Analytical Solutions for Heat Transfer and Flow of Thin Film on an Inclined Wall Using the Optimal Homotopy Asymptotic Method

Farooq, Muhammad; Shahid, Faridoon; Ayaz, Sapna; Gasimov, Yusif S.; Alraddadi, Ibrahim; Ahmad, Hijaz

doi:10.22059/jcamech.2025.390180.1359

Analytical Solutions for Heat Transfer and Flow of Thin Film on an Inclined Wall Using the Optimal Homotopy Asymptotic Method

Document Type : Research Paper

Authors

Muhammad Farooq ¹

Faridoon Shahid ¹

Sapna Ayaz ¹

Yusif S. Gasimov ²

Ibrahim Alraddadi ³

Hijaz Ahmad ³ ^{, 4} ^{, 5}

¹ Department of Mathematics, Abdul Wali Khan University, Mardan, KP, 23200, Pakistan

² Department of Mathematics and Informatics, Azerbaijan University, Baku, Azerbaijan

³ Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia

⁴ Operational Research Center in Healthcare, Near East University, Nicosia, 99138, Turkey

⁵ Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea

10.22059/jcamech.2025.390180.1359

Abstract

This study explores the analytical solutions for the non-isothermal couple stress fluid in thin-film flow over an inclined plane. The strongly nonlinear ordinary differential equations governing the momentum and energy transport are derived and solved analytically using the Optimal Homotopy Asymptotic Method (OHAM) under appropriate boundary conditions. The study provides explicit expressions for temperature distribution, vorticity, shear stress, volume flow rate, and velocity profile. A comprehensive comparison of numerical and graphical results demonstrates good agreement, validating the accuracy of the proposed method. The findings contribute to understanding heat transfer and fluid dynamics in industrial, biomedical, and engineering applications. Additionally, the influence of key parameters such as couple stress effects, heat transfer rates, and thin-film thickness variations are analyzed in detail. The study’s results can be applied in lubrication systems, microfluidics, and coating technologies, where non-Newtonian fluid behavior plays a crucial role. The effectiveness of OHAM in handling nonlinear problems is highlighted, showcasing its advantages over conventional numerical techniques. The study further emphasizes the significance of thermophysical properties in determining flow characteristics, offering valuable insights for researchers and engineers in applied fluid mechanics.

Keywords

Couple Stress Fluid

Thin Film Flow

OHAM

Temperature Distribution

Subjects

Nano-fluid, phenomena wetting phenomena, numerical methods

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