TY - JOUR
T1 - Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution
AU - Khan, Ghani
AU - Safdar, Muhammad
AU - Taj, Safia
AU - Munir, Adnan
AU - Nasir, Muhammad Tauseef
PY - 2025
Y1 - 2025
N2 - Various mathematical frameworks have been developed to study dynamics of the fluid flow in stretching films. In this work, a three–dimensional flow induced by an unsteady stretching of an infinite flat sheet is analyzed through the Lie symmetry approach. Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. Invariants for these Lie symmetries are obtained to construct a new class of similarity transformations. With the deduced similarity transformations, the flow equations are converted to ordinary differential equations which are solved using the Homotopy analysis method. The deduced analytic solution enables an exploration of the effects of various parameters on the flow and heat transfer, which have not been revealed previously using the Lie method as per the authors’ knowledge. The influences of the stretching rate, parameters that maintain the non-uniformity and unsteadiness of sheet temperature, and the Prandtl number, are demonstrated with the help of graphs and tables. These results show that for certain values of the system parameters, heat transfer reverses its direction and occurs from the fluid to the sheet. At these values, maximum heat transfer does not occur at the sheet but rather slightly above it.
AB - Various mathematical frameworks have been developed to study dynamics of the fluid flow in stretching films. In this work, a three–dimensional flow induced by an unsteady stretching of an infinite flat sheet is analyzed through the Lie symmetry approach. Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. Invariants for these Lie symmetries are obtained to construct a new class of similarity transformations. With the deduced similarity transformations, the flow equations are converted to ordinary differential equations which are solved using the Homotopy analysis method. The deduced analytic solution enables an exploration of the effects of various parameters on the flow and heat transfer, which have not been revealed previously using the Lie method as per the authors’ knowledge. The influences of the stretching rate, parameters that maintain the non-uniformity and unsteadiness of sheet temperature, and the Prandtl number, are demonstrated with the help of graphs and tables. These results show that for certain values of the system parameters, heat transfer reverses its direction and occurs from the fluid to the sheet. At these values, maximum heat transfer does not occur at the sheet but rather slightly above it.
KW - Analytic solutions
KW - Homotopy analysis method
KW - Invariants
KW - Lie transformations
KW - Similarity transformations
KW - Thin films
KW - Three-dimensional flow
UR - http://www.scopus.com/inward/record.url?scp=85208288179&partnerID=8YFLogxK
U2 - 10.1016/j.aej.2024.10.121
DO - 10.1016/j.aej.2024.10.121
M3 - Article
AN - SCOPUS:85208288179
SN - 1110-0168
VL - 112
SP - 424
EP - 435
JO - Alexandria Engineering Journal
JF - Alexandria Engineering Journal
ER -