Natural convection flow due to a heat source in a vertical channel

An analysis is presented of the laminar natural convection flow due to a localized heat source on the centerline of a long vertical channel or pipe whose walls are kept at a constant temperature. Stationary solutions are obtained for infinitely long and finite length channels, the asymptotic limit of infinite Rayleigh numbers is discussed, and an optimal height of the channel is found leading to maximum mass flux and minimum temperature for a given heat release rate.     

Approximate solution to the natural convection heat transfer from a vertical plate

A new model for laminar natural convection heat transfer between an isothermal vertical plate to a power-law fluid is proposed. The difficulty caused by the fact that the momentum and energy equations are coupled is avoided by introducing an approximation based on the partial similarity between the velocity fields for forced and natural convections. The model proposed in this work agrees well with the available experimental data and correlations. Further, we have extended the analysis to turbulent natural convection heat transfer. The predicted turbulent heat transfer rates are in satisfactory agreement with the data and the correlations published in the literature.     

Turbulent natural convection cooling of electronic components mounted on a vertical channel

The paper presents a numerical simulation of conjugate, turbulent natural-convection air cooling of three heated ceramic components, which are identical and mounted on a vertical adiabatic channel. A two-dimensional, conjugate heat transfer model and the standard k–ϵ turbulence model were used to obtain the dynamic and thermal fields. The finite-volume method has been used to solve the model equations throughout the entire physical domain (solid and fluid). After validation of the method with available measurements for a single source, it was applied to investigate the effects on cooling of spacing between the heated electronic components and of the removal of heat input in one of the components. The former modification led to better cooling while the latter can be partially advantageous only when the non-powered components are mounted between the powered ones: this reduces the temperature of the powered components situated downstream from the non-powered component.     

Simulation of mixed convection in a vertical channel containing discrete porous-covering heat blocks

A numerical investigation is made of fully developed laminar mixed convection in a vertical channel with multiple porous-covered heated blocks on one channel wall. The Brinkman–Forchheimer-Extended Darcy model with the Boussinesq approximation is used to characterize the flowfield inside the porous region. Solution of the coupled governing equations for the fluid/porous/solid composite system is obtained by utilizing control volume method through the use of a stream function-vorticity approach. The dependence of streamlines, isotherms, and local and overall mean Nusselt numbers on the governing parameters, such as the Darcy number, Reynolds number, Grashof number, effective conductivity ratio, and geometric parameter, is documented in detail. The results show that the strength and extent of recirculating flow induced by porous-covering block make significant changes in the cooling of block heater, especially on block back faces.     

Natural convection heat transfer from a thermal heat source located in a vertical plate fin

A steady state conjugate conduction–convection investigation is performed on vertical plate fin in which a small heat source is located. Heat from the fin surface is transferred to the surroundings by laminar natural convection. The governing equations for the problem are the heat conduction equation for the fin and the boundary layer equations, which are continuity, momentum and energy equations, for the fluid. A computer program is written by using the finite difference method in order to solve the governing equations which are nonlinear and coupled. The best location of the heat source in the fin for maximum heat transfer rate depends on two parameters which are the conduction–convection parameter and the Prandtl number. The obtained results have shown that for the fin with large conduction–convection parameter, a heat source location for maximum heat transfer rate exists.     

Effect of surface radiation on conjugate mixed convection in a vertical channel with a discrete heat source in each wall

The results of a numerical analysis of the problem of two-dimensional, steady, incompressible, conjugate, laminar, mixed convection with surface radiation in a vertical parallel-plate channel, provided with a flush-mounted, heat generating, discrete heat source in each wall, are presented here. Air, a radiatively non-participating medium, is used as the cooling agent. A computer code based on the finite volume method is written exclusively for solving the above problem. The effect of surface emissivity, aspect ratio, discrete heat source position and modified Richardson number on the fluid flow and heat transfer characteristics is explored. Useful correlations are evolved for the maximum temperature of the left and the right channel walls, the mean friction coefficient and the forced convection component of the mean friction coefficient.     

Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.     

Combined heat and mass transfer in natural convection on a vertical flat plate

In analyzing the combined heat and mass transfer in natural convection, most of the surface conditions are either maintained at an uniform wall temperature and uniform wall concentration or subjected to an uniform heat flux and uniform mass fluc. Other conditions are seldom investigated. This study is to investigate the effects of the coupled thermal and mass diffusion on the natural convection of a vertical plate for a moist air system. The surface conditions of the plate are uniform heat flux and uniform relative humidity. A finite difference numerical method is used to solve the governing equations simultaneously. The results that the relative humidity of the surface is both larger and smaller than that of the ambient are examined in detail.     

Suppression of natural convection heat transfer along a vertical flat plate with concavities

To clarify the effect of the suppression of natural heat transfer, the local heat transfer coefficients on a vertical cooled flat plate with circular grooves were measured by a multi‐type thermocouple method. Two flat plates with and without periodic circular grooves were tested in this experiment. The characteristics of heat transfer along the plate for both plates were compared. The local heat transfer coefficients on the periodic grooved plate became smaller than that of the flat plate. The flow pattern was changed when it passed over the grooves, and circulation was generated in the grooves in the downstream. As a result, the thickness of the thermal boundary layer on the grooved plate was more developed than the normal flat plate. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20294     

Non-darcy mixed convection in a vertical porous channel with discrete heat sources at the walls

A numerical study of mixed convection in a parallel-plate vertical channel filled with a fluid-saturated porous medium and containing discrete heat sources at the walls is performed using the Brinkman-Forchheimer-extended Darcy model. The evolution of buoyancy-assisted mixed convection is examined for both the Darcy and the non-Darcy regimes. The results indicate that as the Darcy number is decreased, the location of flow separation from the cold wall did not change while reattachment moved further downstream. The Nusselt number increased with decreasing Darcy number and the effect of Darcy number is more pronounced over the first heat source and in the non-Darcy regime.     

