In this study, an analytical solution of a porous fin with natural convection and radiation heat transfer is carried out. For the first time, the analysis is accomplished in Local Thermal Non-Equilibrium (LTNE) model. The investigation is carried out on a porous fin with finite length and adiabatic tip. The Darcy model and Boussinesq approximation for buoyancy effects are used to evaluate the infiltration velocity in the porous medium. Two energy equations are solved using the Adomian Decomposition Method (ADM). The solution is validated with the numerical solution of the finite difference method, and with the asymptotic solution for the Local Thermal Equilibrium (LTE) model. The results are presented in terms of temperature profiles and total average Nusselt numbers. They pointed out the effects of internal and external radiation and convection heat transfer, as well as thermal conductivity ratio and dimensionless thickness. It was found that solid phase temperature profiles decrease as the Biot, Bi, and Rayleigh, Ra*, numbers decrease, whereas the difference between the solid phase and fluid phase temperatures, for assigned Bi, decreases for lower Ra. Thermal conductivity ratio and dimensionless thickness increase engender higher solid phase temperature for assigned Bi and Ra*. The total Nusselt number increases as Ra*, Bi and external radiation increase, whereas it decreases with the thermal conductivity ratio. Criteria to compare LTNE and LTE assumptions are proposed, and they highlight the fact that the minimum Biot number to accept the LTE assumption becomes lower as the Rayleigh number decreases.

在这项研究中，进行了具有自然对流和辐射传热的多孔翅片的解析解。首次在局部热非平衡 (LTNE) 模型中完成了分析。研究是在具有有限长度和绝热尖端的多孔翅片上进行的。浮力效应的达西模型和 Boussinesq 近似用于评估多孔介质中的渗透速度。使用 Adomian 分解方法 (ADM) 求解两个能量方程。该解通过有限差分法的数值解和局部热平衡 (LTE) 模型的渐近解进行了验证。结果以温度曲线和总平均努塞尔数表示。他们指出了内外辐射和对流传热的影响，以及热导率和无量纲厚度的影响。发现固相温度曲线随着 Biot、Bi和瑞利Ra * 数值减小，而固相和流体相温度之间的差异，对于指定的Bi，Ra越低，数值就越小。对于指定的Bi和Ra *，热导率比和无量纲厚度增加导致更高的固相温度。总努塞尔数随着Ra *、Bi和外部辐射的增加而增加，而随着热导率的增加而减少。提出了比较 LTNE 和 LTE 假设的标准，它们强调了这样一个事实，即接受 LTE 假设的最小 Biot 数随着瑞利数的减少而降低。