Geodesic
Non-stationary heat exchange in cylindrical channel at laminar flow of fluids
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 122-130

Voir la notice de l'article provenant de la source Math-Net.Ru

Using double integral Laplace–Carson transformation and orthogonal method of Bubnov–Galyorkin, the analytical solution of the non-stationary problem of heat transfer in a cylindrical channel in the laminar flow of fluids was obtained. It has two components: stationary and non-stationary, each part has application only in a certain range of temporal and spatial coordinates. For the stationary Graetz-Nusselt problem on the basis of introduction of the temperature perturbation front and additional boundary conditions it was managed to find an analytical solution that allows the assessment of liquid thermal state with small values of spatial variable, directed along the stream flow. It is not possible to obtain such results using the well-known exact analytical methods because of the poor convergence of infinite series of received solutions.
Keywords: cylindrical channel, Graetz–Nusselt problem, integral Laplace–Carson transformation, Fourier method, additional conditions, analytical solution.
Mots-clés : Sturm–Liouville problem 
@article{VSGTU_2013_4_a11,
     author = {A. V. Eremin and E. V. Stefanyuk and A. Yu. Rassypnov and A. E. Kuznetsova},
     title = {Non-stationary heat exchange in cylindrical channel at laminar flow of fluids},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {122--130},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a11/}
}
TY  - JOUR
AU  - A. V. Eremin
AU  - E. V. Stefanyuk
AU  - A. Yu. Rassypnov
AU  - A. E. Kuznetsova
TI  - Non-stationary heat exchange in cylindrical channel at laminar flow of fluids
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 122
EP  - 130
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a11/
LA  - ru
ID  - VSGTU_2013_4_a11
ER  - 
%0 Journal Article
%A A. V. Eremin
%A E. V. Stefanyuk
%A A. Yu. Rassypnov
%A A. E. Kuznetsova
%T Non-stationary heat exchange in cylindrical channel at laminar flow of fluids
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 122-130
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a11/
%G ru
%F VSGTU_2013_4_a11
A. V. Eremin; E. V. Stefanyuk; A. Yu. Rassypnov; A. E. Kuznetsova. Non-stationary heat exchange in cylindrical channel at laminar flow of fluids. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 122-130. http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a11/