# Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

## 3. Invariant Solution Generated by ${X}_{1}$

## 4. Invariant Solution Generated by ${X}_{3}$

## 5. Invariant Solution Generated by ${X}_{2}\text{}\mathrm{and}\text{}{X}_{6}$

## 6. Graphical Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Dimensionless velocity ${R}_{1}(\theta )$ as a function of $\theta $ and (

**b**) dimensionless temperature ${R}_{3}(\theta )$ as a function of $\theta $ for values of the Prandtl number <1.

**Figure 3.**(

**a**) Dimensionless velocity ${R}_{1}(\theta )$ as a function of $\theta $ and (

**b**) dimensionless temperature ${R}_{3}(\theta )$ as a function of $\theta $ for values of the Prandtl number >1.

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**MDPI and ACS Style**

Abd-el-Malek, M.B.; Badran, N.A.; Amin, A.M.; Hanafy, A.M.
Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface. *Symmetry* **2021**, *13*, 175.
https://doi.org/10.3390/sym13020175

**AMA Style**

Abd-el-Malek MB, Badran NA, Amin AM, Hanafy AM.
Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface. *Symmetry*. 2021; 13(2):175.
https://doi.org/10.3390/sym13020175

**Chicago/Turabian Style**

Abd-el-Malek, Mina B., Nagwa A. Badran, Amr M. Amin, and Anood M. Hanafy.
2021. "Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface" *Symmetry* 13, no. 2: 175.
https://doi.org/10.3390/sym13020175