Novel effective thermal conductivity numerical model for distinct shaped pure paraffins (C14-C33)

This paper presents a novel numerical model for "effective thermal conductivity" designed to address the limitations of previous models, which required different constants for each distinct shape. The constants C and m incorporates the natural convection effect through the Rayleigh number (CRam), obviating the need to solve velocity equations such as those for continuity and momentum. Notably, this model is applicable to a wide range of phase change materials (PCMs) using the same constants. Prior investigations predominantly focused on spherical capsule shapes and specific PCMs with varying C and m constants. The present study extends the limitations from spherical to cylindrical, square and rectangular shapes. The PCMs evaluated includes pure paraffins ranging from C14 to C33, all assessed using constant values for the C and m. Initially, the proposed model for effective thermal conductivity, along with the constrained model accounting for natural convection, was verified against experimental data for C18 alkane, achieving a root mean square error of 0.0177 with experimental and 0.0077 with constrained model. Subsequently, the present model's validity was affirmed against a reference constrained model across a wide range of alkanes. Simulations were carried out for both cylindrical and square shapes. For rectangular configurations, the aspect ratio was incorporated into the Rayleigh number to account the effects of both vertical and horizontal orientations.