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We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements.

Mathematical models of heat exchange in the motion of an incompressible viscous liquid through channels with a helical type of symmetry, including polyzonal finning of fuel elements, in curvilinear nonorthogonal coordinates are proposed. For a laminar flow in the domain of thermal stabilization, we reduce the three-dimensional problem to the two-dimensional problem and investigate the influence of a twist parameter on the distribution of a temperature field. Numerical solutions of model multiparameter problems of calculation of stationary temperature fields by the R-function method (RFM) are considered, which enables us to choose appropriate structural means of the RFM for the subsequent solution of real problems.

Normalized equations for regular no-gons translated nd times in a regular nb-gon are set up based on coordinate transformations that allow translating geometric objects on segments. Such approaches are especially important in solving automation problems in solid modeling, geometric design, and boundary-value problems of mathematical physics.

Based on R-functions, a general algorithm is proposed for automatic construction of predicate and analytical functions of a geometrical object consisting of a given list of standard primitives. Normalized functions of standard primitives with alphabetic parameters are constructed that determine the position, sizes, and orientation of the primitives. The capabilities of automation of constructing equations of geometrical objects from standard primitives are illustrated with the help of the system POLYE.