一种用于解决薄膜纳米流体在旋转表面上的不稳定的三维布朗运动的新技术
Payam Jalili1, Ali Ahmadi Azar1, Bahram Jalili2
1Department of Mechanical Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran.
Scientific reports
|August 15, 2023
概括
本研究提出了新的分析方法,用于在三维薄膜纳米材料流中的短暂旋转角度板问题. 该研究为复杂的流体动力学提供了新的解决方案,与数值方法进行验证.
科学领域:
- 流体动力学 流体动力学
- 纳米材料科学 科学 纳米材料科学
- 热量和质量转移是热量和质量转移.
背景情况:
- 旋转盘的流体运动具有重要的工程应用.
- 对非线性,时间依赖的流体动力学问题的分析解决方案具有挑战性.
- 研究短暂的,三维薄膜纳米材料流需要先进的方法.
研究的目的:
- 在3D薄膜纳米材料流中分析研究瞬态旋转角度板问题.
- 应用和开发半分析技术来解决控制的部分微分方程 (PDEs).
- 分析各种无维参数对流体流动行为的影响.
主要方法:
- 使用相似性变量将控制的PDE转换为非线性普通微分方程 (ODE).
- 采用了两个半分析技术:修改后的阿克巴里-甘吉方法 (AGM) 和混合分析-数值 (HAN) 方法.
- 根据Runge-Kutta第四阶数值方法 (RK4) 验证了分析解决方案.
主要成果:
- 通过使用修改的AGM和HAN方法,成功地导出和解决非线性ODEs.
- 为暂时流量问题提出了新的分析解决方案.
- 在四个不同的案例中通过图形分析证明了无维参数 (例如,普兰特尔,施密特数) 的影响.
结论:
- 修改后的AGM和HAN方法为这个复杂的流体动力学问题提供了准确和新的半分析解决方案.
- 该研究成功地解决了对时间依赖的三维薄膜纳米材料流动的分析解决方案的挑战.
- 这些发现为涉及旋转流体动力学的工程和工业应用提供了宝贵的见解.
相关概念视频
01:17Steady, Laminar Flow Between Parallel Plates
237
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
237
01:23Steady, Laminar Flow in Circular Tubes
253
Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
253
01:22Couette Flow
323
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
323
01:28Irrotational Flow
492
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
492
01:30Bernoulli's Equation for Flow Along a Streamline
1.0K
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
1.0K
01:18Newtonian Fluid: Problem Solving
259
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
259