Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions

• Published in: Applied mathematics and mechanics Vol. 39; no. 12; pp. 1691 - 1718
• Main Authors: Yu, Qiang, Xu, Hang
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.12.2018; Springer Nature B.V; Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration(CISSE),State Key Laboratory of Ocean Engineering, School of Naval Architecture Ocean and Civil Engineering, Shanghai Jiao Tong University,Shanghai 200240, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Boundary conditions; Cavity flow; Classical Mechanics; Computational fluid dynamics; Distribution functions; Fluid flow; Fluid mechanics; Fluid- and Aerodynamics; Galerkin method; Heat transfer; Heating; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Parametric analysis; Partial Differential Equations; Phase deviation; Stream functions (fluids); Temperature distribution; Vorticity; Walls; Wavelet analysis; wavelet-homotopy; O357; 34B15; lid-driven inclined cavity; non-uniform heat transfer; 35J60; O29; mixed boundary condition; Galerkin technique
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-018-2397-9

In this paper, a brand-new wavelet-homotopy Galerkin technique is developed to solve nonlinear ordinary or partial differential equations. Before this investigation, few studies have been done for handling nonlinear problems with non-uniform boundary conditions by means of the wavelet Galerkin technique, especially in the field of fluid mechanics and heat transfer. The lid-driven cavity flow and heat transfer are illustrated as a typical example to verify the validity and correctness of this proposed technique. The cavity is subject to the upper and lower walls’ motions in the same or opposite directions. The inclined angle of the square cavity is from 0 to π /2. Four different modes including uniform, linear, exponential, and sinusoidal heating are considered on the top and bottom walls, respectively, while the left and right walls are thermally isolated and stationary. A parametric analysis of heating distribution between upper and lower walls including the amplitude ratio from 0 to 1 and the phase deviation from 0 to 2 π is conducted. The governing equations are non-dimensionalized in terms of the stream function-vorticity formulation and the temperature distribution function and then solved analytically subject to various boundary conditions. Comparisons with previous publications are given, showing high efficiency and great feasibility of the proposed technique.