Русский
English
The formulation and solution of the problem of non-stationary thermal conductivity in a composite material with variable thermophysical characteristics are considered. Density, heat capacity, thermal conductivity, as well as the power of the heat source due to the hydration reactions of the binder components change during the concrete hardening process. The heat transfer problem is formulated for the general case when there are no calculation formulas for thermophysical transfer coefficients. The “microprocess method” was used to calculate the dynamics of the temperature field. According to this method, the space from the outer surface of the heater is modeled by a system of successively located “rings”. When moving from the previous “ring” to the next one, the charge in the transfer coefficients and the power of the volumetric heat source were taken into account. At the same time, the initial and boundary conditions were corrected. The boundary value problems are formulated in the form of a differential equation of non-stationary heat transfer with an arbitrary initial distribution of transfer potentials, Dirichlet boundary conditions, and a heat source in the form Po=f(Fo).The obtained solutions are analyzed for some particular cases. Prospects for further theoretical and experimental research are determined.
[1] Ershov M.N., Lapidus A.A., Telichenko V.I. Technological processesin construction. Moscow, Assosiation of Civil Engineering. 2016. 10.
[2] Korobkov S.V., Petrov E.V. Technology of production of concrete works during construction of monolithic foundation. Tumensky State University of Architecture and Civil Engineering. 2022. 244 p.
[3] Tajmasov B.T., Hudyakova T.M., Dauletiyanov M.S. Physico-chemical methods of analysis of binders. M. – Vologda,Infra-Ingineering, 2024. 144 p.
[4] Borisov B.V., VyatkinA.V., Kuznecov G.V. Formation of scheduled termal conditions in an industrial premises with a radiant heating system and air exchange. Journal of Engineering Physics and Thermophysics. 2023. 96 (7). P. 1717 – 1727.
[5] Tarakanov O.V., Erofeev V.T., Smirnov V.F. Cemical additives for solutions and concrete. M. – Vologda, Infra-Ingineering, 2023. 168 p.
[6] Nesterkina N.P., Sinicyna L.V., Mikaeva S.A. Fundamentals of optical radiation source technology. M. – Vologda, Infra-Ingineering, 2024. 164 p.
[7] Li Y.F., Xiaо S.Z., Zeng P. The applications of some basic mathematical inequalities on the convergence of the primitive equations of moist atmosphere. Journal of Mathematical Inequalities. 2021. 15 (1). P. 293 – 304.
[8] Gamzaev K.M. Numerical solution of the inverse problem of heating a solid body by laser radiation. Journal of Engineering Physics and Thermophysics. 2023.96 (5). P. 1135 – 1141.
[9] Fedosov S.V., Bobylev V.I.,Sokolov A.M. Electrothermal treatment of concrete with high – freguency currents at precast concrete plants. Ivanovo, Ivanovo State Polytechnical University, 2016. 336 p.
[10] Leseduarte M.C., Quintanilla R.Phragmén – Lindelöf of alternative for the Laplace equation with dynamic boundary conditions. Journal of Applied Analysis and Computation. 2017. 7 (4). P. 1323 – 1335.
[11] Fedosov S.V., Isachenko S.L. Mathematical modeling of heat transfer in the system “heated cylindricalconductor – stationary composite medium”. Construction production. 2024. № 2. P. 77 – 83.
[12] Korotkij A.I., StarodubcevaYu.V. Heat and mass transfer theory. Modeling of boundary value problems. Yurait, 2022. 169 p.
[13] Knops R.J., Quintanilla R. Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section. Journal of Elasticity. 2015. 121. P. 89 – 117.
[14] Rudobashta S.P., Kartashov E.M. Diffusion in chemical engineering processes. M., KolosS, 2010. 478 p.
[15] Fedosov S.V. Heat and mass transfer in technological processes of the construction industry. Ivanovo, PresSto, 2010. 364 p.
[16] Horgan C.O., Payne L.E. Phragmén–Lindelöf type results for harmonic functions with nonlinear boundary conditions. Archive for Rational Mechanics and Analysis. 1993. 122 (2). P. 123 – 144.
[17] Gorbachev N.V. Heat and mass transfer, thermal conductivity. Nizegorodsky State Technical University, 2020, 77 p.
[18] Usherov – Marshak A.V. Calorimetry ofcement and concrete. Kharkov, Fact, 2002. 180 p.
[19] BazhenovYu.M. Concrete technology. M., Assosiation of Civil Engineering, 2002. 500 p.
[20] Yang X., Zhou Z. F.Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition. Journal of Differential Equations. 2016. 261. P. 2738 – 2783.
[21] Quintanilla R., Racke R.Spatial behavior in phase-lag heat conduction. Differential and Integral Equations. 2015. 28. P. 291 – 308.
[22] Fedosov S.V., Lapidus A.A., Narmaniya B.E., Aizatullin M.M. Cauchy problem for unsteady mass transfer processes in an unbounded plate by the integral Laplace transform method. Construction Materials and Products. 2024. 7 (4).
[23] Chen W. Cauchy problem for thermoelastic plate equations with different damping mechanisms. Communications in Mathematical Sciences. 2020. 18. P. 429 – 457.
