The present examination is centered around the transfer of heat for the flow of a boundary layer free convective incompressible fluid, past a stretching porous surface, assuming viscosity dependent on temperature linearly along with heat source and sink with imposed magnetic field. Lie group similarity transformation is used to obtain the symmetric graphs of the given problem. Solutions for velocity and heat profile are encountered numerically with fourth-order Runga-Kutta shooting technique and graphically presented and explained the impact on velocity profile and temperature profile of several physical parameters as temperature-dependent parameter of viscosity A, $k_1$ as parameter of permeability, Prandtl number, $\lambda$as parameter of heat generation and absorption and M as parameter of magnetic field. We observed that the thermal boundary layer thickness can be reduced by increasing viscosity parameter A and heat sink parameter$\lambda$. As we give increment in $k_1$ we find a decrement in the horizontal velocity profile, which leads to the enhanced deceleration of the flow and, hence, the velocity decreases.

本研究的重点是通过边界多孔自由对流不可压缩流体流过拉伸多孔表面的传热，假设粘度与温度成线性关系，并随热源和外加磁场而变化。李群相似度变换用于获得给定问题的对称图。用四阶Runga-Kutta射门技术数值地求解速度和热剖面的解，并以图形方式表示和解释了作为粘度A随温度变化的几个物理参数对速度和温度剖面的影响，${ķ}_{\mathrm{1个}}$ 作为渗透率参数，普朗特数， $\lambda$作为热量产生和吸收的参数，M作为磁场的参数。我们观察到通过增加粘度参数A和散热片参数可以减小热边界层的厚度$\lambda$。当我们增加${ķ}_{\mathrm{1个}}$ 我们发现水平速度曲线减小，这导致流的减速度增强，因此速度减小。