Abstract An analytic approach is utilized to investigate the heat transfer mechanism in nanofluids containing spherical nanoelements. The transient thermal conduction process in a cylindrical geometry is assessed according to the Dual-Phase-Lag (DuPhlag) model and then compared with the classic Fourier solution. For the first several seconds, the wire temperature values calculated by the two models as well as their corresponding slopes are different; the curves merge at longer times depending on the nanofluid properties. At the initial stages, the realistic temperature magnitude of the suspension is also smaller than the Fourier solution, since in reality, the transient heat transfer rate is comparatively smaller owing to the certain time lags in the heat flux/temperature gradient relationship. The key parameters that govern in the initial stages of the heat transport inside the domain are the thermophysical properties of the components of a nanofluid, their relative velocity, the size/shape and concentration of the nanoparticles, and the system geometry. Two typical parameters, the conductivity and heat flux indexes, are also introduced to evaluate the deviation of the Fourier theory from the DuPhlag model. The conductivity index has a minimum value at the initial stages, and then, it is beginning to recover. A fluctuating distribution of the heat flux index is observed at the beginning of the process which is smoothed out after a lapse of time. A decrease in the nanoparticle diameter and/or an increase in the concentration may result in accelerating the transient response of the medium to the input thermal excitation.

中文翻译：

---

纳米流体悬浮液中的瞬态热分析

摘要 利用解析方法研究了含有球形纳米元素的纳米流体的传热机理。根据双相滞后 (DuPhlag) 模型评估圆柱形几何中的瞬态热传导过程，然后与经典傅立叶解决方案进行比较。前几秒，两种模型计算出的线温值及其对应的斜率不同；根据纳米流体的特性，曲线在更长的时间内合并。在初始阶段，悬浮液的实际温度幅度也小于傅立叶解，因为实际上，由于热通量/温度梯度关系中存在一定的时间滞后，瞬态传热速率相对较小。控制域内热传输初始阶段的关键参数是纳米流体组分的热物理特性、它们的相对速度、纳米颗粒的尺寸/形状和浓度以及系统几何形状。还引入了两个典型参数，即电导率和热通量指数，以评估傅立叶理论与 DuPhlag 模型的偏差。电导率指数在初始阶段有一个最小值，然后开始恢复。在过程开始时观察到热通量指数的波动分布，该分布在时间流逝后平滑。纳米颗粒直径的减小和/或浓度的增加可能导致介质对输入热激发的瞬态响应加速。