Математика/5.Математическое моделирование

G. Mahambetova, A. Baimankulov

Kostanai State University named after A. Baitursynov, Kazakhstan

NUMERICAL CALCULATIONS OF THE INVERSE TASK FOR FINDING OF THE THERMAL CONDUCTIVITY COEFFICIENT UNIFORM PRIMING

In this paper we study one-dimensional problem of heat propagation in the soil. In general, any problem of heat propagation is three-dimensional, but if the width and length of the region are large enough, and the surface of this region is almost flat, then the gradient of the horizontal distribution of heat is almost zero. In this case, instead of three-dimensional problem can be studied one-dimensional problem.

1 Statement of the Problem. Let in the area occurs heat distribution under the influence of the ambient temperature, in this case - the air. It is required define of the thermal conductivity coefficient . Decision of the task shall search for from minimum functional . Here computable meaning of the temperature of the priming on surface of the land, but actual temperature of the priming on surfaces of the land. After theoretical discourses in work [9] is received follow algorithm of the decision of the deliver task: 1) Is assigned initial approach ; 2) Dares straight line a task , , , and is defined and ; 3) Dares inverse task , , , and is defined ; 4) Is calculating gradient functional ; 5) Following approximation the thermal conductivity coefficient is defined on formula: , .

2 A numerical experiment. For audit of validity received theoretical result is organized numerical experiment. Studied uniform priming with data . Temperature surrounding ambiences , the thickness of the priming 5 m.; the step on time 0.5 hour; step on spatial variable 0.001 m.

Figure 1. The track record to convergence iterations process. Initial approximation the thermal conductivity coefficient .

Figure 2. The Influence iterations coefficient . Initial approximation the thermal conductivity coefficient .

References:

1. A.F.Chudnovsky (1976). Thermo physics of the soil (pp.352). Moscow: Science.

2. A.Franchuk (1941). Thermal conductivity of construction materials depending on the humidity. Gosstroizdat.

3. B.Rysbaiuly& T.Akyshev( 2008). The approximate method of determining the coefficient of heat transfer. The proceedings of International Conference on mathematical methods in geophysics "ММG-2008". Russia, Novosibirsk, Akademgorodok, 13-15 October.