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<p>This study addresses the classical Cheng-Minkowycz free convection problem in porous media by integrating the advanced Cattaneo-Christov heat flux model to capture finite thermal propagation speeds, along with variable viscosity and thermal conductivity effects to reflect realistic fluid behavior. Using the Rosseland diffusion approximation for thermal radiation, the governing nonlinear partial differential equations are transformed into ordinary differential equations and solved numerically via the MATLAB bvp4c solver enhanced by a finite difference-based shooting method. The results not only validate the model against established studies by Nield and Kuznetsov (2009) when variable properties are neglected but also highlight significant impacts of temperature-dependent properties and the Cattaneo-Christov framework on heat transfer and fluid flow, revealing new physical insights. This comprehensive approach advances the understanding of transient heat transfer in porous media, with direct applications in enhanced oil recovery, thermal management, water treatment, solar energy systems, battery performance, and environmental heat regulation.</p>

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Application of the Cattaneo-Christov heat flux model to the Cheng-Minkowycz problem with variable viscosity and thermal conductivity

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • M.A.M. Sharaf,
  • M. M. El Shafee,
  • Mohamed Montaser,
  • Ahmed Saleh

摘要

This study addresses the classical Cheng-Minkowycz free convection problem in porous media by integrating the advanced Cattaneo-Christov heat flux model to capture finite thermal propagation speeds, along with variable viscosity and thermal conductivity effects to reflect realistic fluid behavior. Using the Rosseland diffusion approximation for thermal radiation, the governing nonlinear partial differential equations are transformed into ordinary differential equations and solved numerically via the MATLAB bvp4c solver enhanced by a finite difference-based shooting method. The results not only validate the model against established studies by Nield and Kuznetsov (2009) when variable properties are neglected but also highlight significant impacts of temperature-dependent properties and the Cattaneo-Christov framework on heat transfer and fluid flow, revealing new physical insights. This comprehensive approach advances the understanding of transient heat transfer in porous media, with direct applications in enhanced oil recovery, thermal management, water treatment, solar energy systems, battery performance, and environmental heat regulation.