We would like to thank Kim et al. for appreciating the importance of our work [1]. It should be noted that the introduction of a disk shaped heat pipe by us in the cited paper was done for the very first time in the literature and our comprehensive analytical results for the disk-shaped and rectangular-shaped heat pipes constitute the very first such analysis in the literature. In summary, we are going to show that all of our derivations and results are exactly correct as presented in the paper. We only have a couple of minor misprints in the paper that need to be cited. However, all of our presented analytical results and figures are correct as they are. We will rigorously show that the points raised by Kim et al. are partly due to their misunderstanding of our analysis and partly due to the errors in their work....

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