Rehman Sohail, Alfaleh Ayman, Afef Kallekh, Ali Shah Syed Inayat
Department of Mathematics, Islamia College Peshawar, Peshawar, Pakistan.
College of Engineering, Industrial Engineering Department, Umm Al-Qura University, Al-Khalidiya District, Al-Qunfudhah City, 28821, Saudi Arabia.
Heliyon. 2023 May 3;9(5):e15710. doi: 10.1016/j.heliyon.2023.e15710. eCollection 2023 May.
In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.
在本文中，采用了一种创新的数学方法来构建新的公式，以使用非傅里叶定律探索非平行收敛-发散通道间杰弗里·哈默尔流动中的热特性。由于在许多工业和技术过程中，如薄膜冷凝、塑料片变形、结晶、金属片冷却、喷嘴装置设计、超音速和各种热交换器以及玻璃和聚合物工业中，非牛顿流体通过非均匀表面会出现等温流动，当前的研究聚焦于该主题。为了调节这种流动，让流体在一个非均匀通道中流动。通过在傅里叶定律中引入松弛项，研究了热通量和浓度通量强度。在对流动问题进行数学模拟的过程中，我们构建了一组包含各种参数的控制偏微分方程。使用流行的变量转换方法将这些方程简化为常微分方程。通过选择默认容差，MATLAB求解器bvp4c完成了数值模拟。结果表明，热松弛和浓度松弛以相反的方式影响温度和浓度分布，而热泳则提高了两种通量。收敛通道中的惯性力使收敛通道中的流体加速，而在发散通道中流体则收缩。傅里叶定律的温度分布比非傅里叶热通量模型的更强。该研究在食品行业具有现实意义，并且与能源系统、生物医学技术和当代航空系统相关。
