**5. Conclusions**

This section concludes the main findings of the present research work. The investigation of mass and thermal energy transfer of the 3D Carreau fluid moving through a permeable and stretching (shrinking) sheet is undertaken by considering the effects of thermal radiations, cross diffusion, and Hall current. Suitable similarity relations are employed in order to transform the set of coupled PDEs to a system of coupled ODEs. The set of coupled ODEs is then solved through the well-known standard analytical technique of HAM. The influence of the relevant physical variables on the hydromagnetic behavior of the Carreau fluid 3D flow is examined through various plots. The variations of the coefficients of skin friction, local Nusselt, and Sherwood numbers with the changing parameter values are shown through various tables. The important findings of this work are outlined as below:


**Author Contributions:** Conceptualization, A.U., I., and M.M.S.; software, S.K., A.U., and M.A.; writing—original draft preparation, I., M.M.S., and T.A.; writing—review and editing, A.K., T.A., S.K., and W.K.M.; formal analysis, W.K.M., I., and M.A.; validation, I., S.K., and A.U.; methodology, A.U., T.A., M.A., and W.K.M.; investigation, W.K.M., A.K., and S.K.; resources, M.M.S., A.K., and S.K.; project administration, M.M.S., M.A., and W.K.M.; funding acquisition, A.K. and T.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Acknowledgments:** Aziz Khan and Thabet Abdeljawad acknowledge the support provided by Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM)group number RG-DES-2017–01-17.

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

#### **Abbreviations**

The below mentioned parameters and abbreviations with their possible dimensions are used in this article:

