Investigation of natural convection and entropy generation of non-Newtonian flow in molten polymer-filled odd-shaped cavities using finite difference lattice Boltzmann method

Abstract

This study examines the natural convection heat transfer (NCHT) and entropy generation (EG) of a non-Newtonian (NN) flow inside an odd-shaped cavity filled with molten polymer. The cavity configuration comprises hot internal walls, cold external walls, and insulated remaining walls. The finite difference lattice Boltzmann method (FDLBM) is employed to solve the governing equations involved. The input parameters span a range of values, with Rayleigh number (Ra) varying from 104 to 105, power-law index (n) covering a range from 0.5 to 1.5, and width ratio (WR) ranging from 0.2 to 0.4, while maintaining Prandtl number (Pr) at a constant value of 10. The results revealed that at Ra values of 104 and 105, the overall entropy increases as the WR increases from 0.2 to 0.4 and decreases as the n index increases. In contrast to dilatant fluids, where heat transfer (HT) decreases as the n index increases from 1 to 1.5, pseudo-plastic fluids show an opposite trend with HT increasing as the n index decreases from 1 to 0.5. This trend is attributed to the general decrease in the average Nusselt number (Nu) as the n index increases. Additionally, it is observed that the n index has no significant impact on the average Nu due to low buoyancy force at Ra = 104 and WRs of 0.2 and 0.3. However, it notably influences the Bejan number (Be) across all WRs. Overall, the present model demonstrates excellent agreement with previous numerical results, affirming the FDLBM as a superior, reliable, and well-suited technique for relevant applications. These results suggest the potential to extend the application of the FDLBM approach to various cavity shapes, allowing for a comprehensive exploration of NCHT and EG under various conditions.

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