Heat flow in composite rods - an old problem reconsidered

TL;DR

This paper revisits the classical problem of heat flow in composite rods, revealing that the interface temperature is determined by energy conservation and differs from the equilibrium temperature in finite rods.

Contribution

It demonstrates that the interface temperature in composite rods is governed by energy conservation and can differ from the thermal equilibrium temperature, challenging previous assumptions.

Findings

Interface temperature equals that of two semi-infinite rods due to energy conservation.

The interface temperature generally differs from the equilibrium temperature in finite rods.

Two specific cases illustrate the theoretical results.

Abstract

The interface temperature of two rods with equal cross section joined at one end and with different initial temperatures, initially always acquires the value characteristic for two semi-infinite rods. This value, which is shown to be a consequence of energy conservation is, in general, different from the thermal equilibrium temperature in finite rods. To illustrate this result, two particular cases are discussed.