Abstract
Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity. Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically. The sheet is permeable, and there is an injection effect at the surface of the stretching sheet. The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c. The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer. However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet. The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness. Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process.
Highlights
The discovery of the boundary layer by Prandtl [1] remarked the highest achievement in the development of fluid mechanics and created a proper basis to understand the dynamics of the real fluid.The Prandtl boundary layer is found in a wide range of aerodynamics and engineering applications.The boundary layer idea evolved into the theoretical works on the boundary layer flow over a stretching surface which was contributed by the following literature: Sakiadis [2,3], Crane [4], and Carragher and Crane [5]
The theoretical work in thin film flow was started by Wang [21] by investigating the behavior of thin liquid film flow past an impermeable stretching surface and it was found that the similarity solutions were absent when the value of the unsteadiness parameter (S) falls within the range of S > 2
The present investigation was conducted to observe the effects of thermocapillarity and injection in the Carreau thin film flow and heat transfer past an unsteady stretching sheet
Summary
The discovery of the boundary layer by Prandtl [1] remarked the highest achievement in the development of fluid mechanics and created a proper basis to understand the dynamics of the real fluid. Researchers investigated the impact of thermocapillarity on thin film flow and heat transfer along with other settings such as magnetic field [39], nanofluid [40], thermal radiation [41], and suction/injection effects at the surface of the stretching sheet [42]. Rehman et al [43] solved the thin film flow, heat, and mass transfer problem with several physical effects such as thermocapillarity, heat generation/absorption, mixed convection, chemical reaction, and magnetohydrodynamics (MHD) past an unsteady stretching sheet. Formulation byProblem a thin liquid film of uniform thickness, h t and a horizontal elastic sheet which is stretching are focused incompressible two–dimensional unsteady fluid confined fromWe a narrow slit atwith the an origin of the Cartesian coordinate system, as Carreau illustrated by flow.
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