The rapid movement of heat transferred goes to be the most important target for researchers to deals with the thermal problems of electronic systems. Especially, that has high packing densities in limited space. Consequently, vertical combination between two shapes of fins was considered to improve the thermal performance of heat sink. Here, many models (longitudinal-pin fins) were created as a new approach based on the stable both of material and size.

In the analytical solution, Finite element techniques used to solve the mathematical modeling and signum-sinusoidal-signum function was modified to model both the variable heat transfer area and convection perimeter. While in the numerical procedure, ANSYS simulation used as the validation of temperature distribution. In addition, results from previous work were used as second method of validation process. The results show a high level of agreement by maximum difference does not exceed (3.52%).

In the calculation process, natural convection, range of Ra number (10⁵–10⁷) were applied for all models of which each one is distinguished by the parameter of area ratio (A∗) between hybrid model and longitudinal model. The results show many advantages; a significant drop in temperature profile about (2.7%–8.8%). Also, decrease in thermal resistance by (23%–43%) and increases in heat transferred (29%–78%). Furthermore, all parameters have a significant improve for the models that have A∗<1.48. But this improvement was down to less level at A∗>1.48 as a result of overlapping between the effects of miscellaneous parameters.

Irreversibility that associated with the entropy generation was considered. In this step, it becomes important to find the model that achieves maximize of the thermal performance and minimize of the entropy generation. For that, the optimization procedure using genetic algorithm was adopted. It's clearly the best model exist within a close range between 1.509 and 1.518 based on the behavior of the best fitness function.

传热的快速运动将成为研究人员解决电子系统热问题的最重要目标。特别是在有限的空间内具有高的包装密度。因此，考虑了两种形状的翅片之间的垂直组合以改善散热器的热性能。在此，基于材料和尺寸的稳定，创建了许多模型（纵向销鳍）作为一种新方法。

在解析解决方案中，修改了用于求解数学模型和符号正弦信号函数的有限元技术，以对可变传热面积和对流周长进行建模。在数值过程中，ANSYS仿真用作温度分布的验证。此外，先前工作的结果被用作验证过程的第二种方法。结果表明，最大差异的最高一致性不超过（3.52％）。

在计算过程中，对所有模型应用自然对流，Ra值的范围为（10 ⁵ –10 ⁷），每个模型都用混合模型和纵向模型之间的面积比（A ∗）参数来区分。结果显示出许多优点；温度曲线显着下降约（2.7％–8.8％）。此外，热阻降低（23％–43％），传热增加（29％–78％）。此外，对于A ∗ <1.48的模型，所有参数都有显着改善。但是，由于杂项参数的影响相互重叠，因此在A ∗> 1.48时，这种改进降低到较小的水平。

考虑了与熵产生有关的不可逆性。在此步骤中，找到实现热性能最大化和熵生成最小化的模型变得很重要。为此，采用了基于遗传算法的优化程序。显然，基于最佳适应度函数的行为，最好的模型存在于1.509和1.518之间的范围内。