A Mathematical Description of the Quasi-Periodically Developed Heat Transfer Regime in Channels with Arrays of Periodic Solid Structures

TL;DR

This paper develops a mathematical framework describing the quasi-periodic heat transfer in channels with periodic solid structures, using eigenvalue problems to characterize temperature modes upstream and downstream of flow regions.

Contribution

It introduces a novel eigenvalue problem approach to model quasi-periodically developed heat transfer in channels with periodic structures, incorporating conjugate heat transfer effects.

Findings

Eigenvalue problem characterizes temperature modes in the flow region.

The model accounts for conjugate heat transfer in solids.

The approach parallels developed flow field analysis.

Abstract

In this article, we present the governing equations for the temperature field upstream and downstream of the periodically developed flow region in channels with arrays of periodic solid structures. From the ansatz that the temperature field in this region is determined by exponentially decaying modes, just like the quasi-developed flow field, we arrive at an eigenvalue problem which governs the allowed temperature modes. This eigenvalue problem is virtually identical to the one for periodically developed heat transfer in isothermal solids, except that the conjugate heat transfer in the solid is effectively taken into account.