Enhanced Conjugate Gradient Method for Heat Flux Estimation in Laminar and T-Junction Turbulent Mixing Flow

Abstract

In this paper, the Jaya algorithm is coupled with the traditional conjugate gradient method (CGM) for solving the inverse heat transfer problem. The coupling of two algorithms is termed as enhanced conjugate gradient method (ECGM). Two different applications have been considered to determine the accuracy and stability of ECGM. First, the algorithm is applied in a steady-state two-dimensional laminar flow through a duct for the boundary heat flux estimation. The accuracy of estimation has been compared with traditional CGM by calculating the root mean square (RMS) error. The ECGM algorithm (RMS =0.142 kW/m²) is found to be more accurate than conventional CGM (RMS = 0.198 kW/m²). ECGM is then applied to determine the peripheral variation of heat flux at the fluid-solid interface of a tube at a section downstream to the T-junction. The experimental temperature readings at the outer periphery of the tube required in the inverse algorithm are simulated by solving the direct heat conduction problem. Here, the heat flux at the fluid-solid interface is obtained by solving the governing equations of the turbulent flow by using commercial computational fluid dynamics software. ECGM is found to be a stable and accurate inverse heat transfer algorithm.

Acknowledgment

This work is supported by the grant of SERB division, Department of Science and Technology, Government of India, and the authors greatly appreciate the financial contribution towards this research.

Additional information

Notes on contributors

Sanil Shah

Sanil Shah is pursuing Ph.D. in the Department of Mechanical and Aero-Space Engineering, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad, India. His main research area includes heat transfer, fluid mechanics, computational fluid dynamics and optimization algorithms used for inverse heat transfer analysis.

Ajit Kumar Parwani

Ajit Kumar Parwani is the Department Coordinator and Assistant Professor in the Department of Mechanical and Aero-Space Engineering, IITRAM, Ahmedabad, India. He has over 15 years of teaching and research experience. His research interests include heat transfer, inverse heat transfer, computational heat transfer, renewable energy, and internal combustion engines. He has delivered several invited talks, keynote speeches and presented research work in conferences and reputed institutes. He has conducted several workshops, short-term training programs, and seminars. He has two ongoing sponsored research projects on inverse heat transfer funded by SERB-DST, Government of India, and Institute of Plasma Research, Government of India.