Purpose

To improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.

Design/methodology/approach

The mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.

Findings

The thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.

Originality/value

An extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.

中文翻译：

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使用伽辽金有限元法对纳米级固-液相互作用中的热和质量传递进行非傅里叶计算

 目的

为了提高基液的热性能，将三种类型的纳米粒子分散在基液中。一种新颖的非傅立叶传热理论用于模型的设计和开发。对样品流体的热性能进行比较，以确定哪种类型的纳米粒子组合最适合优化增强流体的热性能。本文的目的是：（i）研究纳米粒子对热性能的影响； (ii) 对热问题实施伽辽金有限元法 (GFEM)。

设计/方法论/途径

数学模型是利用新颖的非傅里叶热通量理论、计算流体动力学 (CFD) 守恒定律和无滑移热边界条件开发的。使用热边界层近似对模型进行近似，并使用 GFEM 对转换后的模型进行数值求解。执行网格灵敏度测试。保证了解的准确性、正确性和稳定性。计算所采用的数值方法已通过已发表的数据进行验证。工程感兴趣的量，即壁剪切应力、壁质量流量和壁热通量，根据新出现的流变参数和热弛豫时间进行计算和检查。

 发现

热弛豫时间测量流体恢复其原始热状态（称为热平衡）的能力，因此，模拟表明，与单纳米流体相关的热弛豫时间对流体的温度具有最显着的影响，而三元纳米流体相关的热弛豫时间对流体的温度具有最显着的影响。纳米流体具有最小的热弛豫时间。与基础纳米流体以及二元和单元纳米流体相比，三元纳米流体具有更宽的热边界厚度。与单一和混合纳米流体的壁剪切应力相比，壁热通量（在三元纳米流体的情况下）具有最显着的值。与傅里叶热和质量传递的情况相比，非傅里叶热和质量扩散情况下的壁热和质量通量具有最高值。

 原创性/价值

广泛的文献综述表明，没有研究使用新的热和质量理论考虑热和浓度记忆效应对跨流变液体中的输运机制的影响[由 Cattaneo (Cattaneo, 1958) 和 Christov (Christov, 2009) 提出] 因此远的。此外，耦合和非线性CFD问题的有限元方法迄今为止尚未实现。据作者所知，首次研究了在热和溶质弛豫时间、欧姆耗散和一级化学反应同时作用下壁热流率和质量流率的动力学。