Prandtl number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid

The Prandtl number dependence of unsteady laminar natural convection along an infinite vertical plate in a thermally stratified fluid is investigated. Flows are induced by an impulsive (step) change in plate temperature and by a suddenly imposed plate heat flux. Analytical solutions of the viscous equations of motion and thermodynamic energy are obtained for Prandtl numbers near unity by the method of Laplace transforms and a regular perturbation expansion. The zeroth-, first- and second-order terms in the expansion are obtained for an impulsive change in plate temperature, while the zeroth- and first-order terms are obtained for a sudden application of a plate heat flux. The developing boundary layers are thicker, more vigorous, and more sensitive to the Prandtl number at smaller Prandtl numbers (<1) than at larger Prandtl numbers (>1). The analytical results are confirmed and extended with results from numerical simulations for Prandtl numbers strongly deviating from unity.     

Effects of pressure work and radiation on natural convection flow around a sphere with heat generation

The effects of pressure work and radiation on natural convection flow around a sphere in presence of heat generation have been investigated in this paper. The governing equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton's linearization approximation. Attention has been focused on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles. Numerical results have been shown graphically and also in tabular form for some selected values of parameter set consisting of heat generation parameter Q, radiation parameter Rd, pressure work parameter Ge and the Prandtl number Pr.     

Technical Note Transient behavior of vertical buoyancy layer in a stratified fluid

horizontal length scale of the vertical channelg acceleration of gravityRa Rayleigh number [ ≡ gβT_oD⁴ν]T temperaturew velocity component in the z-directionx horizontal coordinatez vertical coordinate.Greek symbols coefficient of thermometric expansionδ thermal perturbation thermal diffusivityν kinematic viscosityσ Prandtl number [ ≡ νχ].     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Dynamic simulation of the vertical zone-melting crystal growth

Dynamic behavior of heat transfer, fluid flow, and interfaces in the vertical zone-melting (VZM) crystal growth is studied numerically. The model, which is governed by axisymmetric unsteady-state momentum and heat transfer and interface balance in the system, is solved by a robust finite-volume method. Single crystal growth of NaNO₃ in a computer-controlled transparent multizone furnace is simulated as examples. The effects of gravity levels and heater temperature are considered. Multiple steady states obtained at stationary cases are used as initial conditions to illustrate the transient response and the stability of the VZM crystal growth to the pulse and step changes in thermal environments. For unstable cases, periodically oscillatory flow and growth rate occurring at intermediate values of the Rayleigh number are observed. The upper flow cells beneath the feed front seems to be responsible to the instability, and this is consistent with the observation during crystal growth experiments. For stable cases, a steady state can be achieved smoothly, and the calculated results are in good agreement with the ones from a pseudo steady-state model.     

Transient analysis of incompressible flow through a packed bed

The present investigation aims at numerically simulating the temporal energy transport for incompressible flows through a packed bed. The governing equations are formulated according to the volume averaging method. The generalized momentum equation which accounts for the inertial and viscous forces was used to carry out this research, whereas the two-energy equation model was used for simulating the energy transport. The implications of the non-Darcian terms and the thermal dispersion effects on the transient energy transport were explored. Error maps were introduced for a wide range of flow conditions and bed configurations. In addition, the investigation also tackles the applicability of the local thermal equilibrium condition and the one-dimensional approach for studying the thermal response in packed bed.