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<p>In this work, we analytically address the general steady-state heat conduction problem between two solids in thermal contact, accounting for heat flux continuity and a temperature jump at the interface. The novelty of the proposed approach lies in its generality, as it is applicable regardless of the geometric configuration of the solids, and in the use of variational methods combined with the fixed-point theorem, which allow us to rigorously establish sufficient conditions for the existence and uniqueness of the solution. Moreover, we demonstrate the continuous dependence of the solution on internal heat sources in both solids, providing a robust framework for the analysis of similar systems. The practical relevance and applicability of the method are illustrated through three explicit solutions given for Cartesian, polar and spherical coordinates and four explicit examples with different characteristics, highlighting the added value of this approach for understanding and solving interface heat transfer problems. Unlike previous studies that assume specific geometries or idealized contacts, our method provides a general and rigorous framework applicable to a wide range of interface heat transfer problems.</p>

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Analytical study of steady-state heat transfer in two solids with continuous flow and thermal jump at the interface

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Domingo A. Tarzia,
  • Guillermo F. Umbricht,
  • Mara Rossani

摘要

In this work, we analytically address the general steady-state heat conduction problem between two solids in thermal contact, accounting for heat flux continuity and a temperature jump at the interface. The novelty of the proposed approach lies in its generality, as it is applicable regardless of the geometric configuration of the solids, and in the use of variational methods combined with the fixed-point theorem, which allow us to rigorously establish sufficient conditions for the existence and uniqueness of the solution. Moreover, we demonstrate the continuous dependence of the solution on internal heat sources in both solids, providing a robust framework for the analysis of similar systems. The practical relevance and applicability of the method are illustrated through three explicit solutions given for Cartesian, polar and spherical coordinates and four explicit examples with different characteristics, highlighting the added value of this approach for understanding and solving interface heat transfer problems. Unlike previous studies that assume specific geometries or idealized contacts, our method provides a general and rigorous framework applicable to a wide range of interface heat transfer problems.