Abstract
Lie similarity transformations for unsteady flow in a thin film under the influence of internal heating and thermal radiation have been deduced earlier. These transformations have been employed to reduce the partial differential equations of the fluid flow and heat transfer to ordinary differential equations. Fluid velocity and temperature profiles were presented by constructing homotopic solutions for the obtained system of equations. Here we apply a general linear combination of all the Lie point symmetries associated with the equations describing the flow and heat transfer with internal heating and thermal radiation, to construct the general Lie similarity transformations. By applying these transformations to the flow, we map them to ordinary differential equations. The reduced system of differential equations contains the arbitrary constants used to construct the generalised Lie similarity transformations through the linear combination of all the Lie symmetries of the flow equations. Further, we determine analytic solutions using the homotopy analysis method for the reduced system of equations. We show that the presence of arbitrary constants in the reduced system of differential equations enables control of the deduced homotopic analytic solutions, i.e., these constants serve as control parameters. We illustrate the effects of these control parameters on the temperature profiles graphically.
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Li, S., Safdar, M., Taj, S. et al. Generalised Lie similarity transformations for the unsteady flow and heat transfer under the influence of internal heating and thermal radiation. Pramana - J Phys 97, 203 (2023). https://doi.org/10.1007/s12043-023-02672-4
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DOI: https://doi.org/10.1007/s12043-023-02672-4
Keywords
- Boundary layer
- Lie point symmetry
- invariants
- similarity transformations
- analytic series solutions
- solution convergence control