[24] Hameed A.A., Harfash A.J. Continuous dependence of double diffusive convection in a porous medium with temperature-dependent density. Basrah Journal of Science. 2019. 37, 1. 15.
[25] Li Y.F., Lin C.H. Spatial decay for solutions to 2-D Boussinesq system with variable thermal diffusivity. Acta Applicandae Mathematicae. 2018. 154. P. 111 – 130.
[2] Korobkov S.V., Petrov E.V. Technology of production of concrete works during construction of monolithic foundation. Tumensky State University of Architecture and Civil Engineering. 2022. 244 p.
[3] Tajmasov B.T., Hudyakova T.M., Dauletiyanov M.S. Physico-chemical methods of analysis of binders. M. – Vologda,Infra-Ingineering, 2024. 144 p.
[4] Borisov B.V., VyatkinA.V., Kuznecov G.V. Formation of scheduled termal conditions in an industrial premises with a radiant heating system and air exchange. Journal of Engineering Physics and Thermophysics. 2023. 96 (7). P. 1717 – 1727.
[5] Tarakanov O.V., Erofeev V.T., Smirnov V.F. Cemical additives for solutions and concrete. M. – Vologda, Infra-Ingineering, 2023. 168 p.
[6] Nesterkina N.P., Sinicyna L.V., Mikaeva S.A. Fundamentals of optical radiation source technology. M. – Vologda, Infra-Ingineering, 2024. 164 p.
[7] Li Y.F., Xiaо S.Z., Zeng P. The applications of some basic mathematical inequalities on the convergence of the primitive equations of moist atmosphere. Journal of Mathematical Inequalities. 2021. 15 (1). P. 293 – 304.
[8] Gamzaev K.M. Numerical solution of the inverse problem of heating a solid body by laser radiation. Journal of Engineering Physics and Thermophysics. 2023.96 (5). P. 1135 – 1141.
[9] Fedosov S.V., Bobylev V.I.,Sokolov A.M. Electrothermal treatment of concrete with high – freguency currents at precast concrete plants. Ivanovo, Ivanovo State Polytechnical University, 2016. 336 p.
[10] Leseduarte M.C., Quintanilla R.Phragmén – Lindelöf of alternative for the Laplace equation with dynamic boundary conditions. Journal of Applied Analysis and Computation. 2017. 7 (4). P. 1323 – 1335.
[11] Fedosov S.V., Isachenko S.L. Mathematical modeling of heat transfer in the system “heated cylindricalconductor – stationary composite medium”. Construction production. 2024. № 2. P. 77 – 83.
[12] Korotkij A.I., StarodubcevaYu.V. Heat and mass transfer theory. Modeling of boundary value problems. Yurait, 2022. 169 p.
[13] Knops R.J., Quintanilla R. Spatial behaviour in thermoelastostatic cylinders of indefinitely increasing cross-section. Journal of Elasticity. 2015. 121. P. 89 – 117.
[14] Rudobashta S.P., Kartashov E.M. Diffusion in chemical engineering processes. M., KolosS, 2010. 478 p.
[15] Fedosov S.V. Heat and mass transfer in technological processes of the construction industry. Ivanovo, PresSto, 2010. 364 p.
[16] Horgan C.O., Payne L.E. Phragmén–Lindelöf type results for harmonic functions with nonlinear boundary conditions. Archive for Rational Mechanics and Analysis. 1993. 122 (2). P. 123 – 144.
[17] Gorbachev N.V. Heat and mass transfer, thermal conductivity. Nizegorodsky State Technical University, 2020, 77 p.
[18] Usherov – Marshak A.V. Calorimetry ofcement and concrete. Kharkov, Fact, 2002. 180 p.
[19] BazhenovYu.M. Concrete technology. M., Assosiation of Civil Engineering, 2002. 500 p.
[20] Yang X., Zhou Z. F.Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition. Journal of Differential Equations. 2016. 261. P. 2738 – 2783.
[21] Quintanilla R., Racke R.Spatial behavior in phase-lag heat conduction. Differential and Integral Equations. 2015. 28. P. 291 – 308.
[22] Fedosov S.V., Lapidus A.A., Narmaniya B.E., Aizatullin M.M. Cauchy problem for unsteady mass transfer processes in an unbounded plate by the integral Laplace transform method. Construction Materials and Products. 2024. 7 (4).
[23] Chen W. Cauchy problem for thermoelastic plate equations with different damping mechanisms. Communications in Mathematical Sciences. 2020. 18. P. 429 – 457.
[24] Hameed A.A., Harfash A.J. Continuous dependence of double diffusive convection in a porous medium with temperature-dependent density. Basrah Journal of Science. 2019. 37, 1. 15.
[25] Li Y.F., Lin C.H. Spatial decay for solutions to 2-D Boussinesq system with variable thermal diffusivity. Acta Applicandae Mathematicae. 2018. 154. P. 111 – 130.
Fedosov S.V., Abdullazyanov E.U., Kiyamova L.I. Heat transfer from a cylindrical heater to a medium with variable thermophysical characteristics and heat source power. Construction Materials and Products. 2024. 7 (6). 8. https://doi.org/10.58224/2618-7183-2024-7-6-8