The thermo-dynamical modeling is a powerful tool for predicting the optimal melting of heat transfer; this is because there is a good correlation between numerical and analytical heattransfers via thermodynamic predicted results. A mathematical model is constructed underflow of a non-Newtonian (Reiner-Philippoff) fluid based on certain assumptions. Such mathematical model flow is handled by invoking similarity solutions for governingequations. The obtained system of nonlinear equations is solved numerically by utilizing fourth-fifth order Runge-Kutta-Fehlberg method. The consequences of distinguished parameters onfluid flow are analyzed in details through the plotted graphic visuals. Physical quantities are also considered numerically by tables. The claimed results reveal that the velocity profile reduce due to Forchheimer parameter and porosity parameter. The growing nature of temperature field is observed against temperature ratio parameter. The numerical values of local Nusselt number decline with radiation parameter and surface heating parameter. The obtained results presents novel role in the heat transfer phenomenon, electronic cooling, microheat pipes, electronic cooling, reaction processes, nuclear reactors etc.

热力学模型是预测最佳传热熔化的有力工具；这是因为通过热力学预测结果，数值传热和分析传热之间存在良好的相关性。数学模型是基于某些假设构建的非牛顿 (Reiner-Philippoff) 流体的底流。这种数学模型流是通过调用控制方程的相似性解决方案来处理的。利用四五阶Runge-Kutta-Fehlberg方法对得到的非线性方程组进行数值求解。通过绘制的图形可视化详细分析了不同参数对流体流动的影响。物理量也通过表格在数字上考虑。声称的结果表明，由于 Forchheimer 参数和孔隙度参数，速度剖面减小。根据温度比参数观察温度场的增长性质。局部努塞尔数的数值随着辐射参数和表面加热参数的增加而下降。所得结果在传热现象、电子冷却、微热管、电子冷却、反应过程、核反应堆等方面具有新的作用。