536.21We propose models of thermal conductivity of rib-reinforced polyfoams that are based on the condition of equality of dissipations in the equivalent material and the composite under study. The comparison of the calculated effective coefficients of thermal conductivity for unidirectionally and spatially reinforced polyfoams is performed. It is shown that the proposed models give lower and upper bounds for calculated effective coefficients of thermal conductivity for the composites under study.In recent years, layered constructions with polyfoams as a filler have been frequently used in objects of the aerospace complex and in other branches of industry. Polyfoams can be nonreinforced or reinforced by plates or wires or can form various ribbed structures (cellular, folded, corrugated, etc.).The potentialities of polyfoams as light fillers become more diverse if they are used in the form of reinforced layered structures such as polyfoams with layers of structural materials (metal, plywood, etc.) or, most frequently, in the form of strips [2].The application of modern polyfoams (for example, frothed ones) allows one to produce ribbed constructions (cellular, folded, etc.), in which the cavities are filled with polyfoam. Such fillers, due to the presence of plastic in them, possess good characteristics with respect to vibrations, since polyfoam operates as a damper and ensures a high coefficient of attenuation of vibrations. In addition, polyfoam filling the cavities of a ribbed structure ensures a better joint operation of elements of this structure, supports them, and prevents the loss of their stability under compression and shear, which in the whole determines the stiffness and strength characteristics of fillers (cellular, folded, etc. ones) [6]. Similar structures of fillers can be considered as polyfoams with ribbed structures of reinforcement.Since layered structures with filler used in the aerospace field can undergo intense heat influence in the process of operation, the problem of calculation of the temperature fields in elements of such structures, in particular, in a filler, which can be a spatially and, as a rule, curvilinearly reinforced composite, is urgent.Due to the urgency of the problem of thermal conductivity of reinforced materials, it was a subject of studies of many researchers. For example, the processes of thermal conductivity in layered composites were considered in [8,12], the thermophysical behavior of unidirectionally reinforced fibrous materials was modeled in [7,10,13,[15][16][17]22], and the thermal conductivity of composites cross-reinforced in a plane (in particular, woven ones) was studied in [10,14,19,21]. However in recent years, special attention was paid to spatially reinforced composites, since they allow one to remove such shortcomings of layered composites as the danger of separation due to a weak resistance to the interlayer shear and the cleavage and to localize the propagation of cracks. Works devoted to the study of the thermal conductivity of spatially reinforced mat...