Modelling of the solar heating of a multi-layered spherical cone

• Autorzy: Siedlecka Urszula

Identyfikatory

DOI

10.17512/jamcm.2023.4.05

• Języki publikacji: EN

Abstrakty

EN

In this paper, the solar heating of a multi-layered spherical body with azimuthal symmetry is considered. The mathematical model is related to the determination of the steady state of the temperature distribution in the spherical cone consisting of concentric spherical layers. The solar heating is composed of two parts of the heat flux: direct and diffusion. Also, the simultaneous cooling of the cone by its outer surface (as convective heat flow to the environment) is taken into account. The proposed system of the partial differential equations supplemented by the adequate boundary conditions is solved in the analytical way by using, among others, the Legendre functions of the first kind. The sample results of temperature distribution in the cross-section of the cone with different polar angles are also presented.

Słowa kluczowe

EN

heat conduction; solar heating; Legendre functions

PL

przewodnictwo cieplne; ogrzewanie solarne; funkcje Legendre’a

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2023
• Tom: Vol. 22, nr 4
• Strony: 53--63
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Siedlecka Urszula

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

• 1] Haji-Sheikh, A., & Beck, J.V. (2002). Temperature solution in multi-dimensional multi-layer bodies. International Journal of Heat and Mass Transfer, 45, 1865-1877.
• [2] Lü, X., Tervola, P., & Viljanen, M. (2005). A new analytical method to solve the heat equation for a multi-dimensional composite slab. Journal of Physics A: General Physics, 38(13), 2873.
• [3] Lu, X., Tervola, P., & Viljanen, M. (2006). Transient analytical solution to heat conduction in composite circular cylinder. International Journal of Heat and Mass Transfer, 49, 341-348.
• [4] Siedlecka, U., & Kukla, S. (2013). Application of a Green’s function method to heat conduction problems in multi-layered cylinders. Journal of Applied Mathematics and Computational Mechanics, 12(3), 105-113.
• [5] Kukla, S., & Siedlecka, U. (2014). Green’s function for heat conduction problems in a multi- -layered hollow cylinder. Journal of Applied Mathematics and Computational Mechanics, 13(3), 115-122.
• [6] Lu, X., & Viljanen, M. (2006). An analytical method to solve heat conduction in layered spheres with time-dependent boundary conditions. Physics Letters A, 351, 274-282.
• [7] Siedlecka, U. (2014). Radial heat conduction in a multilayered sphere. Journal of Applied Mathematics and Computational Mechanics, 13(4), 111-118.
• [8] Pawar, S.P., Deshmukh, K.C., & Kedar, G.D. (2013). Effect of generation on quasi-static thermal stresses in a solid sphere. IOSR Journal of Mathematics, 7(5), 21-29.
• [9] Jain, P.K., Singh, S., & Rizwan-uddin (2010). An exact solution for two dimensional, unsteady, multilayer heat conduction in spherical coordinates. International Journal of Heat Mass Transfer, 53, 2133-2142.
• [10] Suneet, S., Prashant, K.J., & Rizwan-uddin (2016). Analytical solution for three-dimensional, unsteady heat conduction in a multilayer sphere. ASME Journal of Heat and Mass Transfer, 138(10), 101301.
• [11] Kumar, S., Kar, V.R., & Khudayarov B.A. (2022). Analytical Solution for the Steady-State Heat Transfer Analysis of Porous Nonhomogeneous Material Structures. In: Advanced Composite Materials and Structures. CRC Press.
• [12] du Toit, J., & Pretorius, Ch. (2021). Steady-state heat transfer analysis in a spherical domain revisited. MATEC Web of Conferences, 347, 00006.
• [13] Conroy, T., Collins, M.N., & Grimes, R. (2020). A review of steady-state thermal and mechanical modelling on tubular solar receivers. Renewable and Sustainable Energy Reviews, 119, 109591.
• [14] Klimenta, D., Minić, D., Pantić-Ranđelović, L., Radonjić-Mitić, I., & Premović-Zečević M. (2023). Modeling of steady-state heat transfer through various photovoltaic floor laminates. Applied Thermal Engineering, 229, 120589.
• [15] Szmytkowski, R. (2006). On the derivative of the Legendre function of the first kind with respect to its degree. Journal of Physics A: Mathematical and General, 39, 15147-15172.
• [16] Kukla, S., Siedlecka, U., & Ciesielski, M. (2022). Fractional order dual-Phase-lag model of heat conduction in a composite spherical medium. Materials, 15(20), 7251.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).