Indrajeet Varhadpande, V. R. K. Murthy, N. K. Lamba

THERMAL BEHAVIOUR OF A CIRCULAR PLATE UNDER CAPUTO-FABRIZIO FRACTIONAL IMPACT WITH SECTIONAL HEATING

Introduction

Thermal behaviour of a circular plate under caputo-fabrizio fractional impact with sectional heating. Investigate thermal behaviour of a circular plate under Caputo-Fabrizio fractional impact with sectional heating. Analyze displacement, temperature, and thermal stresses for aluminium plates using integral transformations.

Abstract

Recent advances in the understanding of the precise physical thermal behaviour of various solids under the effect of fractional-order derivatives have boosted the study of thermoelasticity, which is primarily important in various industrial designs of usable structural materials. We investigated a thin circular plate that was subjected to additional sectional heating on its top and lower surfaces while creating thermal insulation around its outside border. In this work, we maintained the heat transfer equation while accounting for the impact of Caputo-Fabrizio fraction-order derivatives. According to specified boundary constraints, the integral transformation approach is used to assess the analytical solution of the displacement, temperature change, and thermal stresses. Furthermore, various functions and fractional parameters are computed using the material properties of aluminium metal plates for numerical purposes. Received: May 20, 2024Revised: September 2, 2024Accepted: September 16, 2024

Review

This paper, titled "THERMAL BEHAVIOUR OF A CIRCULAR PLATE UNDER CAPUTO-FABRIZIO FRACTIONAL IMPACT WITH SECTIONAL HEATING," investigates a contemporary and highly relevant topic in the field of thermoelasticity. The study addresses the thermal behavior of solids by incorporating fractional-order derivatives, a methodology gaining traction for its potential to more accurately describe complex material responses and memory effects. The authors underscore the importance of this research for advancing the design of various industrial structural materials, setting a clear context for its practical applications. The core of the research focuses on a thin circular plate subjected to specific thermal conditions: additional sectional heating on its top and lower surfaces, alongside thermal insulation around its outside border. A central methodological contribution is the incorporation of the Caputo-Fabrizio fractional-order derivative into the heat transfer equation, which is expected to capture non-local and non-instantaneous thermal phenomena. Utilizing the integral transformation approach, the authors aim to derive analytical solutions for key thermoelastic fields, including displacement, temperature change, and thermal stresses, all under well-defined boundary constraints. Numerical evaluations using the material properties of aluminium metal plates are planned to illustrate the impact of various functions and fractional parameters. Overall, this work promises a valuable analytical contribution to the growing body of literature on fractional thermoelasticity. The choice of the Caputo-Fabrizio derivative for analyzing a circular plate with specific heating and insulation conditions is timely and relevant, potentially offering deeper insights into the material's thermal response than classical models. The combination of analytical solutions and subsequent numerical computations using real material properties suggests a thorough investigation that could be highly beneficial for both theoretical understanding and practical engineering applications, particularly in material design where precise thermal control is critical.

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