Two‐dimensional lattice Boltzmann simulation of natural convection in differentially heated square cavity: Effect of Prandtl and Rayleigh numbers

Abstract

A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre‐line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices.

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

“…1) are written as • The left wall (x=0) is considered as no-slip stationary wall. It is, however, partially heated isothermally (temperature T H ) for the fixed length of heating (l h =H/2) at either of the three (top, middle and bottom) locations, i.e., (5) where, the lengths h 1 and h 2 =(h 1 +l h ) are defined for the different cases ( …”

“…The lattice Boltzmann equations (LBE) for the flow and thermal energy transports are written as follow: (23) where, the equilibrium distribution functions (f k eq and g k eq for the flow and thermal fields, respectively) are given as (24) (25) Here, Δt, Δx (=e k Δt), c (=Δx/Δt=1.0), u, T, e k and w k are lattice time step, lattice space step, lattice streaming speed, velocity vector, temperature, discrete velocity vector and equilibrium distribution of weight for direction k, respectively. The relaxation parameters (τ ν and τ g for the momentum and thermal energy transport fields, respectively) are defined as (26) (27) Under the assumptions that the buoyancy force is directly proportional to the temperature gradient and negligible radiative heat transfer, the Boussinesq approximation is accounted [5,34,47,48] by calculating the buoyancy force in the vertical direction as follow.…”

“…An investigation of the natural convection heat transfer in closed as well as open ended cavity encompasses great scientific interest due to its wide ranging applications in domestic as well as industrial fields [2][3][4][5], in scientific/engineering practices, viz., chemical vapor deposition [6], cooling devices in electronic equipment [7][8][9], polymer processing [10], material processing [11], solar collectors [12], etc.…”

Lattice Boltzmann analysis of natural convection in a partially heated open ended enclosure for different fluids

“…Kefayati et al [26] have explored the natural convection in an open ended cavity for three Prandtl numbers, but the vertical wall of cavity is completely heated. Recently, Gangawane et al [28] studied the influence of wide range of Prandtl number (0.71 ࣘ Pr ࣘ 100) and Rayleigh number (10 4 ࣘ Ra ࣘ 10 6 ) on heat transfer characteristics of differentially heated square cavity by using lattice Boltzmann method.…”

“…The lowest absolute average percentage difference for the experimental and numerical temperature profiles was for the rk − ε t model and the highest was for the sk − ω model. Tables 1 and 2 represent the summary of available literature on the natural convection in open ended as well as differentially heated cavity with wall completely [19][20][21][22][23][24][25][26][27][28] and partially heated [29][30][31][32][33][34][35], respectively with their ranges of physical parameters. It can be concluded that from Tables 1 and 2 and aforementioned discussion that huge amount of the literature pertaining to the convection heat transfer characteristics from cavity with one wall completely heated is now available.…”