Two thermal adiabatic boundary conditions arise on the semitransparent window owing to the fact that whether semitransparent window allows the energy to leave the system by radiation mode of heat transfer. It is assumed that being low conductivity of semitransparent material, energy does not leave by conduction mode of heat transfer. This does mean that the semitransparent window may behave as only conductively adiabatic (qc = 0) or combinedly conductively and radiatively adiabatic (qc + qr = 0). In the present work, the above two thermal adiabatic boundary conditions have been investigated in natural convection problem for the Rayleigh number (Ra) 10^5 and Prandtl number(Pr) 0.71 in a cavity, whose left vertical wall has been divided into upper and lower parts in the ratio of 4:6. The upper section is semitransparent window, while lower section is isothermal wall at a temperature of 296K. A collimated beam is irradiated with different value (0, 100, 500 and 1000 W/m2) on the semitransparent window at an angle of 45^0 . The cavity is heated from the bottom by convective heating with free stream temperature of 305K and heat transfer coefficient of 50 W/m2K while right wall is also isothermal at same temperature as of lower left wall and upper wall is adiabatic. All walls are opaque for radiation except semitransparent window. The results reveal that the dynamics of both the vortices inside the cavity change drastically with irradiation value and also with the boundary conditions on the semitransparent window. The temperature and Nusselt number increase inside the cavity multifold for combinedly conductively and radiatively adiabatic condition than the only conductively adiabatic condition on the semitransparent window.
The effects of the semitransparent winodw's aspect ratio on the interaction of the collimated beam with natural convection have been investigated numerically in the present work. The combination of geometrical parameters of the semitransparent window, i.e., height ratio ($h_r$) and window width ratio ($w_r$) and Planck numbers of the medium have been considered. The other parameters, like flow parameter (Ra$=10^5$), fluid parameter (Pr=0.71), thermal parameter (N), Irradiation (G=1000 $W/m^2$), Angle of incidence ($ϕ=135^0$) and geometrical parameter of the geometry ($A_r$=1) and the wall cond…
In the present work, the effects of diffuse and collimated radiation on the symmetrical cooling case of natural convection in a two-dimensional cavity heated from the bottom have been investigated, numerically. The cavity is convectively heated from the bottom with heat transfer coefficient of 50 W/m2K and free stream temperature 305 K, while both vertical walls of cavity are isothermal at temperature of 296 K. The top wall is adiabatic and all walls are opaque for radiation heat transfer. For collimated case, a small semitransparent window of non-dimensional width of 0.05 at height of 0.7 has…
We investigate the influence of the temperature boundary conditions at the sidewall on the heat transport in Rayleigh-Bénard (RB) convection using direct numerical simulations. For relatively low Rayleigh numbers Ra the heat transport is higher when the sidewall is isothermal, kept at a temperature $T_c+Δ/2$ (where $Δ$ is the temperature difference between the horizontal plates and $T_c$ the temperature of the cold plate), than when the sidewall is adiabatic. The reason is that in the former case part of the heat current avoids the thermal resistance of the fluid layer by escaping through the …
Comment on Effects of transverse magnetic field on mixed convection in wall plume of power-law fluids, by Rama Subba Reddy Gorla, Jin Kook Lee, Shoichiro Nakamura and Ioan Pop [International Journal of Engineering Science, 31 (1993) 1035-1045]. In the above paper the authors treat the boundary layer mixed convection flow of a power-law fluid along a vertical adiabatic surface in a transverse magnetic field with a steady thermal source at the leading edge. The governing non-similar equations are solved by means of a novel finite difference scheme. However, there are two fundamental errors in th…
It is shown that helicity dynamics dominates spectral distribution of the velocity fluctuations in turbulent thermal convection at moderate and large values of the Rayleigh number (distributed chaos and scaling respectively). The large-scale circulation (wind) in the turbulent Rayleigh-Bénard convection is especially sensitive to the helicity dynamics and its chaotic reversals can be associated with the reversals of the mean helicity sign (the ergodic restoration of the reflectional symmetry in a long run). Results of the laboratory experiments and measurements in the free atmospheric convecti…
An experiment of thermal convection with significant compressible effects is presented. The high-gravity environment of a centrifuge and the choice of xenon gas enable us to observe an average adiabatic temperature gradient up to 3.5 K cm$^{-1}$ over a 4 cm high cavity. At the highest rotation rate investigated, 9990 rpm, the superadiabatic temperature difference applied to the gas layer is less than the adiabatic temperature difference. The convective regime is characterized by a large Rayleigh number, about 10$^{12}$, and dominant Coriolis forces (Ekman number of order 10$^{-6}$). The analys…
A series of numerical simulations of Rayleigh-B{é}nard convection in a cubic cavity are conducted in order to examine the structure of the thermal boundary layer in case of mixed boundary conditions. The main goal of the study is the physical mechanism which provides increasing of heat flux with spatial frequency of conducting-adiabatic pattern. Different spatial configuration of conducting plates, including the fractal one, are considered for Rayleigh numbers from $\Ray=10^{7}$ to $\Ray=2.0\times 10^{9}$. We have shown that the temperature boundary layer in case of mixed boundary conditions a…
