Thermal rectification (TR) efficiency has always been an important concern for thermal rectifiers. However, in practical terms, the amount of heat conduction is equally not negligible. To get high values on both of them, the carbon nanotube arrays with high thermal conductivity and large heat conduction areas were considered, along with carbon/boron nitride heteronanotubes (CBNNTs) with excellent TR property. In our work, multiple CBNNT models are constructed, and the TR ratio under different conditions is investigated using nonequilibrium molecular dynamics, with double CBNNTs (D-CBNNTs) aligned in parallel as the main analytical object. It is shown that weakening the intertube coupling is an available way to enhance the TR ratio, and adjusting the heteronanotube length and spacing can also effectively regulate the TR. In the process of changing the coupling coefficient, we analyzed both phonon changes and atomic vibrations and got a good correspondence, and the BN region is more variable in D-CBNNTs. In addition, the covariation of phonon localization and intertube phonon exchange with the coupling coefficient results in an invariant backward heat flux in the D-CBNNT. Furthermore, by adjusting the carbon proportion and lowering the coupling coefficient in the model, an excellent TR ratio in four CBNNTs was obtained and its heat flux is even larger than the value at a carbon percentage of 50% in larger coupling. We fully utilized the phonon density of states, phonon participation rate, and mean square displacement. Our results demonstrate the possibility of multiple CBNNTs as thermal rectifiers and provide theoretical guidance for heteronanotube arrays to be applied.