Heat and mass transfer in a viscous flow over a non-uniform porous plate of variable thickness is investigated in this paper. The variably heated plate is stretched/shrunk in a stagnant fluid with variable velocity and has the non-uniform species concentration. The governing partial differential equations are simplified and solved numerically. The transport of heat and mass in the flow regime is governed by a set of PDE’s satisfying certain necessary boundary conditions. The governing PDE’s are simplified by using boundary layer approximations and transformed into a set of ODE’s by invoking a set of new transformations. The system of ODE’s contains several dimensionless numbers (parameters) which demonstrates the behavior of all field quantities. All the unknown variables, rates of heat and mass transfer are evaluated and effects of the existing parameters are seen on them, whereas, they are significantly changed with the variation of these dimensionless quantities. New solutions and results are presented in graphs and tables, whereas, they are thoroughly examined and discussed. In addition to that the modeled problem and its solutions are exactly matched with the classical problems and their corresponding solutions for specific numerical values of the governing parameters involved in the current modeled problem. The engineering applications of heat and mass transfer problems are very famous in many industrial processes. Therefore, these two phenomena are widely discussed and analyzed, whereas, they are frequently utilized for the formation of metallic devices/objects while using additive manufacturing processes, cryogenics, formation of reasonable and suitable heat exchangers, falling film evaporation and the steam boilers. However, most of the engineering systems with or without magnetized and electrically conducting surfaces cannot be expressed in usual coordinates i.e. cartesian coordinate system, moreover, most of the engineering processes involve fluids of different nature and kinds, whereas, sometime they also require different physical and environmental conditions. Therefore, in such situations we need, to upgrade and modify the present modeled problem according to prevailing situations.

本文研究了粘性流体在厚度可变的非均匀多孔板上的传热和传质。可变加热的板在停滞的流体中以可变的速度拉伸/收缩，并且具有不均匀的物质浓度。控制的偏微分方程被简化并通过数值求解。流动状态下的热量和质量的传输受一组满足某些必要边界条件的PDE支配。通过使用边界层近似来简化控制PDE，并通过调用一组新转换将其转换为一组ODE。ODE的系统包含几个无量纲的数字（参数），这些数字说明了所有场量的行为。所有未知变量 评估了传热速率和传质速率，并观察了现有参数对它们的影响，然而，随着这些无量纲量的变化，它们会发生显着变化。新的解决方案和结果以图形和表格的形式呈现，但将对其进行彻底的检查和讨论。此外，该建模问题及其解决方案与经典问题及其针对当前建模问题所涉及的控制参数的特定数值的相应解决方案完全匹配。传热和传质问题的工程应用在许多工业过程中非常著名。因此，对这两种现象进行了广泛的讨论和分析，而在使用增材制造工艺时，它们经常用于形成金属器件/物体，低温，合理和合适的热交换器的形成，降膜蒸发和蒸汽锅炉。但是，大多数带有或不带有磁化导电表面的工程系统都无法用常规坐标表示此外，即笛卡尔坐标系，大多数工程过程涉及不同性质和种类的流体，而有时它们也需要不同的物理和环境条件。因此，在这种情况下，我们需要根据普遍情况升级和修改当前的建模问题。