Assessment of fire protection distances between the objects of different purpose taking into account the cooling of external surfaces

Abstract

Проведена серия расчетов по оценке температуры при пожаре в режиме, регулируемом вентиляцией, поскольку при этом достигается максимальное значение температуры. Исследуется радиационный и конвективный теплообмен с наружными поверхностями стен помещения. Рассмотрен случай пожара в помещениях складского типа. The application of local variation method for solving fire safety problems with variational formulation (continuous or finite-dimensional) makes it possible to significantly simplify the procedure of mathematical calculations for fire modeling and calculation tasks in the field of fire safety. The choice of the local variation method as a method of direct search for the conditional optimization problem (if there are restrictions) is associated with the absence of the need to calculate the derivatives of the target function (gradient and Hesse matrix). This saves the user from the tedious procedure of getting analytical or finite-difference expressions for the specified derivatives. This choice seems also to be due to the task of non-differentiable optimization. The article provides a justification for choosing the local variation method as one of the alternating-variable descent methods, developed for problems of thermal conductivity, control, etc. Specific features in the implementation of this algorithm are noted, as well as test examples of its application on several well-known test examples representing poorly conditioned “functionals” of small dimension. There are considered the methods of numerical implementation either by Hooke-Jeeves, which is one of the methods of coordinate descent developed for unconditional optimization problems, or by Nelder - Mead, one of the most effective methods if the number of variables does not exceed 6. Example researches showed that regularization contributes to the convergence of the method of local variations. The most effective one is a stabilizer that uses an exact solution. Some predominance of negative test results on the use of regularization is explained by insufficient conditionality of the examples used. This circumstance indicates the need for further search for optimal possibilities of using the method of local variations for applied problems. If it is necessary other stabilizers, not considered in the article, can be used. For the purpose of optimization of the formulated problem, it seems optimal to design a new type of stabilizers.