The stability of a flow in a side-heated vertical layer with internal heat sources

The linear stability of a combined convective flow in a side-heated plane vertical layer of incompressible fluid is considered. The layer contains uniformly distributed heat sources. The steadystate flow is a superposition of the Gershuni convective flow and a flow induced by the action of the internal heat sources. The stability maps of the combined flow are constructed for different values of the Prandtl number. It is found that the internal sources damp the action of the mechanisms of the Gershuni flow crisis. The lateral heating may result in both the stabilization and the destabilization of the flow caused by the action of internal heat sources.     

Instability of the liquid equilibrium state in an ice-water system with account for radiation heating

The problem of the stability of the equilibrium state of a weakly compressible fluid bounded from below by a stationary rigid wall and from above by a heat-conducting finite-thickness wall is studied. The thermal state of the system is investigated with account for volume heat sources due to radiation. It is shown that the mechanical equilibrium of the system is unstable. The neutral curves are plotted and the critical Rayleigh numbers are found.     

Convective stability of a horizontal rotating fluid layer with distributed heat sources

The results of investigating the convective instability of a horizontal layer of rotating fluid, created by a temperature difference applied at the boundaries of the layer and by heat sources distributed according to various laws, are presented. It is shown that, when the other parameters of the problem are fixed, an increase in the internal heat release lowers the limits of both monotonic and oscillatory stability of the layer, increases the wave number and reduces the neutral oscillation frequency. An increase in source concentration towards the center of the layer intensifies the effect. As the strength of the internal heat sources and their concentration towards the center of the layer increase, the oscillating convection that develops at the stability limit when the Prandtl number is low and the rotation fairly fast is first replaced by monotonic convection and then ceases altogether.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–28, January–February, 1989.     

A physical mechanism of large-scale structure generation in turbulent convection

The generation of large-scale structures during turbulent convection in a rotating layer of incompressible fluid heated by internal heat sources is considered. The results of a theoretical and experimental investigation of a physical mechanism of large-scale structure formation which operates under conditions of high-intensity small-scale turbulent convection and low boundary heat transfer are discussed. The theoretical investigation is based on a system of evolutionary equations obtained for the transverse space moments of the physical fields, which describes the motion in thin layers of rotating fluid. The stability of the solution of the mathematical model is studied using the small perturbation method. As a result, a condition of existence of longwave instability of the system and a criterion determining the threshold of its onset are obtained. The theoretical conclusions are confirmed by a series of experiments carried out on a laboratory model. The design of the laboratory apparatus and the experimental technique are described.Moscow, Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–29, September–October, 1996.     

Numerical analysis of mixed convection in three‐dimensional rectangular channel with flush‐mounted heat sources based on field synergy principle

In this paper the fluid flow and heat transfer characteristics of mixed convection in three‐dimensional rectangular channel with four heat sources are investigated numerically. The SIMPLEC algorithm is applied to deal with the coupling between pressure and velocity, and a new high‐order stability‐guaranteed second‐order difference (SGSD) scheme is adopted to discretize the convection term. The influence of four parameters is studied: Richardson number, heat source distribution, channel height and inclination angle. The numerical results are analysed from the viewpoint of the field synergy principle, which says that the enhanced convective heat transfer is related not only to the velocity field and temperature field, but also to the synergy between them. It is found that the effects of the four parameters on the thermal performance can all be explained with the field synergy principle. To obtain better electronic cooling, the synergy between the velocity and temperature gradient should be increased when other conditions are unchanged. Copyright © 2006 John Wiley & Sons, Ltd.     

Natural convection in cavities containing internal sources

 Numerical predictions are reported for buoyancy-induced circulations in a 2D closed cavity with internal heat sources. Two cases are considered: (A) two vertical plates with uniform heat generation, forming a short vertical channel within the enclosure; and, (B) a rectangular heating block with uniform wall temperature, placed central in the enclosure. Air, with a Prandtl number 0.71, is considered as the working fluid. The vertical enclosure walls are isothermal, while the horizontal enclosure walls are adiabatic. Results are presented for two values of the Grashof number, one below the stability limit for laminar flow, and one well above it. In those latter cases, the long-term behaviour of the numerical solution is time-dependent, i.e. no steady-state can be reached. Heat transfer results are compared with predictions from standard correlations for isolated surfaces. Received on 17 January 2000     

Convection in a low prandtl number fluid with internal heating

This paper studies the problem of non-linear thermal convection in a horizontal layer of a low Prandtl number fluid with nearly insulating boundaries and in the presence of horizontally uniform internal heat sources. Two-dimensional rolls and hexagonal cells are found to be the only possible stable convection cells. Subcritical instability associated with the hexagons can occur for a range of the amplitude of convection. It is found that non-uniform internal heating can affect various flow features and the stability of the convective motion. A new subcritical instability which exists even in a symmetric layer with arbitrary Prandtl number is also found for the case where the variations of the internal heating with respect to the vertical variable is sufficiently high.     

