Journal of Applied and Computational Mechanics

Analytical Simulation for Transient Natural Convection in a ‎Horizontal Cylindrical Concentric Annulus

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Science, Basrah University, Basrah, Iraq

Abstract

In this study, a new scheme is suggested to find the analytical approximating solutions for a two-dimensional transient natural convection in a horizontal cylindrical concentric annulus bounded by two isothermal surfaces. The new methodology depends on combining the algorithms of Yang transform and the homotopy perturbation methods. Analytical solutions for the core, the outer layer and the inner layer at small times are found by a new method. Also, the effect of Grashof number, Prandtl number and radius proportion on the heat transfer and the flow of fluid (air) at different values was studied. Moreover, the study calculates the mean of the Nusselt number along with the effect of the Grashof number and radius proportion on it as parameters which acts as clues for heat transfer calculations of the natural convection for the annulus. The results, obtained by using the new method, prove that it is efficient and has high exactness compared to the other methods, used to find the analytical approximate solution for the transient natural convection in a horizontal cylindrical concentric annulus. The convergence of the new method was also discussed theoretically by referring to some theorems, and experientially by a verification of the solutions resulting from the simulations of the convergent condition. Furthermore, the graphs of the new solutions show the veracity, utility and exigency of the new method, and come in line with solutions offered by previous studies.

Keywords

Main Subjects

[1] Crawford, L., Lemlich, R., Natural convection in horizontal concentric cylindrical annuli, Industrial and Engineering Chemistry Fundamentals, 1(4), 1962, 260-264. 
[2] Yang, X., Kong, S., Numerical study of natural convection states in a horizontal concentric cylindrical annulus using smoothed particle hydrodynamics, Engineering Analysis with Boundary Elements, 102, 2019,11-20.
[3] Pop, I., Ingham, D., Cheng, P., Transient natural convection in a horizontal concentric annulus filled with a porous medium, Journal of Heat Transfer, 114, 1992, 990-997.
[4] Kuehn, T., Goldstein, J., An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders, Journal of Fluid Mechanics,74, 1976, 695-719.
[5] Tsui, Y., Trembaly, B., On transient natural convection heat transfer in the annulus between convective horizontal cylinders with isothermal surfaces, International Journal of Heat and Mass Transfer, 27(1), 1983, 103-111.
[6] Sano, T., Kuribayashi, K., Transient natural convection around a horizontal circular cylinder, Fluid Dynamics Research, 10, 1992, 25-37.
[7] Hassan, A., Al-Lateef, J., Numerical simulation of two dimensional transient natural convection heat transfer from isothermal horizontal cylindrical annuli, Engineering and Technology Journal, 25(6), 2007, 728-745.
[8] Abdulateef, J., Effect of Prandtl number and diameter ratio on laminar natural convection from isothermal horizontal cylindrical annuli, Diyala Journal of Engineering Sciences, 9(1), 2016, 39-45.
[9] Mack, L., Bishop, E., Natural convection between Horizontal concentric cylinders for low Rayleigh numbers, The Quarterly Journal of Mechanics and Applied Mathematics, XXI, 1968, 223-241.
[10] Yang, M., Ding, Z., Lou, Q., Wang, Z, Lattice Boltzmann Method Simulation of Natural Convection Heat Transfer in Horizontal Annulus, Journal of Thermophysics and Heat Transfer, 31(3), 2017, 700-711.
[11] Bhowmik, H., Gharibi, A., Yaarubi, A., Alawi, N., Transient natural convection heat transfer analyses from a horizontal cylinder, Case Studies in Thermal Engineering, 14, 2019, 1-8.
[12] Khudhayer, S., Jasim, Y., Ibrahim, T., Natural Convection in a Porous Horizontal Cylindrical Annulus Under Sinusoidal Boundary Condition, Journal of Mechanical Engineering Research and Developments, 43(4), 2020, 230-244.
[13] Mohamad, A., Taler, J., Ocłon, P., Transient natural convection in a thermally insulated annular cylinder exposed to a high temperature from the inner radius, Energies, 13, 2020, 1-13.
[14] Mahmood, M., Mustafa, M., Al-Azzawi, M., Abdullah, A., Natural convection heat transfer in a concentric annulus vertical cylinders embedded with porous media, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 66, 2020, 65-83.
[15] Zubkov, P., Narygin, E., Numerical Study of Unsteady Natural Convection in a Horizontal Annular Channel, Microgravity Science and Technology, 32, 2020, 579-586.
[16] Wei, Y., Wang, Z., Qian, Y., Guo, W., Study on bifurcation and dual solutions in natural convection in a horizontal annulus with rotating inner cylinder using thermal immersed boundary-lattice Boltzmann method, Entropy, 20, 2018, 1-15.
[17] Medebber M., Retiel N., Said B., Aissa A. and El-Ganaoui M., Transient Numerical Analysis of Free Convection in Cylindrical Enclosure, MATEC Web of Conferences, 307, 2020, 1-9.
[18] Touzani, S., Cheddadi, A., Ouazzani, M., Natural Convection in a Horizontal Cylindrical Annulus with Two Isothermal Blocks in Median Position: Numerical Study of Heat Transfer Enhancement, Journal of Applied Fluid Mechanics, 13(1), 2020, 327-334.
[19] Hu, Y., Li, D., Shu, S., Niu, X., Study of multiple steady solutions for the 2D natural convection in a concentric horizontal annulus with a constant heat flux wall using immersed boundary-lattice Boltzmann method, International Journal of Heat and Mass Transfer, 81, 2015, 591–601.
[20] Yuan, X., Tavakkoli, F., Vafai, K., Analysis of natural convection in horizontal concentric annuli of varying inner shape, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 68, 2015, 1155-1174.
[21] Mehrizi, A., A., Farhadi, M., Shayamehr, S., Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method, International Communications in Heat and Mass Transfer, 44, 2013, 147-156.
[22] Kumar, R., Study of natural convection in horizontal annuli, International Journal of Heat and Mass Transfer, 31(6), 1988, 1137-1148
[23] Yang, X. J., A new integral transform method for solving steady heat-transfer problem, Thermal Science, 20, 2016, S639-S642.
[24] Yang, X.-J., Gao, F., A New Technology for solving diffusion and heat equations, Thermal Science, 21(1A), 2017, 133-140.
[25] Aminikhah, H., Hemmatnezhad, M., An efficient method for quadratic Riccati differential equation, Communications in Nonlinear Science and Numerical Simulation, 15, 2010, 835–839.
[26] Mirzazadeh, M., Ayati, Z., New homotopy perturbation method for system of Burgers equations, Alexandria Engineering Journal, 55, 2016, 1619-1624.
[27] Rubab, S., Ahmad, J., Muhammad, N., Exact solution of Klein Gordon equation via homotopy perturbation Sumudu transform method, International Journal of Hybrid Information Technology, 7(6), 2014, 445-452.
Journal of Applied and Computational Mechanics
Volume 7, Issue 2
April 2021
Pages 621-637