Rayleigh Number

The analytical solution for a vertical heated plate subjected to conjugate heat transfer due to natural convection at the surface and conduction below is presented. The heated surface is split into two regions; the uniform heat flux region toward upstream and remaining fraction as the uniform wall temperature region. The fractional areas under the two regions are considered variable. Adopting thermally thin wall regime approximation, the possible solutions were investigated and found to satisfactorily deal with longitudinal conduction and temperature variation in the transverse direction. A test setup was developed and the experiments were conducted to obtain relevant data for comparison with the analytical solutions. The ranges for Rayleigh number and heat conduction parameter (α) during various test conditions were 2×108–6×108, and 0.001–1, respectively. The limiting solutions for stipulated conditions are analyzed and compared with experimental data. Reasonable agreement is obser...

Natural convection heating within a can of liquid food during sterilization is simulated by solving the governing equations for continuity, momentum and energy conservation for an axisymmetric case using a commercial Computational Fluid Dynamics (CFD) package (PHOENICS). Transient flow patterns and temperature profiles within model liquids (sodium carboxy-methyl cellulose (CMC) and water) have been predicted. The model liquids, CMC and water, were assumed to have constant properties except for the viscosity (temperature dependent) and density (Boussinesq approximation). It has been shown that the action of natural convection forces the slowest heating zone (SHZ) to migrate towards the bottom of the can as expected. The shape and the size of the SHZ area are different for CMC and water. The magnitude of the axial velocity was found to be in the range of 10−5–10−4 m/s for CMS and of 10−2–10−1 m/s for water, these magnitudes of course vary with time and position in the can. The time required for the SHZ to reach the sterilization temperature of 100°C was 1800 s for CMC and only, 150 s for water.

Although an extensively studied classical subject, laminar natural convection heat transfer from the vertical surface of a cylinder has generated some recent interest in the literature. In this investigation, numerical experiments are performed to determine average Nusselt numbers for isothermal vertical cylinders (102

Unsteady electrolysis of a dilute solution of a metal salt made up of two ions in a system with vertical electrodes is considered for large values of the Rayleigh and Schmidt numbers. The mass transfer at the electrodes is assumed to be related to the local charge transfer potential and concentration by a nonlinear Butler–Volmer law. Free convection of the electrolyte appears owing to the variation of the concentration field. After a short initial period, the electrolyte becomes strongly stratified and the motion takes place in boundary layers at the solid boundaries. An approximate model equation for the evolution of the stratification is derived by using perturbation theory. Predictions from the simplified model are found to be in good agreement with numerical solutions of the complete problem. Significant differences compared with earlier studies for linear kinetics, i.e. cases in which the electric current density at the electrodes is constant, are found. Among other things, for...

Natural convection in enclosed cavities is widely studied because of its importance in many engineering applications. The most commonly used enclosures in the industries are rectangular, cylindrical, trapezoidal, triangular etc. In recent years, natural convection in triangular shaped enclosures have received a considerable attention. The reason for considering this geometry is, it has application in various fields such as building and thermal insulation systems. In the present study natural convection inside a triangular enclosure is analyzed. The analysis is conducted as 3 different cases. For the first case the bottom wall is heated and other two sides are kept at ambient temperature. For the second case, left wall is heated and other two sides are kept at ambient temperature and for the final case right wall is heated and other two sides are kept at ambient temperature. Simulations are carried out for varying Rayleigh number. Heat transfer rate from the hot surface is obtained numerically. The fluid flow characteristics and heat transfer characteristics are analyzed using computational fluid dynamic software ANSYS FLUENT 14.0.

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.