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<p>A significant amount of research focuses with constant or variable thermophysical properties of the phase change materials. However, limited models address spatially varying functionally graded (FG) thermal conductivity and mass diffusivity with generalized boundary conditions. The study employs generalized boundary conditions on freezing surface, whereas Dirichlet boundary conditions are applied for heat and mass transmission in other scenarios. The similarity transformation technique is highly effective at offering simulated analytical solutions. To justify and analyze our results, we have considered 5% copper–95% aluminum alloy. Higher heat flux reduces the temperature profile, whereas interfaces are expanding, so freezing rate increases according to Newton’s cooling law. In contrast, higher conductive heat transfer coefficients raise the boundary temperature, which slows down the freezing process. We examine the impact of FGthermal conductivity and mass diffusivity over different Peclet numbers. Results indicate that alloy solidification decelerates as the slope of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f(\xi )=1+b\xi\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>ξ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mi>b</mi> <mi>ξ</mi> </mrow> </math></EquationSource> </InlineEquation> increases. With a rise in FG thermal conductivity, the mushy and solid zones reduce under Dirichlet and Neumann situations but expand in Robin conditions. A higher Peclet number increases the freezing process, but a lower slope of FG mass diffusivity accelerates the alloy concentration. Consequently, the combined effects of thermal and concentration gradients accelerate the alloy’s solidification, enhancing overall efficiency and enabling practical applications such as thermal management, alloy casting, and metallurgical processes.</p>

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Analytical study of functionally graded phase change material with convection and generalized boundary condition

  • 期刊论文

  • 发表日期：

    2026年1月4日

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  • Susheel Kumar,
  • Vikas Chaurasiya,
  • Jitendra Singh

摘要

A significant amount of research focuses with constant or variable thermophysical properties of the phase change materials. However, limited models address spatially varying functionally graded (FG) thermal conductivity and mass diffusivity with generalized boundary conditions. The study employs generalized boundary conditions on freezing surface, whereas Dirichlet boundary conditions are applied for heat and mass transmission in other scenarios. The similarity transformation technique is highly effective at offering simulated analytical solutions. To justify and analyze our results, we have considered 5% copper–95% aluminum alloy. Higher heat flux reduces the temperature profile, whereas interfaces are expanding, so freezing rate increases according to Newton’s cooling law. In contrast, higher conductive heat transfer coefficients raise the boundary temperature, which slows down the freezing process. We examine the impact of FGthermal conductivity and mass diffusivity over different Peclet numbers. Results indicate that alloy solidification decelerates as the slope of \(f(\xi )=1+b\xi\) f ( ξ ) = 1 + b ξ increases. With a rise in FG thermal conductivity, the mushy and solid zones reduce under Dirichlet and Neumann situations but expand in Robin conditions. A higher Peclet number increases the freezing process, but a lower slope of FG mass diffusivity accelerates the alloy concentration. Consequently, the combined effects of thermal and concentration gradients accelerate the alloy’s solidification, enhancing overall efficiency and enabling practical applications such as thermal management, alloy casting, and metallurgical processes.