Journal of Applied and Computational Mechanics

Unsteady Meshfree Framework for Double-diffusive Natural Convection with Boundary and Geometry Effects

Document Type : Research Paper

Authors

Department of Civil Engineering, National Yang Ming Chiao Tung University, Hsinchu 300093, Taiwan

Abstract

In this study, a meshfree framework based on the reproducing kernel collocation method is proposed for incremental-iterative analysis of double-diffusive natural convection in a porous enclosure, in which the forward difference method is adopted for temporal discretization, and the two-step version of Newton-Raphson method is used for iteration. As the double-diffusive convection problem is composed of multi phases and is influenced by both material and geometric parameters, the resulting system is highly nonlinear and complicated. From the numerical investigation, the partially heated boundary with different buoyancy ratios can yield monocellular flow problems with opposite phenomena depending on the contribution of thermal/solute buoyancy force. For the domains with burrowing inside, the key feature is the contour of stream function, which is separated into two vortexes by the hole in the simply connected domain while the two vortexes are not separated completely in the multiply connected domain due to the geometric compression of two holes. It is further shown that the framework is capable of solving various double-diffusive convection problems with satisfactory accuracy and efficiency by uniform discretization as well as few source points in the approximation.

Keywords

Main Subjects

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[1] Huppert, H. E., Turner, J. S., Double-diffusive convection, Journal of Fluid Mechanics, 106, 1981, 299-329.
[2] Nishimura, T., Wakamatsu, M., Morega, A. M., Oscillatory double-diffusive convection in a rectangular enclosure with combined horizontal temperature and concentration gradients, International Journal of Heat and Mass Transfer, 41(11), 1998, 1601-1611.
[3] Nield, D. A., Kuznetsov, A.V., The onset of double-diffusive convection in a nanofluid layer, International Journal of Heat and Fluid Flow, 32, 2011, 771-776.
[4] Maatki, C., Ghachem, K., Kolsi, L., Hussein, A. K., Borjini, M. N., Aissia, H. B., Inclination effects of magnetic field direction in 3D double-diffusive natural convection, Applied Mathematics and Computation, 273, 2016, 178-189.
[5] Chamkha, A. J., Double-diffusive natural convection in a porous enclosure with cooperating temperature and concentration gradients and heat generation or absorption effects, Numerical Heat Transfer, 47(12-13), 2002, 2699-2714.
[6] Yang, J. Q., Zhao, B. X., Numerical investigation of double-diffusive convection in rectangular cavities with different aspect ratio I: High-accuracy numerical method, Computer and Mathematics with Applications, 94, 2021, 155-169.
[7] Goyeau, B., Songbe, J.P., Gobin, D., Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-Brinkman formulation, International Journal of Heat and Mass Transfer, 39, 1996, 1363-1378.
[8] Hasnaoui, S., Amahmid, A., Raji, A., Beji, H., Hasnaoui, M., Dahani, Y., Benhamed, H., Double diffusive natural convection in an inclined enclosure with heat generation and Soret effect, Engineering Computations, 35, 2018, 2753-2774.
[9] March, R., Coutinho, A. L.G.A., Elias, R. N., Stabilized Finite Element Simulation of Double Diffusive Natural Convection, Mecánica Computacional, Buenos Aires, Argentina, 2010.
[10] Hao, Y., Nitao, J., Buscheck, T. A., Sun, Y., Double diffusive natural convection in a nuclear waste repository, International High-Level Radioactive Waste Management Conference, Las Vegas, United States, 2006.
[11] Wang, D., Wang, J., Wu, J., Arbitrary order recursive formulation of meshfree gradients with application to superconvergent collocation analysis of Kirchhoff plates, Computational Mechanics, 65, 2020, 877-903.
[12] Wang, L., Qian, Z., A meshfree stabilized collocation method (SCM) based on reproducing kernel approximation, Computer Methods in Applied Mechanics and Engineering, 371, 2020, 113303.
[13] Yang, J. P., Lin, Q., Investigation of multiply connected inverse Cauchy problems by efficient weighted collocation method, International Journal of Applied Mechanics, 12(1), 2020, 2050012.
[14] Yang, J. P., Li, H. M., Recovering heat source from fourth-order inverse problems by weighted gradient collocation, Mathematics, 10(2), 2022, 241.
[15] Fan, C. M., Chien, C. S., Chan, H. F., Chiu, C. L., The local RBF collocation method for solving the double-diffusive natural convection in fluid-saturated porous media, International Journal of Heat and Mass Transfer, 57, 2013, 500-503.
[16] Li, P. W., Chen, W., Fu, Z. J., Fan, C. M., Generalized finite difference method for solving the double-diffusive natural convection in fluid-saturated porous media, Engineering Analysis with Boundary Elements, 95, 2018, 175-186.
[17] Yang, J. P., Liao, Y. S., Direct collocation with reproducing kernel approximation for two-phase coupling system in a porous enclosure, Mathematics, 9(8), 2021, 897.
[18] Yang, J. P., Chang, H. C., Meshfree collocation method for double-diffusive natural convection in a porous enclosure using reproducing kernel approximation, Journal of Thermal Stresses, 2023, accepted.
[19] Li, P. W., Grabski, J. K., Fan, C. M., Wang, F., A space-time generalized finite difference method for solving unsteady double-diffusive natural convection in fluid-saturated porous media, Engineering Analysis with Boundary Elements, 142, 2022, 138-152.
[20] Yang, J. P., Chang, H. C., Meshfree collocation framework for multi-phase coupling nonlinear dynamic system in a porous enclosure, International Journal of Structural Stability and Dynamic, 22(15), 2022, 2271004.
[21] Costa, V. A. F., Double-diffusive natural convection in parallelogrammic enclosures filled with fluid-saturated porous media, International Journal of Heat and Mass Transfer, 47, 2004, 2699-2714.
[22] Shiina, Y., Hishida, M., Critical Rayleigh number of natural convection in high porosity anisotropic horizontal porous layers, International Journal of Heat and Mass Transfer, 53(7-8), 2010, 1507-1513.
[23] Bilal Ashraf, M., Hayat, T., Alsaedi, A., Shehzad, S. A., Soret and Dufour effects on the mixed convection flow of an Oldroyd-B fluid with convective boundary conditions, Results in Physics, 6, 2016, 917-924.
[24] Bourich, M., Hasnaoui, M., Amahmid, A., Double-diffusive natural convection in a porous enclosure partially heated from below and differentially salted, International Journal of Heat and Fluid Flow, 24, 2004, 1034-1046.
[25] Wang, D., Wang, J., Wu, J., Superconvergent gradient smoothing meshfree collocation method, Computer Methods in Applied Mechanics and Engineering, 340, 2018, 728-766.
[26] Deng, L., Wang, D., An accuracy analysis framework for meshfree collocation methods with particular emphasis on boundary effects, Computer Methods in Applied Mechanics and Engineering, 404, 2023, 115782.
[27] Trevisan, O. V., Bejan, A., Natural convection with combined heat and mass transfer buoyancy effects in a porous medium, International Journal of Heat and Mass Transfer, 28, 1985, 1597-1611.
[28] Yang, J. P., Lin, Q., Investigation of multiply connected inverse Cauchy problems by efficient weighted collocation method, International Journal of Applied Mechanics, 12(1), 2020, 2050012.
[29] Yang, J. P., Lam, H. F. S., Detecting inverse boundaries by weighted high-order gradient collocation method, Mathematics, 8(8), 2020, 1297.
Journal of Applied and Computational Mechanics
Volume 10, Issue 2
April 2024
Pages 272-286