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566 X. D. Niu et al. / Adv. Appl. Math. Mech., 5 (2010), pp. 564-572 The lattice Boltzmann model (LBM) is based on that of Guo et al. [6], in which two particle distribution functions are used to describe the velocity and the temperature fields, respectively. Different from the model of Guo et al. using only temperature- dependent viscosity but constant thermal diffusivity to determine the relaxations of the particle collisions [6], the present LBM uses both temperature-dependent viscosity and thermal diffusion coefficients to calculate the particle relaxations so that the local information of flow field can be simulated. The two-dimensional channel studied in the present work is based on the collector tube used in the experiment [3, 4]. Particular interest is focused on the heat transfer characteristics with mass flow rates measured in the experimental tests within the range of the Reynolds number of 210 to 840. In the numerical model, the horizontal channel is heated at different constant heat fluxes being close to the values of solar radiations measured in the experiments. The present investigation mainly attempts to shed light on the convective heat transfer enhancement occurring in the experiments. In addition, the effects of the governing parameters such as Reynolds number and heat flux on the heat transfer problem under consideration are presented. 2 Lattice Boltzmann model In mathematics, the hydrodynamics of supercritical CO2 is described by the following equations ∂tρ + ∇ρu = 0, ∂tρu + ∇ρuu = −∇p + η∇2u, ∂tρT + ∇ρTu = D∇2T, (2.1a) (2.1b) (2.1c) where t is the time, ρ, u, p and T are density, velocity, pressure and temperature, re- spectively, η and D are dynamic viscosity and thermal diffusivity of fluid, respectively. In the lattice Boltzmann frame, the above hydrodynamics can be solved by the following lattice Boltzmann equations [6] f (x+e δt,t+δt)− f (x,t) = − 1 [f (x,t)− feq(x,t)], (2.2a) (2.2b) (2.3a) (2.3b) α α α τfα α g (x+e δt,t+δt)−g (x,t) = − 1 [g (x,t)−geq(x,t)], α α α τgα α and the respective equilibrium distribution functions f eq and geq are given by αα eq eα · u (eα · u)2 1 u2 fα (x,t)=wαρ 1+ c2 + 2c4 −2c2 sss , geq(x,t)=w T 1+eα·u , α α c2sPDF Image | Study of Forced Convection Heat Transfer of Supercritical CO2 in a Horizontal Channel by Lattice Boltzmann Method
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