The Magnetohydrodynamics (MHD) flow of second grade and viscoelastic fluids due to a linearly stretching sheet in a Darcy porous medium considering Cattaneo-Christov heat flux model (with the thermal relaxation time playing a significant role) is tackled analytically. Closed form analytic solution is presented for the energy equation employing the properties of Appell hypergeometric function of two variables presumably for the 1st time in the literature. It is shown that the associated energy equation yields closed form solution only iff″(0)² > aλPr; in particular, being a structural constraint for the existence of thermal solutions under the studied model. Here, f″(0)is the normalized shear stress at the wall, λis the relaxation time parameter in Cattaneo-Christov model, Pris Prandtl number and ais the positive stretching ratio.

通过分析解决了考虑Cattaneo-Christov热通量模型（热弛豫时间起重要作用）的Darcy多孔介质中线性拉伸片材引起的第二级和粘弹性流体的磁流体力学（MHD）流动。利用两个变量的Appell超几何函数的性质，针对能量方程式提出了封闭形式的解析解，这在文献中大概是第一次。结果表明，只有当f ''（0）²  >  aλPr ;时，相关的能量方程才产生封闭形式的解。特别是在所研究的模型下存在热解的结构约束。在这里，f ''（0）是墙的标准化剪应力，λ是Cattaneo-Christov模型中的弛豫时间参数，Pris Prandtl数，a是正拉伸比。