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

doi:10.1007/s10483-018-2397-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (12): 1691-1718.doi: https://doi.org/10.1007/s10483-018-2397-9

• 论文 • 下一篇

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

Qiang YU, Hang XU

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

收稿日期:2018-05-15 修回日期:2018-07-09 出版日期:2018-12-01 发布日期:2018-12-01
通讯作者: Hang XU E-mail:hangxu@sjtu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11272209, 11432009, and 11872241)

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

Qiang YU, Hang XU

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

Received:2018-05-15 Revised:2018-07-09 Online:2018-12-01 Published:2018-12-01
Contact: Hang XU E-mail:hangxu@sjtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11272209, 11432009, and 11872241)

摘要/Abstract

摘要： 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 2π 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.

关键词: phase transformation, thermo-elasto-plasticity, stress, non-uniform heat transfer, wavelet-homotopy, liddriven inclined cavity, Galerkin technique, mixed boundary condition

Abstract: 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 2π 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.

Key words: phase transformation, thermo-elasto-plasticity, stress, mixed boundary condition, non-uniform heat transfer, liddriven inclined cavity, wavelet-homotopy, Galerkin technique

中图分类号:

34B15
35J60

Qiang YU, Hang XU. Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1691-1718.

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

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

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