Gravity-driven convection of fluid at parameters near its thermodynamic critical point inside a porous layer heated from below (Rayleigh-Darcy convection) is studied. The fluid having the temperature slightly above the critical one is one-component. The hydrodynamic model describing a high compressible fluid phase at variable physical properties inside a solid matrix at a uniform porosity is analyzed. A near-critical fluid is assumed to be the van der Waals gas. In the limit of small variations in the density and thermodynamic coefficients where the Oberbeck-Boussinesq approximation is applica…
Direct Numerical Simulation have been carried out for a two dimensional flow in a Lid driven cavity at Reynolds number 5000 and Prandtl number 7 with water as the working fluid. Both the side walls of the enclosure are insulated(i.e. adiabatic boundary condition), while the bottom plate is at higher temperature and the top wall is at colder temperature. Effects of heating of the bottom wall and movement of the top lid have been investigated by conducting numerical simulations at different Richardson numbers by varying from low and moderate magnitudes within the limits of Boussinesq-approximati…
This report summarises the results for the numerical simulation of thermocapillary convection in a two-fluid system with a deformable interface. An explicit technique with 3rd order Runge-Kutta method in time, 2nd order ENO for the advection terms, and 2nd order central-differencing for the diffusion terms are employed in the momentum equations for simulating the flow on a staggered grid using a Marker and Cell method. An energy equation is solved numerically and a level-set method is used to implicitly capture the interface. A constant contact angle condition is assumed between the end walls …
We examine the dynamics associated with weakly compressible convection in a spherical shell by running 3D direct numerical simulations using the Boussinesq formalism [1]. Motivated by problems in astrophysics, we assume the existence of a finite adiabatic temperature gradient $\nabla T_{\rm{ad}}$ and use mixed boundary conditions for the temperature with fixed flux at the inner boundary and fixed temperature at the outer boundary. This setup is intrinsically more asymmetric than the more standard case of Rayleigh-Bénard convection in liquids between parallel plates with fixed temperature bound…
The parameterization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density -or both- develop highly non-linear mean profiles due to the interactions between the turbulent boundary layer and the unmixed -stable- flow above/below it. We present a second order closure able to cope simultaneously with both bulk and …
A numerical solution is presented for the natural convection from inclined wall plumes which arise from a line thermal source imbedded at the leading edge of an adiabatic plate with arbitrary tilt angle and embedded in a fluid-saturated porous medium. An appropriate transformation of the governing boundary-layer equations is proposed and a very efficient novel numerical solution is proposed to obtain rigorous numerical solutions of the transformed nonsimilar equations over a wide range of tilt angle from the vertical to the horizontal.
We numerically simulate three-dimensional Rayleigh-Bénard convection, the flow in a fluid layer heated from below and cooled from above, with inhomogeneous temperature boundary conditions to explore two distinct regimes described in recent literature. We fix the non-dimensional temperature difference, i.e.~the Rayleigh number to $Ra=10^8$, and vary the Prandtl number between $1$ and $100$. By introducing stripes of adiabatic boundary conditions on the top plate, and making the surface of the top-plate only $50\%$ conducting, we modify the heat transfer, average temperature profiles and the und…
The vertical structure of stationary thin accretion discs is calculated from the energy balance equation with heat generation due to microscopic ion viscosity η and electron heat conductivity κ, both depending on temperature. In the optically thin discs it is found that for the heat conductivity increasing with temperature, the vertical temperature gradient exceeds the adiabatic value at some height, suggesting convective instability in the upper disc layer. There is a critical Prandtl number, Pr = 4/9, above which a Keplerian disc become fully convective. The vertical density distribution of …
In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. In the present work, we consider a very peculiar equation of state, whereby entropy is solely dependent on density, so that a nearly isentropic fluid domain is nearly isochoric. Within this class of equations of state, there is a thermal adiabatic gradient and a key property of compressible convection is still present, namely its capacity to viscously dissipate a large fraction of the thermal energ…
This paper presents the study and implementation of finite element method to find the temperature distribution in a rectangular cavity which contains a fluid substance. The fluid motion is driven by a sudden temperature difference applied to two opposite side walls of the cavity. The remaining walls were considered adiabatic. Fluid properties were assumed incompressible. The problem has been approached by two-dimensional transient conduction which applied on the heated sidewall and one-dimensional steady state convection-diffusion equation which applied inside the cavity. The parameters which …
Wall cooling has substantial effects on the development of instabilities and transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional DNSs is used to analyze Mach~6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability radiates energy. Fluid-thermodynamic analysis shows that this radiation comprises both acoustic as well as vortical waves. 2D simulations show that the conventional "trapped" nature of second-mode instability is ru…
