In the study of boundary layer regions, it is in practice to dimensionalize the governing system and grouping variables together into dimensionless quantities in order to curtail the total number of variables. In similar flow phenomenon the physical parameters do not vary along the streamwise direction. However in non-similar flows the physical quantities change in the streamwise direction. In non-similar flows we are forced to non-dimensionalize the governing equations through non-similarity transformations. The forced flow of Oldroyd-B fluid is initiated as a result of stretching of a surface at an exponential rate. Flows over stretching surfaces are important because of their applications in extrusion processes. The forthright purpose of this study is to consider the non-similar aspects of forced convection from flat heated surface subjected to external viscoelastic fluid flow, described by the freely growing boundary layers enclosed by a region that involves without velocity and temperature gradients. The governing system of nonlinear partial differential equations (PDE’s) is transformed into dimensionless form by proposing new non-similar transformations. The dimensionless partial differential system is solved by using local non-similarity via bvp4c. Thermal transport analysis is conducted for distinct values of dimensionless numbers. It is revealed that heat shifting process expanded by the increase in the numerical values of Prandtl number and relaxation time. The dimensionless convective heat transfer coefficient results revealed that it is declining by expanding relaxation time constant ${\beta }_1$ and a boost is observed by enlarging the Pr and retardation time constant ${\beta }_2$. A comparison of Nusselt number is presented.

在边界层区域的研究中，实际上是对控制系统进行量纲化并将变量分组为无量纲的量，以减少变量的总数。在类似的流动现象中，物理参数不沿流向变化。然而，在非相似流中，物理量沿流向变化。在非相似流中，我们被迫通过非相似变换对控制方程进行无量纲化。Oldroyd-B 流体的强制流动是由于表面以指数速率拉伸而开始的。由于它们在挤出过程中的应用，拉伸表面上的流动很重要。这项研究的直接目的是考虑来自受外部粘弹性流体流动的平坦加热表面的强制对流的非相似方面，由自由生长的边界层描述，该边界层被一个没有速度和温度梯度的区域包围。通过提出新的非相似变换，非线性偏微分方程 (PDE) 的控制系统被转换为无量纲形式。无量纲偏微分系统通过 bvp4c 使用局部非相似性求解。热传输分析是针对无量纲数的不同值进行的。结果表明，热位移过程随着普朗特数和弛豫时间数值的增加而扩大。${\beta }_1$并且通过增大Pr和延迟时间常数观察到提升${\beta }_2$. 提供了 Nusselt 数的比较。