Buoyancy convection in a cavity with mutually orthogonal heated plates

Abstract

Buoyancy driven convection in a square cavity induced by two mutually orthogonal arbitrarily placed heated thin plates is studied numerically under isothermal and isoflux boundary conditions. The flow is assumed to be two-dimensional. The coupled governing equations were solved by the finite difference method using the Alternating Direction Implicit technique and Successive Over Relaxation method. The steady state results are depicted in terms of streamline and isotherm plots. It is found that the resulting convection pattern is stronger for the isothermal boundary condition. A better overall heat transfer can be achieved by placing one of the plates far away from the center of the cavity for isothermal boundary condition and near the center of the cavity for isoflux boundary condition.

Thermogravitational and hybrid convection in an obstructed compact cavity

“…The values of the Nusselt number corresponding to all these situations can be found in Table III (where it is shown that the intensity of heat exchange between the surface of the step and the fluid increases as the Rayleigh number becomes higher). Interestingly, the set of values reported there also indicates that the mechanism of the Hadley type (being operative near the vertical side of the step) is much more efficient in transporting heat than that due to a heating-from-below condition at work along the horizontal side of the step (this finding being in line with other studies where square cavities with a heated plate built in vertically or horizontally or with a finned heated plate were considered, see, e.g., Oztop et al [58]; Saravanana et al [59]; Saravanan and Sivaraj [60]; Nadjib et al [61]; we will come back to this concept in Sect. 3.1.3).…”

Internal natural convection driven by an orthogonal pair of differentially heated plates

“…Unlike in [24,25] we have plate-plate and plate-wall temperature ratios. We introduce them through the non-dimensional temperature ratios…”

“…The grids 101 × 101 and 121 × 121 gave almost identical results. Hence considering both the accuracy and the computational time, the computations were all performed with a 101 × 101 grid and further details including validation of the code developed and grid independency study can be seen in our earlier works [24,25].…”

“…Papanicolaou and Jaluria [22] and Icoz and Jaluria [23] have considered such configuration in their design and optimization of cooling systems for electronic equipments. Natural convection in a square cavity induced by two mutually perpendicular heated plates were studied by the authors [24,25]. Mixed convection in a lid-driven enclosure filled with a nanofluid and induced by two mutually orthogonal thin plates have been investigated by Wang et al [26].…”

Natural Convection in a Square Cavity with Uniformly Heated and/or Insulated Walls Using Marker-and-Cell Method

“…Kakarantzas et al [11] used a direct numerical method with a fractional semi-implicit scheme approach to simulate natural hydromgnetic convection in a vertical cylindrical cavity with sinusoidal top wall temperature variation. Saravanan et al [12] examined numerically the two-dimensional buoyancy-driven convection in a square cavity with isoflux and isothermal boundary conditions. Walker and Homsy [13] investigated buoyancy-driven convection in a porous cavity.…”