Modeling and Simulations of Laminar Mixed Convection in a Vertical Pipe Conveying Slurries of a Microencapsulated Phase-Change Material in Distilled Water

Abstract

Steady, laminar, mixed convection in a straight and vertically oriented pipe conveying slurries of a microencapsulated phase-change material (MCPCM) suspended in distilled water (flowing upwards), with essentially uniform heat flux imposed on its outside surface, are considered. A cost-effective homogenous mathematical model is proposed and shown to be applicable to the aforementioned mixed convection phenomena with slurries of a sample MCPCM. Correlations for the effective properties of the sample MCPCM slurries and procedures for their implementation are presented. The energy equation, in which the latent-heat effects are handled using an effective specific heat, is cast in a form akin to that of a general advection-diffusion transport equation. Difficulties with the standard definition of bulk temperature when the specific heat of the fluid changes significantly with temperature are elaborated, and a modified bulk temperature that overcomes these difficulties is proposed. A finite volume method (FVM) was used to solve the mathematical model. The proposed model and FVM were validated by using them to solve problems involving slurries of the sample MCPCM, and comparing the results to those of a complementary experimental investigation. The numerical results compare very well with those of the complementary experimental investigation. They also demonstrate the need for optimizing the various parameters involved, if full benefits of the MCPCM slurries are to be achieved for specific applications.