An extended Taylor–Aris Framework for Thermal Front Propagation in Conjugate Pipe Flows: The Plug-Flow Limit

A reduced one-dimensional unsteady description of thermal-front propagation in conjugate pipe flows is developed here for the plug-flow limit. The starting point is the analytical advection–diffusion solution for an adiabatic fluid domain, with its characteristic exponential–error-function form. The plug-flow assumption provides a zero-shear reference case. Wall storage, finite-rate fluid–wall exchange, external heat release, and solid axial conduction can then be examined without the additional contribution of velocity-profile shear. This provides the first step of a broader reduction procedure in which the different mechanisms affecting thermal-front propagation can be introduced and identified separately. The reduced description is written in terms of the fluid bulk temperature. The model separates front motion, local spreading, and the thermal level of the upstream heated region, rather than combining all departures from the reference solution into a single effective dispersion coefficient. The corresponding closure quantities are identified from finite-element simulations of the full axisymmetric conjugate problem. Hydronic radiator columns provide a representative benchmark. The results confirm the importance of this separation. For the fluid-only adiabatic case, the reduced model recovers the expected advection–diffusion response. External heat exchange lowers the temperature of the already heated upstream region while producing little change in the local front transition. With a thermally active wall, the larger deformation of the bulk-temperature profile is primarily associated with transient energy storage in the solid and the resulting depletion of the upstream branch. Because velocity-profile shear is absent in the present configuration, these effects should not be interpreted as classical Taylor–Aris dispersion. The plug-flow case instead provides a controlled benchmark that isolates the conjugate contributions. It also provides the basis for the cross-sectional reduction and identification procedure. The same framework can then be extended to Poiseuille flow, where shear-induced Taylor–Aris dispersion enters together with the wall effects identified here. The resulting ROM offers a compact and physically interpretable alternative to full conjugate simulations for applications requiring repeated transient calculations.