Abstract
Based on the determination of the temperature perturbation front and additional boundary conditions, an approximate analytical solution is obtained for the stationary heat exchange problem when fluid flows in a cylindrical channel with a constant parabolic velocity profile (the Gretz–Nusselt problem), which allows us to investigate the temperature distribution in the fluid in a wide range of distances from the pipe inlet, including small and very small distances. Based on the data of numerical calculations of temperature change at a certain value of the spatial variable using the solution obtained by solving the inverse heat conduction problem, the Peclet number was found (in the case where it is unknown in the solution obtained), from which we can determine the velocity profile and the flow rate of the liquid. Graphs of the distribution of isotherms and the their velocities in space over time are plotted.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Petukhov, B.S., Teploobmen i soprotivlenie pri laminarnom techenii zhidkosti v trubakh (Heat Exchange and Resistance under Laminar Flow of Liquid in Pipes), Moscow: Energiya, 1967.
Tsoi, P.V., Sistemnye metody rascheta kraevykh zadach teplomassoperenosa (System Methods for Calculating Boundary Problems on Heat and Mass Transfer), Moscow: Moscow Power Engineering Institute, 2005.
Graetz, L., Über die Wärmeleitungsfähigkeit von Flüssigkeiten, Ann. Phys. Chem., 1885, no. 25, pp. 337–357.
Nusselt, W., Die Abhangigkeit der Warmeubergangszahl von der Rohrlange, Z. Ver. Dtsch. Ing., 1910, vol. 54, pp. 1154–1158.
Kudinov, V.A., Kartashov, E.M., and Stefanyuk, E.V., Tekhnicheskaya termodinamika i teploperedacha (Technical Thermodynamics and Heat Transfer), Moscow: Yurait, 2011.
Kudinov, V.A., Stefanyuk, E.V., and Antimonov, M.S., Analytical solutions of the problems of heat transfer during liquid flow in plane-parallel channels by determining the temperature perturbation front, Inzh.-Fiz. Zh., 2007, vol. 80, no. 5, pp. 176–186.
Stefanyuk, E.V., Kudinov, I.V., and Largina, E.V., The way for generating approximate analytical solutions of nonlinear ordinary differential equations by using additional boundary conditions, Vestn. Samar. Gos. Tekh. Univ. Ser.: Fiz.-Mat. Nauki, 2009, no. 1 (18), pp. 122–132.
Stefanyuk, E.V. and Kudinov, V.A., Additional boundary conditions in nonstationary problems of heat conduction, High Temp., 2009, vol. 47, no. 2, pp. 250–262.
Sellars, J.R., Tribus, M., and Klein, J.S., Heat transfer to laminar flow in a round tube or flat conduit–the Graetz problem extended, Trans. ASME, 1956, vol. 78, no. 2, pp. 441–448.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Eremin, V.A. Kudinov, E.V. Stefanyuk, 2018, published in Prikladnaya Matematika i Mekhanika, 2018, Vol. 82, No. 1, pp. 31–43.
Rights and permissions
About this article
Cite this article
Eremin, A.V., Kudinov, V.A. & Stefanyuk, E.V. Heat Exchange in a Cylindrical Channel with Stabilized Laminar Fluid Flow. Fluid Dyn 53 (Suppl 1), S29–S39 (2018). https://doi.org/10.1134/S0015462818040171
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462818040171