Natural convection in a square cavity with uniformly heated and/or insulated walls using marker-and-cell method

In this study, a numerical investigation has been performed using the computational Harlow-Welch MAC (Marker and Cell) finite difference method to analyse the unsteady state two-dimensional natural convection in lid-driven square cavity with left wall maintained at constant heat flux and remaining walls kept thermally insulated. The significant parameters in the present study are Reynolds number (Re), thermal Grashof number (Gr) and Prandtl number (Pr) and Peclét number (Pe =PrRe). The structure of thermal convection patterns is analysed via streamline, vorticity, pressure and temperature contour plots. The influence of the thermophysical parameters on these distributions is described in detail. Validation of solutions with earlier studies is included. Mesh independence is also conducted. It is observed that an increase in Prandtl number intensifies the primary circulation whereas it reduces the heat transfer rate. Increasing thermal Grashof number also decreases heat transfer rates. Furthermore the isotherms are significantly compressed towards the left (constant flux) wall with a variation in Grashof number while Peclét number is fixed. The study is relevant to solar collector heat transfer simulations and also crystal growth technologies

Heat transfer in differentially heated non-newtonian cavities

The flow development and heat transfer in a differentially heated cavity containing a non-Newtonian fluid is studied using CFD techniques. Investigations are made for a fluid obeying a power-law type behaviour, for a nominal Rayleigh number of 105. Both dilatant and pseudoplastic regimes are considered and the Nusselt number is obtained for a range of power-law index values. The results, given in a graphical and tabular form, suggest that deviations from Newtonian stress-strain behaviour can lead to large changes in overall heat transfer. These changes are due to the behaviour of the wall boundary layers. In the dilatant, or shear-thickening regime, the isothermal wall layers are thick and slow-moving; as a consequence, buoyancy induced flow affects the whole of the cavity volume. In contrast, the pseudoplastic (or shear-thinning) regime leads to thin, fast-moving wall layers whose effect does not propagate to the core of the cavity which remains stagnant. This behaviour, which is directly attributable to the local value of the fluid viscosity, causes the average Nusselt number to decrease with the power-law index, n. Pseudoplastic fluids are therefore better at conducting heat than Newtonian fluids, and conversely dilatant fluids are worse. The information contained in this paper is of general interest to workers in heat transfer, but is more specifically relevant to researchers in non-Newtonian fluids. Example applications include biotechnology, where close temperature control of bio-cultures in enclosed vessels is required, the food processing industry, the metals casting industry and areas where heat transfer in fine suspensions is required