Natural Convective Heat Transfer From a Narrow Isothermal Vertical Flat Plate With a Uniform Heat Flux at the Surface

2007 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Vertical Plate ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Heated Plate ◽  
Dimensional Flow ◽  
Uniform Heat ◽  
Two Dimensional Flow ◽  
The Mean

Natural convective flow over a vertical plate with a uniform heat flux over its surface has been numerically studied. When the plate is wide compared to its height the flow can be adequately modeled by assuming two-dimensional flow. However, when the width of the plate is relatively small compared to its height, the heat transfer coefficient can be considerably greater than that predicted by these two-dimensional flow results. The Nusselt number distribution over a narrow vertical plate, with a uniform heat flux at the plate surface, has been numerically determined. This heated plate is embedded in a plane adiabatic surface, the surface of the adiabatic surface being in the same plane as the heated plate. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in dimensionless form. The solution has the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have been numerically determined for a relatively wide range of Rayleigh numbers and dimensionless plate widths for a Prandtl number of 0.7. The dimensionless plate width has been found to have a significant influence on the mean Nusselt number for the plate when the plate is narrow and the Rayleigh number is low. The conditions under which three dimensional flow effects can be neglected have been deduced and an empirical equation for the mean Nusselt number for narrow plates with a uniform surface heat flux has been derived from the numerical results.

scholarly journals NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

2004 ◽  
Vol 3 (2) ◽  
pp. 100
Author(s):  
T. Dias Jr. ◽  
L. F. Milanez
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

scholarly journals NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

2004 ◽  
Vol 3 (2) ◽  
Author(s):  
T. Dias Jr. ◽  
L. F. Milanez
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

2006 ◽  
Vol 129 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Kamil Kahveci
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

Numerical Investigation on Thermal and Fluid Dynamic Behavior of Laminar Slot-Jet Impinging on a Surface at Uniform Heat Flux in a Confined Porous Medium in Local Thermal Non-Equilibrium Conditions

2014 ◽  
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
Guy Lauriat
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Numerical Investigation ◽  
Forced Flow ◽  
Uniform Heat Flux ◽  
Nusselt Numbers ◽  
Uniform Heat ◽  
The Mean ◽  
Non Equilibrium

A numerical investigation on a single slot jet impinging in a porous parallel-plate channel containing an air-saturated high permeability porous medium is accomplished. The wall opposite the slot jet is partially heated at uniform heat flux and the buoyancy effects are taken into account. The fluid flow is assumed two dimensional, laminar and steady. The porous medium is modeled using the Brinkman–Forchheimer-extended Darcy model and the Boussinesq approximation. The local thermal non-equilibrium (LTNE) hypothesis is invoked. The results are discussed in terms of streamlines, fluid and solid phase temperature fields, wall temperature profiles and local and average Nusselt numbers. The porous medium allows a more significant heat transfer close to the end of the heated part of the plate. For low Peclet numbers, forced flow and natural convection are opposite and the mean Nusselt number shows a decrease in heat transfer, whereas they are aiding for high Peclet numbers. Porosity effects on the mean Nusselt numbers were found weak.

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