Purpose

The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method.

Design/methodology/approach

The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs.

Findings

Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method.

Originality/value

The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

中文翻译：

---

利用重心函数对非线性拉伸板上传热传质的三维纳米流体流动进行数值研究

目的

本文的目的是研究一种非线性边界层流动的三维边界层流动，该流动是基于新颖的基于操作矩阵的方法，它考虑了非线性拉伸片的传热和传质问题。

设计/方法/方法

考虑适当的相似变换，将控制该问题的偏微分方程转换为非线性常微分方程（ODE）系统。利用基于积分和乘积的运算矩阵的线性重心有理基本函数的直接数值方法来求解ODE的非线性系统。

发现

提供了图形和表格结果，以说明问题中涉及的各种参数对速度分布，温度分布，纳米粒子体积分数，Nusselt和Sherwood数以及皮肤摩擦系数的影响。将获得的结果，基于Maple的dsolve（类型=数字）命令的数值结果与以前的现有结果进行比较，证明了该方法的效率和准确性。

创意/价值

本研究的目的是提供一种基于重心基数函数的运算矩阵的有效计算方法，以解决三维传热传质的纳米流体问题。讨论了所提出方案的收敛性分析。提出的方法（PM）的好处在于，在不使用任何搭配点的情况下，控制方程可转换为代数方程组。