Conjugate mixed convection in a lid-driven differentially heated square cavity with two heat conducting cylinders made of SS 304 is numerically investigated by using the finite element method. Both the heat conducting cylinders are assumed to be rotating in counter clockwise direction. The right and the left vertical walls of the cavity are maintained at a constant higher temperature (T~h~) and lower temperature (T~c~) while keeping the horizontal walls adiabatic. The left vertical wall is maintained at constant lower temperature and is moving downwards with a constant velocity (u~l~). The two-dimensional mathematical model includes the system of four partial differential equations: which are continuity, linear momentum equations and energy equation. The cavity is filled with air (*Pr* = 0.71). No slip boundary conditions are imposed on the cavity walls. The investigation is performed for six different diameter ratios of the rotating cylinders keeping D~1~/D~2~ = 0.5, 1.0 and 2.0. Flow and thermal field patterns are presented via streamline and isotherm contours. The average Nusselt number is calculated along the right vertical heated wall. Parametric simulation is performed with the variation of Nusselt number with respect to the Reynolds number based on the velocity of the vertical lid. The cylinder Reynolds number (*Re~c~*) is defined based on the peripheral velocity of rotating cylinder. The ratio of cylinder Reynolds number and the Reynolds number based on velocity of the vertical lid is denoted by Ω and is defined as Ω = *Re~c~*/ *Re*. Laminar simulation is performed in the range of 10 ≤ *Re* ≤ 2000 as beyond *Re* = 2000, the fluid flow becomes turbulent. A turbulent simulation is also performed in the range of 10 ≤ *Re* ≤ 5000. For turbulent simulation, Turbulent k-ε model has been used. The computational results show that the diameter ratio (D~1~/D~2~) = 0.1 shows improved heat transfer performance among the six diameter ratios. Based on this diameter ratio further simulation is done for varying the Reynolds number of the lid in the range of 10 ≤ *Re* ≤ 10000 with six different Reynolds numbers for the cylinders (*Re~c~*) varying from 5 to 50. The observation shows that up to Reynolds number 500 of the moving lid, the heat transfer increases with the increment of rotational speed of cylinders. Beyond this range, the heat transfer remains unaffected with the change in rotational speed of the cylinders. The Richardson number (Ri) is fixed at unity ensuring pure mixed convection phenomena. Finally, combined effects of both Reynolds number and Grashof number on heat transfer performance have been investigated keeping the Richardson number in the range of 0.1≤ Ri ≤10 ensuring laminar mixed convection region. Boussinesq approximation was used where the properties of the air are considered to be constant except for the density variation as a function of temperature.


Conjugate Mixed Convection in a Differentially Heated Lid-Driven Square Cavity With Rotating Cylinders

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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