This investigation examines the Williamson nanofluid flow over an exponentially stretched surface with variable thickness. Cattaneo-Christov double diffusion (CCDD) heat flux model is applied while examining two cases of heat transfer, i.e., prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF). A mathematical model of the problem based on momentum, mass, and energy conservation. The governing non-linear partial differential equation (PDEs) are converted into non-linear ordinary differential equations (ODEs) via similarity transformations. The velocity, temperature, and concentration profiles are obtained numerically.

Additionally, the impacts of numerous physical parameters of engineering significance are visually depicted through graphs and tables. It is noted that by raising the thermal relaxation parameter ${\gamma }_1$, the temperature profile decreases. When the concentration relaxation parameter ${\gamma }_2$ rises, then the concentration distribution also decays. When the magnetic parameter M increases, then the velocity profile decreases. For the selected numeric values of the Prandtl number Pr, the temperature profile decreases for both PEST and PEHF cases.

这项研究检查了威廉姆森纳米流体在具有可变厚度的指数拉伸表面上的流动。Cattaneo-Christov 双扩散 (CCDD) 热通量模型在研究两种传热情况时应用，即规定的指数表面温度 (PEST) 和规定的指数热通量 (PEHF)。基于动量、质量和能量守恒的问题的数学模型。控制非线性偏微分方程 (PDE) 通过相似变换转换为非线性常微分方程 (ODE)。以数值方式获得速度、温度和浓度分布。

此外，通过图形和表格直观地描述了许多具有工程意义的物理参数的影响。值得注意的是，通过提高热弛豫参数${\gamma }_1$，温度曲线减小。当浓度松弛参数${\gamma }_2$上升，然后浓度分布也衰减。当磁参数 M 增加时，速度剖面减小。对于 Prandtl 数Pr的选定数值，温度曲线在 PEST 和 PEHF 情况下都会降低。