Effect of Longitudinal Forced Motion on the Stability of Convection in a Plane Vertical Layer with Internal Heat Sources

The effect of longitudinal forced fluid motion on the mechanisms of instability of a convection flow developing in a plane vertical layer in the presence of internal heat sources is considered. It is found that forced motion which intensifies the central stream of the convection flow can lead to moderate stabilization of the hydrodynamic and thermal crisis mechanisms. In the presence of counterstream forced motion the flow stability increases sharply.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 14–17.Original Russian Text Copyright © 2005 by Lobov.     

Combined interface boundary condition method for coupled thermal simulations

A new procedure for modeling the conjugate heat‐transfer process between fluid and structure subdomains is presented. The procedure relies on higher‐order combined interface boundary conditions (CIBC) for improved accuracy and stability. Traditionally, continuity of temperature and heat flux along interfaces is satisfied through algebraic jump conditions in a staggered fashion. More specifically, Dirichlet temperature conditions are usually imposed on the fluid side and Neumann heat‐flux conditions are imposed on the solid side for the stability of conventional sequential staggered procedure. In this type of treatment, the interface introduces additional stability constraints to the coupled thermal simulations. By utilizing the CIBC technique on the Dirichlet boundary conditions, a staggered procedure can be constructed with the same order of accuracy and stability as those of standalone computations. Using the Godunov–Ryabenkii normal‐mode analysis, a range of values of the coupling parameter is found that yields a stable and accurate interface discretization. The effectiveness of the method is investigated by presenting and discussing performance evaluation data using a 1D finite‐difference formulation for each subdomain. Copyright © 2007 John Wiley & Sons, Ltd.     

Local Thermal Non-Equilibrium and Heterogeneity Effects on the Onset of Convection in a Layered Porous Medium

The effect of local thermal non-equilibrium on the onset of convection in a porous medium consisting of two horizontal layers is studied analytically. Linear stability theory is applied. Variations of permeability, fluid conductivity, solid conductivity, interphase heat transfer coefficient and porosity are considered. It is found that heterogeneity of permeability and fluid conductivity have a major effect, heterogeneity of interphase heat transfer coefficient and porosity have a lesser effect, while heterogeneity of solid conductivity is relatively unimportant.     

Transient forced convection heat transfer in a channel

A numerical analysis is made of incompressible transient turbulent flow heat transfer between two parallel plates when there is a step jump in space along the channel in wall heat flux or wall temperature. The variation of the fluid velocity and effective diffusivity over the channel cross section are accounted for. The fluid is assumed to have a fully-developed turbulent velocity profile throughout the length of the channel. The thermal responses of the system are obtained by solving energy equation for air by a digital computer. The results are presented in graphical forms. The stability of the finite difference solution is studied and condition for the stability of the difference solution is derived. A method is given to obtain velocity distributions from the distribution of turbulent eddy diffusivity of momentum. Variations of Nusselt numbers are obtained as a function of time and space. Steady-state values are also given and compared with the published results.     

Transient conjugated mixed-convective heat transfer in a vertical plate channel with one wall heated discretely

 This study presents a numerical solution of the unsteady conjugated mixed-convection heat transfer in a vertical plate channel with one wall suddenly subjected to either isoflux or isothermal discrete heat sources. The effects of the dimensionless heat source length H ₁, the dimensionless spacing between heat sources H ₂, the dimensionless channel length L, the dimensionless heated-plate thickness B _l, the wall-to-fluid conductivity ratio K and the ratio of Grashof number to Reynolds number Gr/Re on the interface heat flux, Nusselt number and bulk fluid temperature are discussed in detail. Results show that the discrete heating can cause the heat transfer direction conversely from the fluid to the heated plate during the transient period, which is more significant for the cases with larger L and H ₂. For the system with isoflux discrete heat sources, the time required to reach the steady-state is shorter for larger H ₂. While the trend is reverse for system with isothermal discrete heat sources. Additionally, a higher ratio of the input energy is axially conducted through the plate wall from heated sections to unheated regions for a larger H ₂ and B _l or smaller L. Received on 9 November 1998     

Conjugate free convection along a thin vertical plate with internal nonuniform heat generation in a porous medium

