Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet

Kohilavani Naganthran, Ishak Hashim and Roslinda Nazar
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Kohilavani Naganthran: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, Malaysia
Ishak Hashim: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, Malaysia
Roslinda Nazar: Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, Malaysia

Energies, 2020, vol. 13, issue 12, 1-17

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.

Keywords: thin film; boundary layer; thermocapillarity; triple solutions; Carreau fluid (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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