Innovative heat flux modeling for enhanced heat transfer efficiency: Conjugate heat transfer analysis with Cattaneo-Vernotte equation incorporating Maxwellian fluid dynamics

A mathematical investigation explored the combined influence of vibration and conjugation on enhancing heat transfer in a laminar oscillatory flow through a heat pipe, also known as the “ D r e a m P i p e ”. Explicit solutions for the momentum and heat equations are provided, considering the use of viscoelastic fluids ( C P y C l / N a S a l ) as heat carriers. While many studies have relied on Fourier’s law to describe heat transport, this approach may overlook thermal inertia, potentially leading to non-physical behaviors. Instead of Fourier’s law, the Cattaneo-Vernotte equation, incorporating thermodynamic inertia in the heat transport process, is employed to model heat transfer through a circular tube with thermally conducting walls. The analysis examines the impact of conjugation and oscillation parameters on heat transfer characteristics. Optimizing wall thickness leads to a 710.4 % increase in effective thermal diffusivity in the present work, using non-Fourier’s law which is 14 times higher than that (50.63 %) obtained using Fourier’s law approach. The maximum heat flux achieved using the non-Fourier heat conduction law is approximately 7.2 × 10 9 W/m 2 for the fluid with a molar ratio of R M = 7 and an acrylic wall material. This occurs at a frequency of 8.7 Hz, which is significantly lower than the frequency used in the analysis based on Fourier’s heat conduction law. Hence, the energy needed to induce fluid oscillation may be diminished, representing a beneficial aspect of the current analysis employing the Cattaneo-Vernotte equation. Hence, the non-Fourier’s law approach offers advantages over the Fourier’s law approach. Indeed, the maximum heat flux obtained with viscoelastic fluid is three orders of magnitude higher than that obtained with Newtonian fluid. The sensitivity analysis confirms that viscoelastic relaxation and non-Fourier effects play the most significant roles in controlling the system’s thermal behavior. The reported results align well with the existing literature.