Forced, natural and mixed convection of Non-Newtonian fluid flows in a square chamber with moving lid and discrete bottom heating

Abstract

The aim of the present study is to examine the thermal performance of a power-law fluid for a discretely heated lid-driven enclosure. This numerical outcome can determine the ideal heat transfer medium for a given design, thus reducing unnecessary expenditures on experiments. The chamber's side walls move at a constant speed under constant ambient conditions. The finite element approach is used to solve governing Navier-Stokes and energy equations. A parametric investigation is carried out by varying the Richardson number (Ri) within the range of 2 × 10−3 ≤ Ri ≤ 105 at a fixed Reynolds or Grashof number in different cases and changing them simultaneously while keeping the Richardson number at unity. In all cases, the power-law index (n) is varied within 0.6 ≤ n ≤ 1.4. The results have been presented in terms of a quantitative evaluation of the average Nusselt number of the heated source, the average fluid temperature of the chamber, the maximum temperature of the heat source, and the normalized average Nusselt number. Furthermore, qualitative contour plots of stream function and temperature for different cases are presented. This research shows that the higher the power-law index, the greater the heat transfer for forced and pure mixed convection and that heat transfer performance differs with the increment/decrement of the Richardson number while keeping either Reynolds or Grashof number constant. Besides, the highest heat transfer performance is observed during the natural convection case of the pseudo-plastic fluid, and the lowest heat is transferred when the fluid is dilatant.

Keywords

• Square chamber
• Non-Newtonian
• Power-law fluid
• Discrete heat source
• Average Nusselt number