed), or that and some other way at the same time. In work the method of determination of coefficient of heat conductivity of uniform soil taking into account moisture convections is studied. The equation movement of heat registers in the following look:

(1)

For the equations (1) the following initial and boundary conditions are laid down

, (2)

The equation movement of moisture registers in the following look:

(3)

The equation of moisture (3) is solved under following conditions

(4)

Besides, upon transition from one layer to other layer conditions are laid down

(5)

Here coordinates of a point of transition. To define coefficient of heat conductivity conditions are set

(6)

In net area.

The differential task for temperature is studied:

(7)

, (8)

And also a differential task for humidity

(9)

(10)

This work studies the inverse problem of the propagation of heat in a homogeneous medium.