Rayleigh Number

The effect of magnetic field-dependent viscosity on the revolving axi-symmetric steady flow of ferrofluid in a disc is investigated by solving the boundary layer equations using Neuringer–Rosenweig model. Besides numerically calculating the velocity components and pressure for different values of magnetic field-dependent viscosity with variation in dimensionless parameter α (Karman’s parameter), we also have calculated the thickness of the boundary layer and the total volume flowing outward the z-axis. Here, the solutions of non-linear differential equations are obtained in the form of asymptotic series.

This paper presents a numerical study of the conjugate heat transfer (natural convection, surface thermal radiation and conduction) in a square cavity with turbulent flow. The cavity has one vertical isothermal wall, two horizontal adiabatic walls and one vertical semitransparent wall with a selective coating applied to the inner side to control the solar radiation transmission. Later on the semitransparent wall is replaced with another one without the selective coating. The mathematical model for the turbulent flow in the cavity was solved using the finite volume method. The system had the following conditions: the uniform temperature in the isothermal wall was 21 °C, the external ambient temperature was fixed at 35 °C and on the semitransparent wall the direct normal solar irradiation of 750 W/m2 was considered constant. The Rayleigh number was varied in the range of 109 ⩽ Ra ⩽ 1012 by changing the lengths of the cavity from 0.70 m to 6.98 m, respectively. The results show that, e...

A three-dimensional analytical solution to the steady-state free convection problem in a long rotating porous box is presented for large values of the porous media Ekman number. The convection results from differential heating of the horizontal walls leading to temperature gradients orthogonal to the centrifugal body force. The solution to the nonlinear set of partial differential equations was obtained through an asymptotic expansion of the dependent variables in terms of two small parameters representing the reciprocal Ekman number in porous media and the aspect ratio of the domain. The results are focused towards the Coriolis effect on the flow. Secondary circulation was obtained in a plane orthogonal to the leading free convection plane. The results show that the Coriolis effect on free convection is controlled by a combined dimensionless group representing the ratio of the centrifugal Rayleigh number to the porous media Ekman number.

The intention of this work is to investigate the natural convection effect in a 2-D single-slope solar still. The flow is assumed as steady, laminar, and incompressible ideal gas. A numerical model based on SIMPLEC algorithm is used for the solution of mass, momentum, energy, and concentration equations. The solutions are performed for several values of aspect ratio and Rayleigh number between 2.5 and 5.5 and between 5× 106 and 5× 107, respectively. Moreover, a new correlation for estimating the convective heat ...

Natural convection in an inclined differentially heated square enclosure containing internally heated fluid has been investigated numerically using the Galerkin finite element method. The horizontal walls are adiabatic, while the side walls are isothermal but kept at different temperatures. Flow and heat transfer characteristics through isotherms, streamlines and average Nusselt numbers have been presented for the external Rayleigh number 10^3 to 10^6, internal Rayleigh number 10^5 to 10^8 and inclination angles 0º to 30º. The obtained computational results indicate that the strength of the convective currents depends on the internal energy. Heat removal rate is optimized at zero inclination angle for relatively weak external heating mode for all values of internal energy.

We numerically investigate turbulent thermal convection driven by a horizontal surface of constant heat flux and compare the results with those of constant temperature. Below Ra ≈ 109, where Ra is the Rayleigh number, when the flow is smooth and regular, the heat transport in the two cases is essentially the same. For Ra > 109 the heat transport for imposed heat flux is smaller than that for constant temperature, and is close to experimental data. We provide a simple dimensional argument to indicate that the unsteady emission of thermal plumes renders typical experimental conditions closer to the constant heat flux case.

This paper presents a numerical study of the conjugate heat transfer (natural convection, surface thermal radiation and conduction) in a square cavity with turbulent flow. The cavity has one vertical isothermal wall, two horizontal adiabatic walls and one vertical semitransparent wall with a selective coating applied to the inner side to control the solar radiation transmission. Later on the semitransparent wall is replaced with another one without the selective coating. The mathematical model for the turbulent flow in the cavity was solved using the finite volume method. The system had the following conditions: the uniform temperature in the isothermal wall was 21 °C, the external ambient temperature was fixed at 35 °C and on the semitransparent wall the direct normal solar irradiation of 750 W/m2 was considered constant. The Rayleigh number was varied in the range of 109 ⩽ Ra ⩽ 1012 by changing the lengths of the cavity from 0.70 m to 6.98 m, respectively. The results show that, e...

The present work deals with numerical study of natural convective heat transfer in a 2D square enclosure heated from below. The top wall is exposed to ambient temperature whereas the side walls are kept adiabatic. The study is conducted for different conducting mediums inside. The conducting mediums considered for the study are air and Al2O3-water nanofluid. Simulations are run for a Rayleigh Number variation of 5x107 to 25x107. The heat transfer rate is found to increase with increase in hot wall temperature. For air, the thermal interactions are achieved through bulk motion of fluid. For Al2O3-water nanofluid, the mechanism of heat transfer is attained through local fluid interactions. But the nanofluids are also found to exhibit bulk movement at higher hot wall temperatures. Numerical study was done using FLUENT 14.0.