**5. Conclusions**

The present communication reports a theoretical study on the magnetohydrodynamic flow and the heat exchange of carbon nanotube (CNT)-based nanoliquid over a variable thicker surface. Kerosene oil is taken as the base fluid for the suspension of nanoparticles. Two types of carbon nanotubes (CNTs) are accounted for saturation in base fluid, particularly the single-walled and multi-walled carbon nanotubes, best known as SWCNTs and MWCNTs. The system of nonlinear equations is gained by a reasonable transformation. Analytic solution is obtained by utilizing a notable procedure called the optimal homotopic analysis technique. The key points are given below:


**Author Contributions:** Conceptualization, A.S. and G.R.; methodology, A.S.; software, A.S., G.R., I.K.; validation, A.S., I.K. and G.R.; formal analysis, A.S., I.K. and G.R., E.-S.M.S. and A.H.S.; investigation, A.S. and G.R.; resources, I.K., E.-S.M.S. and A.H.S.; data curation, A.S.; writing—original draft preparation, A.S., I.K. and G.R.; writing—review and editing, A.S., I.K. and G.R., E.-S.M.S. and A.H.S.; visualization, A.S. and G.R.; supervision, A.S.; project administration, A.S.; funding acquisition, I.K., E.-S.M.S. and A.H.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Researchers Supporting Project number (RSP-2019/33), King Saud University, Riyadh, Saudi Arabia.

**Acknowledgments:** Researchers Supporting Project number (RSP-2019/33), King Saud University, Riyadh, Saudi Arabia. The first author is supported by the Talented Young Scientist Program of Ministry of Science and Technology of China (Pakistan-19-007).

**Conflicts of Interest:** The authors declare no conflict of interests.
