Purpose

This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach.

Design/methodology/approach

The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B₀ has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid.

Findings

The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease.

Originality/value

The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.

中文翻译：

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用并行算法的EFGM在磁场下填充纳米流体的波浪方形外壳内自然对流的数值模拟

目的

本文旨在通过并行实现的无网格方法研究在磁场效应下填充有铜水纳米流体的波浪形外壳内的流动和传热。

设计/方法/方法

已经对二维模型进行了模拟，该模型具有填充在波浪外壳内部的纳米流体的稳定、层流和不可压缩流动，其中一个壁是正弦曲线，使得振幅 (A = 0.15) 和起伏数 ( n = 2) 固定。以倾斜角γ施加了均匀磁场B ₀。通过使用顺序和并行方法实施无元素伽辽金方法 (EFGM)，已经对传输现象的控制方程进行了数值求解。研究了各种参数，即纳米颗粒体积分数 (φ)、瑞利数 (Ra)、哈特曼数 (Ha) 和磁场倾角 (γ) 对纳米流体自然对流的影响。

发现

结果是根据在冷波浪壁、流线和等温线处计算的平均努塞尔数获得的。已经观察到，瑞利数的增加值导致传热速率增加，而哈特曼数阻碍流体运动。另一方面，磁场倾角使传热率上升到其临界值。高于此值，传热率开始下降。

原创性/价值

磁场及其倾斜度的实施为热和流体流动提供了非常有趣的结果，这些结果可用于药物输送，其中纳米流体用于许多生理问题。该论文的另一个重要新颖之处是这里使用了无网格方法（EFGM），因为域是不规则的。结果发现非常令人满意。此外，方案的并行化（在此类问题中早期尚未实现）提高了计算效率。