Analytic similarity solutions for fully resolved unsteady laminar boundary layer flow and heat transfer in the presence of radiation. Issue 4 (April 2023)

• Record Type: Journal Article
• Authors: Bilal, M.; Safdar, M.; Ahmed, S.; Ahmad Khan, R.
• Is Part Of: Heliyon. Volume 9:Issue 4(2023)
• Publication Date: 2023-04
• Subjects: Heat transfer -- Unsteady boundary layer flow -- Lie similarity transformations -- Exact solutions -- Homotopy analysis method; Research -- Periodicals; Medical sciences -- Periodicals; Natural history -- Periodicals; Social sciences -- Periodicals; Earth sciences -- Periodicals; Physical sciences -- Periodicals; 507.2
• DOI: 10.1016/j.heliyon.2023.e14765
• Languages: English
• ISSNs: 2405-8440

Abstract

Abstract: In this paper, we have compared a new type of similarity transformation derived systematically by using Lie point symmetries with the existing similarity transformations for unsteady fluid flow and heat transfer in the boundary layer in the presence of radiation. It is observed that the existing transformations map the steady and marginally accelerating flows only, while the Lie similarity transformations provide solutions for all types of accelerating flows and are independent of unsteadiness in the fluid. The previous transformations are valid for a specific time interval which depends on a range of unsteadiness parameter, however the Lie similarity transformations provide valid solutions at any given time. This implies that the Lie similarity transformations yield solutions for previously unexplored ranges of unsteadiness in the fluid. Boundary layer flow physics for both types of transformations is discussed by employing the Homotopy analysis method. We show that for accelerating fluids, in the developing region, the boundary layer thickness first increases and than starts to decrease with increase in unsteadiness for fully developed flow. Detailed comparison of velocity and temperature profiles in the boundary layer is made using the tables and graphs which show that with Lie similarity transformations the region of study of the considered flow extends significantly for the unsteadiness parameter. The effect of the Prandtl number and radiation parameter on temperature distribution is also compared for both types of similarity transformations. The Lie symmetry similarity transformations are shown to explain the unsteady laminar boundary layer flow and heat transfer to an extent where the existing similarity transformations do not work. Highlights: Lie symmetry algebra concept is utilized to systematically derive the similarity transformations. Comparison of Lie similarity transformations is made with the existing similarity transformations. Existing similarity transformations provide valid soultion in the limited regions. Exact solutions for Lie transformations address that limitation by providing the solution in unexplored regions.