The fascinating properties of hybrid nanofluid consisting of chemical and mechanical strength, excellent thermal and electrical conductivity, lower cost, high heat transfer rates, and physico-chemical reliability make it a desirable fluid in thermal energy system. Bearing in mind such exhilarating features of hybrid nanofluid, our intention in current research is to examine the heat and flow transfer rates in water-based hybrid nanofluid with suspension of hybrid nanoparticles (Cu–\(\hbox {Fe}_{3}\hbox {O}_{4}\)) past a vertical cone enclosed in a porous medium. The effects of external magnetic field, thermal radiation, and non-uniform heat source/sink are additional features to the innovation of the constructed mathematical model. The set of nonlinear coupled equations supported by related initial and boundary conditions is executed numerically using finite difference method. In the analysis of coupled distribution, the impact of various controlling parameters on velocity and temperature are scrutinized and the obtained results are exhibited graphically. The physically important quantities such as heat transfer coefficient and wall shear stress are evaluated versus governing constraints. In addition, the heat transfer performance of (Cu–\(\hbox {Fe}_{3}\hbox {O}_{4}\))–water hybrid nanofluid is compared with \({\hbox {Fe}_{3}\hbox {O}_{4}}\)–water and Cu–water, and their results are summarized in the tables. For both types of nanofluids, solo and hybrid, it is witnessed that the temperature of the system increases in the presence of magnetic field and thermal radiation. Moreover, the velocity of the fluid increases due to high permeability effects. It is also observed that the Nusselt number increases by increasing nanoparticles concentrations in the fluid; however, it decreases in presence of internal heat source. A striking highlight of the executed model is the validation of the findings by comparing them with a content already reported in the literature. In this respect, a venerable coexistence is achieved.

混合纳米流体的迷人特性包括化学和机械强度、优异的导热性和导电性、低成本、高传热率和物理化学可靠性，使其成为热能系统中理想的流体。考虑到混合纳米流体的这些令人振奋的特性，我们目前研究的目的是检查具有混合纳米颗粒 (Cu– \(\hbox {Fe}_{3}\ hbox {O}_{4}\)) 经过一个封闭在多孔介质中的垂直锥体。外部磁场、热辐射和非均匀热源/汇的影响是构建数学模型创新的附加特征。由相关初始和边界条件支持的非线性耦合方程组采用有限差分方法进行数值计算。在耦合分布分析中，仔细研究了各种控制参数对速度和温度的影响，并以图形方式显示了所获得的结果。物理上重要的量，例如传热系数和壁面剪应力，是根据控制约束进行评估的。此外，(Cu– \(\hbox {Fe}_{3}\hbox {O}_{4}\) )–水杂化纳米流体的传热性能与\({\hbox {Fe}_{3}\hbox {O}_{4}}\) –水和铜 – 水，其结果总结在表中。对于两种类型的纳米流体，单独的和混合的，可以看到系统的温度在磁场和热辐射的存在下增加。此外，由于高渗透性效应，流体的速度增加。还观察到努塞尔数随着流体中纳米颗粒浓度的增加而增加；然而，它在内部热源的存在下会降低。执行模型的一个显着亮点是通过将结果与文献中已经报道的内容进行比较来验证结果。在这方面，实现了令人尊敬的共存。