The study of magnetically influenced flows in conjunction with non-Newtonian dusty fluids finds wide-ranging applications in minerals processing, environmental engineering, and biomedical sciences. These include, but are not limited to, wastewater management, soil remediation and groundwater treatment, removal of contaminants from water or soil, magnetic separation techniques, controlled and site-specific drug delivery, and biomedical diagnostic procedures. This research focuses on the dynamic behaviour of a conducting dusty fluid, modelled using the Casson framework, in the presence of a thermally active plate with ramped movement and the effects of a magnetic field. The model also incorporates several key physical phenomena, including thermal radiation, heat generation, and Newtonian heating wall conditions. To describe the time-dependent flow behaviour mathematically, partial differential equations are employed. Analytical solutions are derived using mathematical approach, notably the Laplace transform (LT). The results, including changes in flow profiles and various physical quantities due to various influencing factors, are depicted through graphs and tables, offering a clear visual representation of the findings. The research concludes that a higher thermal relaxation time parameter significantly improves thermal characteristics. Higher levels of particle concentration parameter correspond to slower fluid flow. Both the heat transfer rate and shearing stress on the plate exhibit temporal variations for a range of physical parameters. The particle concentration parameter has a notable impact on thermal transmission. The study’s findings may be applied in climate modelling, weather prediction, contaminant transport, and studying phenomena such as dust storms, air pollution, and dispersion of volcanic ash clouds.

与非牛顿尘埃流体相结合的磁力影响流研究在矿物加工、环境工程和生物医学科学中有着广泛的应用。这些包括但不限于废水管理、土壤修复和地下水处理、去除水或土壤中的污染物、磁分离技术、受控和特定地点的药物输送以及生物医学诊断程序。这项研究的重点是在存在斜坡运动的热活性板和磁场影响的情况下，使用 Casson 框架进行建模的导电尘埃流体的动态行为。该模型还结合了几个关键的物理现象，包括热辐射、热量产生和牛顿热墙条件。为了以数学方式描述随时间变化的流动行为，采用偏微分方程。解析解是使用数学方法得出的，特别是拉普拉斯变换（LT）。结果，包括由于各种影响因素导致的流量剖面和各种物理量的变化，通过图表和表格进行描述，提供了结果的清晰直观表示。研究得出的结论是，较高的热弛豫时间参数可显着改善热特性。较高水平的颗粒浓度参数对应于较慢的流体流动。板上的传热速率和剪切应力都表现出一系列物理参数的时间变化。颗粒浓度参数对热传递有显着影响。该研究的结果可应用于气候建模、天气预报、污染物输送以及沙尘暴、空气污染和火山灰云扩散等现象的研究。