Research Initiation Award: Stochastic and Deterministic Solutions to Unsteady Nanofluid Mixed Convection Problems

研究启动奖为传统黑人学院和大学的初级和中期职业教师提供支持，他们正在建立新的研究项目或重新指导和重建现有的研究项目。期望该奖项有助于提高教师的研究能力和效率，改善所在机构的研究和教学，并使本科生参与研究经验。授予奥尔巴尼州立大学的奖项在许多领域具有潜在的更广泛的影响。本计划的目标是发展奈米流体在轴对称及三维流动中的数学建模与分析，并透过让本科生参与数学建模，提升本校的教与学。本计划将发展轴对称及三维流动的非线性耦合偏微分方程的数学模型及分析，这些非线性耦合偏微分方程出现在纳米流体的非定常混合对流中。本课题的具体目标是：(1)获得轴对称体中非定常混合对流纳米流体流动的确定性解；（ii）开发非定常混合对流纳米流体在轴对称和三维物体上流动的随机解；(3)研究轴对称运动体上混合对流流动的稳定性。该项目的成功将为理解复杂纳米流体中的非定常对流换热现象提供基础。这些研究的结果可用于优化流体特性和现有的关键应用，如汽车、空调和超级计算机的冷却剂，以及新兴和新颖的应用。该项目将与俄亥俄州立大学数学生物科学研究所合作进行。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. The award to Albany State University has potential broader impacts in a number of areas. The goal of this project is to develop mathematical modeling and analysis of nanofluid in axisymmetric and three-dimensional flows, and to enhance teaching and learning at the university by involving undergraduate students in mathematical modeling. The project will develop mathematical modeling and analysis of nonlinear coupled partial differential equations in axisymmetric and three-dimensional flows that arise in nanofluid flow in unsteady mixed convection. The specific goals of this project are to: (i) obtain deterministic solutions to the unsteady mixed convection nanofluid flow in axisymmetric bodies; (ii) develop stochastic solutions to unsteady mixed convection nanofluid flow over axisymmetric and three-dimensional bodies; and (iii) investigate the stability properties of the mixed convection flow over moving axisymmetric bodies. The success of this project will provide fundamental understanding of unsteady convective heat transfer phenomena in complex nanofluids. The results of such studies could be used to optimize fluid properties and for existing critical applications such as coolant for automobiles, air conditioning, and supercomputers, as well as emerging and novel applications. This project will be conducted in collaboration with the Mathematical Biosciences Institute at Ohio State University.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.