The main objective of the present article is to provide an analytical simulation for time dependent boundary layer flow of non-Newtonian Williamson fluid due to stretchable curved oscillatory Riga surface. Also the characteristics of heat and mass transport are studied under the influence of variable thermal conductivity and diffusivity along with convective heat and mass boundary conditions. Additionally, energy equation is also characterized with the impact of heat production. Curvilinear coordinate scheme is followed to attain the boundary layer expressions for the flow model. The governing nonlinear partial differential equations are solved analytically via homotopy analysis method (HAM). Graphs are plotted to examine comprehensively the consequences of various concerned parameters like modified magnetic parameter and radius of curvature, Williamson fluid parameter, relation of the surface's oscillating frequency to its stretching rate constant, Prandtl number, variable conductivity and heat production parameters, Schmidt number and variable diffusivity parameter on concentration, temperature, pressure and velocity profile. Also the outcomes of afore said variables on surface drag force, rate of temperature and mass transmission (Nusselt and Sherwood numbers) are shown in tabular form. The liquid velocity amplitude is enhanced with modified magnetic parameter and shows opposite behavior for Williamson fluid parameter.

本文的主要目的是提供非牛顿威廉姆森流体由于可拉伸弯曲振荡里加表面的时间相关边界层流动的分析模拟。还研究了在可变热导率和扩散率以及对流热量和质量边界条件的影响下的热量和质量传输特性。此外，能量方程还以产热的影响为特征。遵循曲线坐标方案以获得流动模型的边界层表达式。控制非线性偏微分方程通过同伦分析方法 (HAM) 解析求解。绘制图形以全面检查各种相关参数的后果，如修正的磁参数和曲率半径，威廉姆森流体参数、表面振荡频率与其拉伸速率常数的关系、普朗特数、可变电导率和产热参数、施密特数和关于浓度、温度、压力和速度分布的可变扩散率参数。此外，上述变量对表面阻力、温度和传质率（努塞尔特数和舍伍德数）的结果也以表格形式显示。修改后的磁参数增强了液体速度幅度，并显示出与威廉姆森流体参数相反的行为。压力和速度分布。此外，上述变量对表面阻力、温度和传质率（努塞尔特数和舍伍德数）的结果也以表格形式显示。修改后的磁参数增强了液体速度幅度，并显示出与威廉姆森流体参数相反的行为。压力和速度分布。此外，上述变量对表面阻力、温度和传质率（努塞尔特数和舍伍德数）的结果也以表格形式显示。修改后的磁参数增强了液体速度幅度，并显示出与威廉姆森流体参数相反的行为。