Analytical Solutions for Unsteady Thin Film Flow with Internal Heating and Radiation

Author:

Naseer Ahsan Ali1,Safdar Muhammad1,Taj Safia2,Ali Muhammad Umair3ORCID,Zafar Amad3ORCID,Kim Kwang Su45ORCID,Byun Jong Hyuk67ORCID

Affiliation:

1. School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan

2. College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan

3. Department of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Republic of Korea

4. Department of Scientific Computing, Pukyong National University, Busan, Republic of Korea

5. Interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Nagoya, Japan

6. Department of Mathematics and Institute of Mathematical Science, Pusan National University, Busan 46241, Republic of Korea

7. Finance Fishery Manufacture Industrial Mathematics Center on BigData, Pusan National University, Busan 46241, Republic of Korea

Abstract

This study determines Lie point symmetries for differential equations that mathematically express a time-dependent thin film fluid flow with internal heating and thermal radiation to construct invariants. These invariants are used in the derivation of similarity transformations for reducing the flow equations into systems of equations that possess only one independent variable. The homotopy analysis method is employed to analytically solve the reduced system of equations. The new similarity transformations and the corresponding analytical solutions comprehensively consider flow dynamics and heat transfer under multiple physical conditions. These solutions are presented graphically to demonstrate the effects of variations in the radiative heat flux with internal heating on the flow dynamics and heat transfer properties. Moreover, the variations in fluid dynamics are described graphically using the obtained analytical homotopy solution under different values of the unsteadiness parameter and Prandtl number.

Funder

Ministry of Education, South Korea

Publisher

Hindawi Limited

Subject

General Mathematics

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