Studying heat conduction taking into account the finite rate of heat propagation
V. A. Kudinov, I. V. Kudinov

This publication is cited in the following articles:

1. B. A. Garibyan, “Wave Heat Transfer Modeling in Nonlinear Nonequilibrium Bounded Media”, Her. Russ. Acad. Sci., 95:5 (2025), 823  
2. E. M. Kartashov, “Development of model representations of thermal reaction viscoelastic bodies on the temperature field”, Rossijskij tehnologičeskij žurnal, 12:6 (2024), 80  
3. V. V. Zhukov, Yu. A. Kryukov, K. V. Trubitsyn, V. A. Kudinov, E. V. Kotova, “Study of linear parabolic and linear hyperbolic thermal conduction operators”, Mathematical notes of NEFU, 31:1 (2024), 89–102      
4. Yuri B. Zudin, Mathematical Engineering, Theory of Periodic Conjugate Heat Transfer, 2023, 201  
5. E. M. Kartashov, “New energy effect in non-cylindrical domains with a thermally insulated moving boundary”, Rossijskij tehnologičeskij žurnal, 11:5 (2023), 106  
6. E. M. Kartashov, “Thermal State of a Region with a Thermally Insulated Moving Boundary”, High Temp, 61:5 (2023), 652  
7. Eremin V A., Kudinov V I., Kudinov V.A., Stefanyuk V E., “Mathematical Model of Interrelated Heat and Mass Transfer With Account For the Two-Phase Lag”, J. Eng. Phys. Thermophys., 94:6 (2021), 1432–1437      
8. Kudinov I. Kudinov V. Eremin A. Trubitsyn K., “A Mathematical Model For Electromagnetic Oscillation Propagation That Accounts For Single and Dual-Phase Lag”, J. Electromagn. Waves Appl., 35:17 (2021), 2304–2322      
9. Igor V. Kudinov, Vasiliy K. Tkachev, Anton V. Eremin, Konstantin V. Trubitsyn, CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2021 (CEST 2021), 2429, CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2021 (CEST 2021), 2021, 020019  
10. Yuri B. Zudin, Mathematical Engineering, Non-equilibrium Evaporation and Condensation Processes, 2021, 47  
11. V V Zhukov, “Study of analytical solution of the thermal conductivity equation considering relaxation phenomena under the third class boundary conditions”, J. Phys.: Conf. Ser., 1889:2 (2021), 022027  
12. G V Mikheeva, A V Pashin, “Investigation of heat transfer in metal nanofilms irradiated with ultrashort laser pulses: two-temperature model”, J. Phys.: Conf. Ser., 2094:2 (2021), 022023  
13. Kudinov V I. Eremin V A. Kudinov V.A. Dovgyallo I A. Zhukov V.V., “Mathematical Model of Damped Elastic Rod Oscillations With Dual-Phase-Lag”, Int. J. Solids Struct., 200 (2020), 231–241      
14. I V Kudinov, A V Eremin, V A Kudinov, G V Mikheeva, “Theoretical research on electromagnetic wave propagation in plasma”, IOP Conf. Ser.: Mater. Sci. Eng., 919:5 (2020), 052039  
15. A.V. Eremin, “Modeling methodology of locally non-equilibrium heat conductivity processes”, Vestnik IGEU, 2020, no. 2, 65  
16. M. I. Supelnyak, “Temperature fluctuations in a half-space under spatially inhomogeneous heat-transfer conditions”, High Temperature, 57:5 (2019), 681–693          
17. Kudinov V I. Kudinov V.A. Gavrilova T.Y., “Mathematical Modelling of Thermal Dynamic Stresses on the Basis of a Dual - Phase Lag Model”, Int. J. Heat Mass Transf., 138 (2019), 326–334      
18. Yu. A. Kirsanov, A. Yu. Kirsanov, A. E. Yudakhin, “Method of measuring thermal relaxation in the solid state”, High Temperature, 56:3 (2018), 425–432            
19. I. V. Kudinov, “Razrabotka matematicheskikh modelei i issledovanie neravnovesnykh yavlenii s uchetom prostranstvenno-vremennoi nelokalnosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:1 (2018), 116–152        
20. V. A. Kudinov, A. V. Eremin, I. V. Kudinov, V. V. Zhukov, “Strongly nonequilibrium model of thermal ignition with account for space-time nonlocality”, Combust. Explos., 54:6 (2018), 649–653      
21. I. V. Kudinov, V. A. Kudinov, A. V. Eremin, V. V. Zhukov, “Mathematical model of rod oscillations with account of material relaxation behaviour”, International Conference on Mechanical Engineering, Automation and Control Systems 2017, IOP Conference Series-Materials Science and Engineering, 327, IOP Publishing Ltd, 2018, UNSP 042059      
22. Yu. A. Kirsanov, A. Yu. Kirsanov, A. E. Yudakhin, “Measurement of thermal relaxation and temperature damping time in solid”, High Temperature, 55:1 (2017), 114–119          
23. Yu. A. Kirsanov, “The influence of thermal relaxation and thermal damping on transient processes with cyclic boundary conditions”, High Temperature, 55:4 (2017), 535–540            
24. V. A. Kudinov, A. V. Eremin, I. V. Kudinov, “The development and investigation of a strongly non-equilibrium model of heat transfer in fluid with allowance for the spatial and temporal non-locality and energy dissipation”, Thermophys. Aeromechanics, 24:6 (2017), 901–907      
25. V. A. Kudinov, A. V. Eremin, V. V. Zhukov, “Mathematical models of heat ignition and explosion considering local non-equilibrium of processes”, International Conference Problems of Thermal Physics and Power Engineering (PTPPE-2017), Journal of Physics Conference Series, 891, IOP Publishing Ltd, 2017, UNSP 012100      
26. A. V. Eremin, V. A. Kudinov, I. V. Kudinov, “Mathematical model of heat transfer in a fluid with account for its relaxation properties”, Fluid Dyn., 51:1 (2016), 33–44      
27. I. V. Kudinov, V. A. Kudinov, “Problems of dynamic thermoelasticity on the basis of an analytical solution of the hyperbolic heat conduction equation”, High Temperature, 53:4 (2015), 521–525            
28. Kudinov I.V. Kudinov V.A., “Exact Closed-Form Solution of the Hyperbolic Equation of String Vibrations With Material Relaxation Properties Taken Into Account”, Mech. Sol., 49:5 (2014), 531–542