Numerical simulation of conjugate,turbulent mixed convection heat transfer in a vertical channel with discrete heat sources

This paper presents the results of a comprehensive numerical study to analyze turbulent mixed convection in a vertical channel with a flush-mounted discrete heat source in each channel wall. The conjugate heat transfer problem is solved to study the effect of various parameters like the thermal conductivity of the wall material (k_s), the thermal conductivity of the flush-mounted discrete heat source (k_c), Reynolds number (Re_s), modified Richardson number (Ri⁎) and the aspect ratio of the channel (AR). The standard k–ε turbulence model, modified by including buoyancy effects, without wall functions, has been used for the analysis. The two-dimensional governing equations are discretised on a semi-staggered, non-uniform grid, using the finite volume method. The asymptotic computational fluid dynamics (ACFD) technique has been then applied to obtain a correlation for the non-dimensional maximum temperature θ¯_max, which can be used for a wide range of parameters.     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Turbulent natural convection heat transfer from a vertical plate to the power-law fluid at high prandtl numbers

A simple analytical technique for turbulent natural convection heat transfer from an isothermal vertical plate to a power-law fluid is developed. The model is based on the assumption that the turbulent heat transfer rate is controlled by the flow characteristic near the surface in the limit of large Prandtl numbers. The formulation proposed in this work agrees well with the correlations available in the literature.     

Augmentation of thermophoretic deposition in natural convection flow through a parallel plate channel with heat sources

Submicron sized particles suspended in a hot flue gas exposed to a cold wall are driven towards the wall where they finally get deposited. The driving force and velocity acquired by the particles are known as thermophoretic force and thermophoretic velocity respectively. Natural convection through parallel plate channel is considered for analysis in this paper. Two dimensional free convection boundary layer equations are solved using a finite difference marching technique. Incompressible steady flow is considered. Effect of axial laser heating is studied by incorporating heat source term in the energy equation. It is found that the axial laser heating results in enhanced mass deposition rate on the channel wall. Deposition rate is found to be a function of intensity of heating. Results are presented in the form of graphs. Axial heating is useful to enhance smoke particle deposition rate from medium sized wood-fired appliances on account of increasing demand for such appliances throughout the world including developed countries owing to the depleting nature of fossil fuel.     

Heat transfer enhancement of turbulent natural convection adjacent to a vertical heated plate

Enhancement of heat transfer was investigated experimentally on natural convection adjacent to a vertical heated plate. In order to promote heat transfer from the heated plate, a V-shaped promoter of which the edge faced upstream was attached onto the surface of the vertical plate. The promoter redirects high-temperature fluids toward both sides of the promoter and also introduces low-temperature ambient fluids behind the promoter. These two mechanisms enhance heat transfer, in particular, in the region behind the promoter. Local heat transfer coefficients around the promoter were measured using water as the test fluid. These coefficients behind the promoter reached 2.5 times of those without the promoter. The optimal heights and attack angles of the promoter that maximize the heat transfer were also studied experimentally. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res. 25(1): 39–50, 1996     

Transient effects in natural convection cooling of vertical parallel plates

This work presents results from a numerical study of transient natural convection between vertical parallel plates. Two boundary conditions – uniform wall temperature and uniform heat flux – are considered. Results presented include the rate of heat transfer for uniform wall temperature and the maximum wall temperature for uniform heat flux. Also presented are simple correlations to calculate the minimum heat transfer and the maximum wall temperature during the transient period. It is found that for uniform wall temperature the ratio of the minimum heat transfer to the steady state heat transfer decreases with length of the channel, and for uniform heat flux the maximum transient temperature has a maximum of about 9% over the steady state temperature.     

Turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in a vertical parallel plate channel has been investigated both experimentally and numerically. The experimental channel is formed of a uniform temperature heater wall and an opposing glass wall. A fibre flow laser doppler anemometer (LDA) is used to measure velocity profiles along the channel. Simultaneous velocity and temperature profile measurements are made at the channel outlet. A commercial computational fluid dynamics (CFD) code is used to simulate heat transfer and fluid flow in the channel numerically. The code is customised building in some low Reynolds number (LRN) k–ε turbulence models. The numerical method used in this study is found to predict heat transfer and flow rate fairly accurately. It is also capable of capturing velocity and temperature profiles with some accuracy. Experimental and numerical data are presented comparatively in the form of velocity, temperature, and turbulent kinetic energy profiles along the channel for a case. Correlating equations are obtained from the numerical results for heat transfer and induced flow rate and, are presented graphically comparing with other studies available in the literature.     

Turbulent large-scale structures in natural convection vertical channel flow

We analyzed a database of a direct numerical simulation of natural convection in a vertical channel. The flow is driven by a constant temperature difference imposed at the walls (Ra = 5.4 × 10⁵, Pr = 0.7). The averaged flow and turbulent statistics are in good agreement with previous direct numerical simulations reported in the literature. Contrary to forced convection flows, the fluctuations of the heat transfer rate are uncorrelated with the fluctuations of the wall shear stress, which exhibit a symmetric probability density function. At the low Rayleigh number considered, the large-scale structures, which consist mainly in two counter-rotating vortices, with sizes comparable to the separation of the walls, are responsible for the extreme fluctuations of the wall heat transfer rate. The occurrence and the averaged topology of these structures have been determined using a conditional sampling technique.