Numerical modeling and simulation of heat transfer and fluid flow in a two-dimensional sudden expansion model using poro
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Numerical modeling and simulation of heat transfer and fluid flow in a two‑dimensional sudden expansion model using porous insert behind that Ziqiang Zhao1 Received: 2 February 2020 / Accepted: 29 February 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract A sudden expansion is a classical problem which is happened in different industries such as energy conversion, environmental control, and chemical processing. The current investigation is done to numerically analyze the fluid flow behavior and heat transfer over a sudden expansion when a porous medium is placed right after that. Effect of different parameters including Reynolds number (Re = 100, 200, 300), porous block height (D/H = 0.1, 0.2, 0.3, 0.4, 0.5), porous block length (L/H = 0.5, 1.0, 1.5, 2.0), and solid matrix–fluid thermal conductivity ratio (RK = 1, 10, 102, 103, and 104) on the heat transfer and pressure drop are examined. Results show that the average Nusselt number and performance number (the ratio of Nusselt number improvement to pressure drop increment) on the heated wall, located after the expansion, enhanced when Reynolds number rises (about 40% in Nusselt number at Re = 300). As well as, the results show that even low-permeable porous media could augment heat transfer at the expense of a little higher pressure drop (PN = 0.94 and about 16% better Nusselt number at L/H = 15, D/H = 0.5, Re = 300). The main achievement of this paper is that if the porous cover permeability is tuned, a good heat transfer enhancement could be achieved. Keywords Numerical modeling · Darcy number · Porous media · Heat transfer · Thermal conductivity ratio · Sudden expansion List of symbols C1 Binary constants Cp Specific heat capacity (J K−1 kg−1) D Porous block height (m) Da Darcy number F Inertial factor H Channel height (m) k Thermal conductivity (W m−1 K−1) K Permeability (m2) keff Effective thermal conductivity (W m−1 K−1) kf Thermal conductivity of the working fluid (W m−1 K−1) ks Thermal conductivity of the porous medium (W m−1 K−1) L Porous block length (m) Nu Average Nusselt number Nux Local Nusselt number * Ziqiang Zhao [email protected] 1
P Pressure (N m−2) PN Performance number Pr Prandtl number Re Reynolds number RK The ratio of thermal conductivity of porous to fluid layers T Temperature (°C) T* Normalized temperature Tin The temperature of the incoming flow (°C) Tw Temperature of bottom wall (°C) u, v x, y-component of velocity (m s−1) Uin Inlet velocity (m s−1) V Velocity magnitude (m s−1) X* Normalized horizontal distance x, y Horizontal, vertical distance (m) Greek symbols α Thermal diffusivity (m2 s−1) ε Porosity μ Dynamic viscosity (Pa s) ρ Density (kg m−3)
School of Mathematics and Statistics, Henan Finance University (Longzihu Campus), Zhengzhou 450046, China
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Subscripts eff Effective f Fluid in Inlet s Solid w Wall
Introduction Transport in porous media and investigation of various phenomena in such media have been widely applied in different fields of e
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