A Review on Analytical Heat Transfer in Functionally Graded Materials, Part I: Fourier Heat Conduction

Fourier heat conduction in functionally graded materials (FGMs) has attracted considerable scientific interest due to its simplicity in modeling. FGMs, characterized by a gradual variation in material composition and properties, exhibit unique thermal conductivity behaviors that differ from conventional homogeneous materials. Understanding and analyzing heat transfer in FGMs is crucial for optimizing their thermal performance in various applications. The analytical analysis of Fourier heat conduction in FGMs has facilitated a more profound understanding of the heat transfer phenomena that occur within these advanced materials. This paper provides a comprehensive overview of the research conducted on Fourier heat conduction in FGMs, highlighting the key methodologies, findings, and implications. The literature review showed that the thermal conductivity in FGMs varies spatially, affecting the temperature distribution and heat flux within the material. The gradual variation in material properties in FGMs necessitates the development of specialized analytical solutions to accurately describe the heat transfer behavior. Additionally, the choice of appropriate analytical functions has been found to significantly impact the accuracy and efficiency of the analytical solutions. Researchers have explored various functions, including power functions, exponential functions, and polynomial functions, to represent the temperature distribution within FGMs. It has been observed that the choice of these functions should be based on compatibility with the analytical solution of the heat conduction equation, ensuring accurate predictions of temperature profiles and heat transfer rates.