A Simplified Model with a Hybrid Analytical-Numerical Solution for Predicting the Unsteady Conjugate Heat Transfer Process in Pipelines

This work presents a new, simplified and yet efficient model for studying the transient conjugate heat transfer process in pipelines. The simplified model consists of assuming the thermal transport by fluid flow in bulk form and the pipe–wall heat conduction as two-dimensional. The scale analysis of the dimensionless equations resulting from the simplified model allows for the identification of two predicting parameters useful in determining when axial diffusion in the pipe wall is important, ψ = Pe Γ/ξ < 1 and λ = 4 Nu E ²/ξ < 1, and when radial diffusion is important, ψ > 1 and λ > 1. When these criteria are satisfied, in which case the existing analytical solution becomes invalid, the simplified model proposed here becomes an efficient alternative to the full-scale numerical simulations required for solving the problem. The scale analysis predictions and the hybrid analytical-numerical solutions of the simplified model, involving the Laplace transform and the finite-volume method, are validated first by comparison against the existing analytical solution, and then by comparison against experimental results of turbulent flow, showing excellent agreement in both cases.