A Complete Heatline Analysis on Visualization of Heat Flow and Thermal Mixing during Mixed Convection in a Square Cavity with Various Wall Heating

Abstract

A wide range of applications involving mixed-convection studies can be found in various engineering processes such as thermal discharge of water bodies, float glass production, heat exchangers, nuclear reactors, and crystallization process. The present study focuses on understanding the thermal mixing scenarios for mixed-convection lid-driven flow in a square cavity using heatlines. Thermal mixing is analyzed for four different thermal boundary conditions, and heat flow patterns in mixed convection are analyzed using Bejan's heatlines concept for wide ranges of parameters (Pr = 0.015À7.2, Re = 1À100, and Gr = 10 3 À10 5 , where Pr, Re, and Gr denote the Prandtl, Reynolds, and Grashof numbers, respectively). The results indicate that, at low Pr values (Pr = 0.015), the transport is conduction-dominant irrespective of the values of Gr and Re. The trends of heatlines and streamlines are identical near the core for high-Re cases. A single circulation cell was observed in the streamlines for any Pr g 0.7 at high Re and low Gr values for uniform heating of the bottom surface with cold side walls. It was observed that thermal mixing increased significantly with subsequent rises in Gr for high-Pr fluids. Patterns of heatlines and multiple circulation cells of heatlines were found to lead to enhanced thermal mixing, with the thermal boundary layer much compressed toward the walls for linearly heated side walls. The heat-transfer rates along the walls are illustrated by the local Nusselt number distribution based on gradients of heatfunctions for the first time in this work. Nusselt numbers with infinitely large magnitudes were observed at hotÀcold junctions, illustrating high heattransfer rates. An oscillatory distribution in the local heatfunction rate was observed as a result of sinusoidal heating of the bottom surface for high-Pr fluids. Negative heat-transfer rates or local Nusselt numbers were observed along the side walls when side wall(s) was/were linearly heated, as explained based on negative heatfunction gradients. Also, the effect of Gr on the local and average Nusselt numbers in different cases can be adequately explained based on heatlines. Dense heatlines signifying higher overall heattransfer rates along the bottom surface and side walls were observed for uniform bottom surface heating, whereas lower heat-transfer rates were observed for sinusoidal heating. Nonmonotonic distributions in overall heat-transfer rates along the bottom surface and left wall were observed when both walls were linearly heated, whereas a smooth and exponential increase was observed when the right wall was isothermally cooled.

Laminar Mixed Convection in a Lid-Driven Square Cavity with Two Isothermally Heated Square Internal Blockages

“…Waheed (2009) heated cavity better heat transfer can be obtained. Basak et al (2011) analyzed four different thermal boundary conditions, and heat flow patterns in mixed convection using heatlines concept of Kimura (1983) for wide ranges of parameters (Pr = 0.015-7.2, Re = 1 -100, and Gr = 10 3 -10 5 ). The results indicate that, at low Prandtl number, the heat transfer is conduction dominant irrespective of Grashof number and Reynolds number.…”

A comprehensive review on mixed convection for various patterns of kinematically and thermally induced scenarios within cavities

“…As mentioned earlier, the governing equations for fluid medium, porous medium and nanofluids can be solved with the appropriate boundary conditions [equations (20)–(22)]. Post processing of velocity and temperature variables in terms of streamlines (fluid flow) (Basak et al , 2011b; Bhattacharya et al , 2013; Roy et al , 2015, 2016, 2017), heatlines (heat flow) (Khorasanizadeh et al , 2013; Basak et al , 2011a, 2011b; Biswal et al , 2017; Roy et al , 2017, 2015, 2016; Biswas et al , 2016) and heat transfer rates (Nusselt number) can be carried out based on computations using various numerical techniques (see Table 1).…”

“…Model 1 discusses about various works involving the movement of the top adiabatic wall (Talebi et al , 2010; Khorasanizadeh et al , 2013; Sivasankaran et al , 2010; Sivasankaran and Pan, 2012; Arani et al , 2012; Sivakumar and Sivasankaran, 2014; Sivasankaran et al , 2016; Nayak et al , 2015; Basak et al , 2009a, 2009b, 2011a, 2010, 2011b, 2012). The other walls are maintained stationary.…”

Dual Solutions in the Boundary Layer Flow and Heat Transfer in the Presence of Thermal Radiation with Suction Effect

“…Numerical simulation of unsteady mixed convection in a driven cavity using an externally excited sliding lid has been studied by [14]. According to [15], correlations for heat and mass transfer in the cooperating case taking into account the effect of natural convection in porous media. The dual solutions for the upper and lower branch of the porous medium significantly affect the rate of heat transfer and mass transfer in the cavity.…”