Rayleigh–Bénard Power-Law Fluid Convection in Rectangular Enclosures

Sahin Yigit, Nilanjan Chakraborty
2017 Journal of thermophysics and heat transfer  
Influences of aspect ratio (ratio of height to length) on laminar Rayleigh-Bénard convection of powerlaw fluids in rectangular enclosures have been numerically investigated for constant wall heat flux boundary condition for horizontal walls. The steady state simulations have been conducted for the range of aspect ratio 0.25 to 4, nominal Rayleigh number range 10 3 to 10 5 , power-law index 0.6 to 1.8 for a representative single value of nominal Prandtl number (10 3 ). It has been found that
more » ... ective transport weakens with increasing aspect ratio and thermal conduction dominates thermal transport for tall enclosures. Moreover, the critical Rayleigh number for the onset of convection increases with increasing values of power-law index and aspect ratio. Thermal convection irrespective of the value of aspect ratio has been found to augment with increasing (decreasing) Rayleigh number (power-law index) due to strengthening of buoyancy force in comparison to viscous resistance with increasing Rayleigh number (shear-thinning behaviour with decreasing power-law index). The simulations reveal that flow patterns and mean Nusselt number are dependent on the initial condition, and it is possible to obtain different steady-state solutions for different initial conditions. The numerical findings have been explained with the help of scaling arguments and in turn have been utilised to propose a correlation for the mean Nusselt number. Nomenclature AR Aspect ratio [-] Thermal diffusivity [m 2 /s] a 0 , a 1 Correlation parameter [-] Thermal expansion coefficient [1/K] b Correlation parameter [-] Velocity boundary layer thickness [m] c p Specific heat at constant pressure [J/kgK] Thermal boundary layer thickness [m] e Relative errror [-] Dimensionless temperature [-] e ij Rate of strain tensor [s -1 ] Dynamic viscosity [Ns/m 2 ] g gravitational acceleration [m/s 2 ] Kinematic viscosity [m 2 /s] Gr Grashof number [-] Density [kg/m 3 ] H Height of the enclosure [m] Stress tensor (stress) [N/m 2 ] h Heat transfer coefficient [W/m 2 K] Stream fuction [m 2 /s] P Pressure [Pa] Special characters Pr Prandtl number [-] ∆ Temperature difference hot and cold wall q Heat flux [W/m 2 ] ∆ , Minimum cell distance r e Grid expansion ratio [-] Ra Rayleigh number [-] T Temperature [K] u i ith component of velocity [m/s] U Dimensionless horizontal velocity ( / ) [-] V Dimensionless vertical velocity ( / ) [-] x i ,x j Coordinate in ith and jth directions [m]
doi:10.2514/1.t5108 fatcat:2nsd2u5f7rd6djuqezvg7ob6ny