Abstract
In this paper, a 3D mathematical model is proposed to determine the dynamics of the temperature field in a three-layer composite sapropel-hemp slab. The proposed model consists of a system of three initial-boundary value problems with respect to the temperature function for each layer, respectively, and one initial-boundary value problem with respect to the unknown velocity of heat propagation along the thickness dimension of the composite sapropel-hemp slab.
Highlights
INTRODUCTIONOne of the main ways to study the dynamics of the temperature field in multilayer building structures is the apparatus of the thermal conductivity theory, where the hypothesis of a continuous medium is used in modelling, which leads to obtaining linear and nonlinear differential equations: there appears smoothness requirement both in time and by spatial variables [1]-[3] related to the functions characterizing the properties and states of the components of the medium
One of the main ways to study the dynamics of the temperature field in multilayer building structures is the apparatus of the thermal conductivity theory, where the hypothesis of a continuous medium is used in modelling, which leads to obtaining linear and nonlinear differential equations: there appears smoothness requirement both in time and by spatial variables [1]-[3] related to the functions characterizing the properties and states of the components of the medium.The main goal of such studies is to find the temperature field inside a composite body under known initial and boundary conditions [4]
Et al 3D Mathematical Model Characterizing the Dynamics of the Temperature Field of a Wall Structure with a Double-Sided Facing from a Sapropel-Hemp Composite Material if the energy release in the inner layer of a sapropel-hemp slab is caused by chemical reactions, which rate is described by the Arrhenius equation, the dependency of the volumetric power of energy release on temperature has a reverse exponential character [5],[8]
Summary
One of the main ways to study the dynamics of the temperature field in multilayer building structures is the apparatus of the thermal conductivity theory, where the hypothesis of a continuous medium is used in modelling, which leads to obtaining linear and nonlinear differential equations: there appears smoothness requirement both in time and by spatial variables [1]-[3] related to the functions characterizing the properties and states of the components of the medium. The coefficient of temperature conductivity ( ) α θ T can be considered a step function along the vertical axis OX3 (i.e. relating to the layers) This circumstance, together with the assumption about the insignificance of thermal perturbations [13] in directions OX1 and OX 2 , allows to construct a one-dimensional by the spatial variable (i.e. in the vertical component) nonlinear inhomogeneous equation with respect to the heat propagation averaged over directions OX1 and OX 2 vector velocity in a composite sapropel-hemp slab, i.e. with respect to scalar function θx ( x,t ). Note that this mathematical model includes an unknown function (see (10)-(12)), defined only on the second layer (i.e. on the inner layer – in the sapropel-hemp component) of the composite slab This means that without knowing the function T {2} ( x,t ), it is impossible to determine the required function T {1} ( x,t ).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
