Analytical And Numerical Investigation Of Coupled Boundary Layer Flow And Heat Transfer Over Stretching And Shrinking Surfaces

Sunita J¹, Arnab Bhattacharyya², T Hymavathi^3*, Sandeep Dongre⁴

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ABSTRACT

The interaction between fluid flow and thermal transport in boundary layer regions has attracted considerable attention due to its importance in numerous industrial and engineering applications such as polymer extrusion, coating processes, aerodynamic heating, and cooling technologies. In particular, stretching and shrinking surfaces introduce complex flow characteristics that significantly influence momentum and heat transfer within the boundary layer. The present study provides a comprehensive analytical and numerical investigation of coupled boundary layer flow and heat transfer over surfaces undergoing stretching and shrinking motions. The research aims to deepen the understanding of how surface deformation, thermal gradients, and flow parameters interact to shape velocity and temperature distributions in the boundary layer. The mathematical formulation of the problem is based on the steady two-dimensional boundary layer equations governing viscous incompressible fluid flow and heat transfer. Through the application of similarity transformations, the governing partial differential equations are converted into a system of nonlinear ordinary differential equations. These equations describe the coupled relationship between momentum and thermal transport within the boundary layer. Analytical insights are obtained using approximate solution techniques that reveal the fundamental behavior of the flow field, while numerical solutions are generated using stable computational schemes to capture the detailed dynamics of the system. The numerical analysis explores the influence of key governing parameters, including the stretching or shrinking rate, thermal boundary conditions, and fluid properties. The results demonstrate that stretching surfaces generally enhance fluid motion and stabilize the boundary layer, leading to smoother velocity profiles and more efficient heat transfer. In contrast, shrinking surfaces often produce complex flow patterns, including the possibility of multiple solutions and boundary layer separation under certain parameter conditions. The interaction between velocity and temperature fields is found to play a crucial role in determining the rate of heat transfer from the surface. Furthermore, the study highlights the sensitivity of thermal boundary layer thickness to variations in flow parameters. Increased stretching rates tend to thin the thermal boundary layer, thereby improving surface heat dissipation, whereas shrinking surfaces can increase thermal resistance due to the compression of flow structures near the wall. The comparative analysis between analytical approximations and numerical computations confirms the consistency and reliability of the obtained results. Overall, the investigation provides meaningful insights into the coupled mechanisms governing boundary layer flow and heat transfer over deformable surfaces. The findings contribute to the theoretical understanding of fluid-thermal interactions and offer useful guidance for optimizing thermal management in industrial processes involving moving surfaces. The analytical numerical framework developed in this work may serve as a valuable reference for future studies dealing with complex boundary layer phenomena in advanced engineering systems.

Keywords: Boundary layer flow, Stretching and shrinking surfaces, Heat transfer analysis, Numerical simulation, Fluid thermal coupling.

How to cite this article: J S, Bhattacharyya A, Hymavathi T and Dongre S, Analytical and Numerical Investigation of Coupled Boundary Layer Flow and Heat Transfer over Stretching and Shrinking Surfaces. Int J Drug Deliv Technol. 2026;16(12s): 328-336. DOI: 10.25258/ijddt.16.12s.36

Source of support: Nil.

Conflict of interest: None