 The steady state heat transfer characteristics of a thin vertical strip with internal heat generation placed in a porous medium is studied in this work. The non-dimensional temperature distribution in the strip is obtained as a function of the intensity and distribution of the internal heat sources. Both the thermally thin as the thick wall approximations are considered in this paper. The mass flow rate of fluid induced by heating the strip decreases as the longitudinal heat conduction effects along the strip decreases. Received on 22 November 2000 / Published online: 29 November 2001     

Thermal Non-Equilibrium Porous Convection with Heat Generation and Density Maximum

Linear stability criterion for the onset of natural convection in a fluid saturated porous medium with uniform internal heat generation and density maximum is determined. The porous medium is not in local thermal equilibrium (LTE) and we follow a two-field model for the energy equation. It is found that both the heat generation and density maximum have an additive effect in advancing the onset condition. In general the destabilising effect of density maximum increases for large values of the fluid heat generation parameter. This effect becomes prominent even for small values of the fluid heat generation parameter when the flow is of Darcy type and LTE is not valid.     

Mixed convection heat transfer from a horizontal channel with protruding heat sources

A numerical investigation is carried out to study fluid flow and heat transfer characteristics of conjugate mixed convection from a two dimensional horizontal channel with four protruding heat sources mounted on one of the finite thick channel walls. The flow is assumed as laminar, hydrodynamically and thermally developing. Water and FC70 are the fluids under consideration. The geometric parameters such as spacing between the channel walls (S), size of protruding heat sources (L_h×t_h), thickness of substrate (t) and spacing between heat sources (b) are fixed. Results are presented to show the effect of parameters such as Re_S, Gr_S^*, Pr, k_p/k_f and k_s/k_f on fluid flow and heat transfer characteristics. Using the method of asymptotic expansions, correlations are also presented for the maximum temperature of heat source.     

Convective Plume Paths in Anisotropic Porous Media

Free convection motions induced by point sources or horizontal line sources of heat are usually assumed to take the form of a vertically orientated plume. In this paper we consider how material anisotropy affects the path of the plume centreline and we show that it is strongly affected by both the anisotropy and the presence of impermeable bounding surfaces. The plume path is a straight line whose angle from the vertical is determined by a balance between the upward buoyancy force, the need for the plume to entrain equal amounts of fluid from the external regions either side of it, and the ease of fluid motion in the direction of the principal axis with the highest permeability.     

Double-diffusive convection induced by selective absorption of radiation in a fluid overlying a porous layer

A linear instability analysis for the inception of double-diffusive convection with a concentration based internal heat source is presented. The system encompasses a layer of fluid which lies above a porous layer saturated with the same fluid. Detailed stability characteristics results are presented for key physical parameters including the solute Rayleigh number, depth ratio of the fluid to porous layer and strength of radiative heating.     

Throughflow Effects on Penetrative Convection in Superposed Fluid and Porous Layers

The effect of vertical throughflow on the onset of penetrative convection simulated via internal heating in a two-layer system in which a layer of fluid overlies and saturates a layer of porous medium is studied. Flow in the porous medium is governed by Forchheimer-extended Darcy equation, and Beavers?CJoseph slip condition is applied at the interface between the fluid and the porous layers. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The eigenvalue problem is solved using a regular perturbation technique with wave number as a perturbation parameter. The ratio of fluid layer thickness to porous layer thickness, ??, the direction of throughflow, and the presence of volumetric internal heat source in fluid and/or porous layer play a decisive role on the stability characteristics of the system. In addition, the influence of Prandtl number arising due to throughflow is also emphasized on the stability of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and vertical throughflow so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible.     

Parametric studies and correlations for combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate

The present paper reports the parametric studies and correlations for the problem of combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate. Three discrete heat sources of non-identical heights but with identical volumetric rate of heat generation are assumed to be flush-mounted in a thin vertical plate. The longest and the shortest heaters are provided at the leading and trailing edges of the plate, while the remaining heater is located centrally. The governing fluid flow and heat transfer equations are considered in their full strength without the boundary layer approximations and are solved using the finite volume method. A computer code is written to solve the problem and various parametric studies have been performed. The relative roles of free convection, forced convection and radiation in various fluid flow and heat transfer results have been elucidated. In conclusion, based on a large set of data generated from the code, correlations for maximum non-dimensional plate temperature, average non-dimensional plate temperature and mean friction coefficient have been evolved.     

Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. Part II: Weakly non-linear solutions

The buoyancy-driven instability of a monocomponent or binary fluid that is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and weakly-non-linear solutions are generated via Galerkin's technique using an expansion in the eigensolutions of the associated linear stability problem. Various types of fluid mixtures and cylindrical domains are considered. Flow structure and associated heat transfer are computed and experimental observations are cited when possible.