Similarity solution analysis of dynamic and thermal boundary layers: further formulation along a vertical flat plate

This work aims to propose a simplified formulation of the similarity solution for the boundary layers problem occurring along a vertical heated flat plate under buoyancy effect. A new formulation is analytically developed. The case of the isothermal vertical infinite flat plate is investigated using a Taylor Series Expansion Model (TaSE) from which excellent agreement is reached with the results of the fifth Runge-Kutta-Fehlberg Method (RKF45) and experimental data. The boundary layer phenomena that occur along the vertical isothermal walls of the differentially heated cavity cannot be considered as portions of an infinite hot / cold plate due to the transverse entry of cold fluid and the intrusion flow under the ceiling.