Flows and heat transfer over stretching/shrinking and porous surfaces are studied in this paper. Unusual and generalized similarity transformations are used for simplifying governing equations. Current model includes all previous cases of stretched/shrunk flows with thermal effects discussed so far. Moreover, we present three different cases of thermal behavior (i) prescribed surface temperature (ii) Variable/uniform convective heat transfer at plat surface and (iii) prescribed variable/uniform heat flux. Stretching/shrinking velocity U_w(x), porosity $V_w\left(x\right)$, heat transfer $T_w(x)$, heat flux $q_w\left(x\right)$ and convective heat transfer at surface are axial coordinate dependent. Boundary layer equations and boundary conditions are transformed into nonlinear ODEs by introducing unusual and generalized similarity transformations for the variables. These simplified equations are solved numerically. Final ODEs represent suction/injection, stretching/shrinking, temperature, heat flux, convection effects and specific heat. This current problem encompasses all previous models as special cases which come under the scope of above statement (title). The results of classical models are scoped out as a special case by assigning proper values to the parameters. Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter. A stability analysis is accomplished and apprehended in order to establish a criterion for determining linearly stable and physically compatible solutions. The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable (uniform) thickness with variable (uniform) stretching/shrinking and injection/suction velocities.

本文研究了拉伸/收缩和多孔表面上的流动和传热。不寻常的和广义的相似变换用于简化控制方程。当前模型包括迄今为止讨论过的所有具有热效应的拉伸/收缩流情况。此外，我们提出了三种不同的热行为情况（i）规定的表面温度（ii）平台表面的可变/均匀对流传热和（iii）规定的可变/均匀热通量。拉伸/收缩速度U _w (x)，孔隙率${伏}_{瓦}\left(X\right)$， 传播热量 ${吨}_{瓦}(X)$, 热通量 $q_{瓦}\left(X\right)$和表面的对流传热是轴向坐标相关的。通过为变量引入异常和广义的相似变换，边界层方程和边界条件被转换为非线性常微分方程。这些简化的方程通过数值求解。最终 ODE 代表吸力/注入、拉伸/收缩、温度、热通量、对流效应和比热。这个当前的问题包括所有以前的模型作为属于上述陈述（标题）范围的特殊情况。通过为参数分配适当的值，经典模型的结果被视为一种特殊情况。数值结果表明，对于收缩参数的不同可能值，可以找到对偶解。完成并理解稳定性分析，以建立确定线性稳定和物理兼容解决方案的标准。通过从具有可变（均匀）拉伸/收缩和注射/吸入速度的可变（均匀）厚度的均匀加热片中恢复流体流动和传热的先前问题，来仔细检查建模方程的显着特征和多样性。