Purpose

The purpose of this paper is to investigate the hydromagnetic third-grade non-Newtonian fluid flow and heat transfer between two coaxial pipes with a variable radius ratio.

Design/methodology/approach

To solve the approximate nonlinear and linear problems with variable coefficients, a trial function was applied. Methods include collocation, least square and Galerkin that can be applied for obtaining these coefficients.

Findings

It is revealed that an increase of the non-Newtonian parameter, Hartmann number, and radius ratio leads to an augmentation of the absolute value of the dimensionless velocity, temperature, velocity gradient, and temperature gradient of about 10-60%. Further, the augmentation of Bi₁ reduces the absolute value of the dimensionless temperature profile and dimensionless temperature gradient about three to four times; hence, the dimensionless heat transfer rate reduces. However, the growth of Bi₂ has a contrary impact. Besides, the increase of Pr and Ec leads to an increase in the dimensionless temperature profile and dimensionless temperature gradient; therefore, the dimensionless heat transfer rate increases.

Originality/value

The convection heat transfer on the walls of the pipes is considered, and the nonlinear coupled momentum and energy equations are solved using the least squared method and collocation methods, respectively.

中文翻译：

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具有磁场可变半径比的两根同轴管中的三级非牛顿流体流动和传热

目的

本文的目的是研究具有可变半径比的两根同轴管道之间的水磁第三级非牛顿流体流动和传热。

设计/方法/方法

为了解决具有可变系数的近似非线性和线性问题，应用了试验函数。方法包括搭配，最小二乘和Galerkin，可用于获取这些系数。

发现

发现非牛顿参数，哈特曼数和半径比的增加导致无量纲速度，温度，速度梯度和温度梯度的绝对值增加约10-60％。此外，Bi ₁的增加将无因次温度分布和无因次温度梯度的绝对值降低了约三到四倍；因此，无量纲的传热速率降低。但是，Bi ₂的生长具有相反的影响。另外，Pr和Ec的增加导致无因次温度分布和无因次温度梯度的增加。因此，无量纲的传热速率增加。

创意/价值

考虑了管道壁上的对流传热，分别使用最小二乘法和搭配法求解了非线性耦合动量和能量方程。