Study of Natural Convection in Inclined Square Enclosures With Uniform Heat Generation

2007 ◽  
Author(s):  
Manish Kulkarni ◽  
Sushanta K. Mitra ◽  
U. N. Gaitonde
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Generation ◽  
Inclination Angle ◽  
Local Nusselt Number ◽  
Internal Heat ◽  
Square Enclosure ◽  
Inclination Angles ◽  
Inclined Cavity

Two-dimensional laminar natural convection in an inclined square enclosure with uniform internal heat generation is studied here. The steady-state solutions are obtained for inclination angles of 45°, 30° and 15° and at Rayleigh number of 1.5 × 105. For these cases, the two counter-rotating rolls of fluid are present in the cavity. Streamlines, isotherms and heat transfer for these results are compared with the existing experimental results and are found to be in reasonably good agreement. It is found that the location of maximum non-dimensional temperature in the inclined cavity is higher than that for pure conduction case. The maximum non-dimensional temperature in the cavity decreases as the Rayleigh number increases. For Ra > 5 × 104, the maximum non-dimensional temperature in inclined cavity is almost independent of the inclination angle. It is also observed that the local Nusselt number at the top wall is greater than the pure conduction solution, whereas that for bottom wall it is lower than the Nusselt number for pure conduction. The effect of Rayleigh number and inclination angle on the local Nusselt number and modified local Nusselt number are also studied. For horizontal cavity, at Rayleigh number greater than or equal to 5 × 104, periodic solutions are obtained. In this case, two unstable secondary rolls are present near the center of top wall, in addition to the primary rolls. The secondary rolls are dissipated and recreated during one period of oscillation.

Natural Convection in a Cylindrical Porous Enclosure With Internal Heat Generation

1989 ◽  
Vol 111 (4) ◽  
pp. 916-925 ◽  
Author(s):  
V. Prasad ◽  
A. Chui
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Numerical Study ◽  
Vertical Wall ◽  
Internal Heat ◽  
Heat Removal ◽  
Maximum Temperature ◽  
Wall Boundary Conditions

A numerical study is performed on natural convection inside a cylindrical enclosure filled with a volumetrically heated, saturated porous medium for the case when the vertical wall is isothermal and the horizontal walls are either adiabatic or isothermally cooled. When the horizontal walls are insulated, the flow in the cavity is unicellular and the temperature field in upper layers is highly stratified. However, if the top wall is cooled, there may exist a multicellular flow and an unstable thermal stratification in the upper region of the cylinder. Under the influence of weak convection, the maximum temperature in the cavity can be considerably higher than that predicted for pure conduction. The local heat flux on the bounding walls is generally a strong function of the Rayleigh number, the aspect ratio, and the wall boundary conditions. The heat removal on the cold upper surface decreases with the aspect ratio, thereby increasing the Nusselt number on the vertical wall. The effect of Rayleigh number is, however, not straightforward. Several correlations are presented for the maximum cavity temperature and the overall Nusselt number.

scholarly journals Nonlinear Radiation and Variable Viscosity Effects on Free Convection of a Power-Law Nanofluid Over a Truncated Cone in Porous Media With Zero Nanoparticles Flux and Internal Heat Generation

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
Chuo-Jeng Huang ◽  
Kuo-Ann Yih
Keyword(s):  
Nusselt Number ◽  
Heat Generation ◽  
Power Law ◽  
Local Nusselt Number ◽  
Variable Viscosity ◽  
Internal Heat ◽  
Lewis Number ◽  
Internal Heat Generation ◽  
Truncated Cone ◽  
Power Law Nanofluid

Abstract This study used numerical analysis to investigate the effects of nonlinear radiation and variable viscosity on free convection of a power-law nanofluid over a vertical truncated cone in porous media with Rosseland diffusion approximation considering zero nanoparticles flux and internal heat generation. The internal heat generation is of an exponential decaying form and the viscosity of the fluid is assumed to follow Reynolds viscosity model. The surface boundary conditions of vertical truncated cone is maintained at the uniform wall temperature (UWT) and the zero nanoparticle flux (ZNF) to cause the results to be more realistic and useful. The nanofluid model considered the effects of Brownian motion and thermophoresis. The nonsimilar governing equations are obtained by using a suitable coordinate transformation and then solved by Keller box method (KBM). Comparisons with previously published work obtained good agreement. Graphical and tabular presentations of numerical data for the dimensionless temperature profile and the local Nusselt number were presented for main parameters: dimensionless streamwise coordinate, thermophoresis parameter, Lewis number, radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and internal heat generation coefficient. The local Nusselt number increased when the following parameters were increased: radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and dimensionless streamwise coordinate. In contrast, the local Nusselt number decreased when the following parameters were increased: internal heat generation coefficient, thermophoresis parameter, and Lewis number. Besides, the physical aspects of the problem are discussed in details.

scholarly journals Effect of Various Tilted Positions of a Thin Fin on Natural Convection of Laminar Viscous Flow in a Square Cavity

2021 ◽  
Vol 39 (5) ◽  
pp. 1634-1642
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G Sankara Sekhar Raju
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Average Nusselt Number ◽  
Vertical Position ◽  
Inclination Angles ◽  
Rayleigh Numbers

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

Natural Convective Flow in a Three Enclosure System Involving Two High Aspect Ratio Side Enclosures Joined to a Large Square Enclosure With Interfacial Heat Generation

2003 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Generation ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Square Enclosure ◽  
Number Variation ◽  
Resistance To Heat

A numerical study of free convective flow in a vertical joined three enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is joined to a second high aspect ratio rectangular side enclosure which has the same height as the first side enclosure, the two enclosures being separated by a vertical impermeable dividing wall which offers no resistance to heat transfer. The second side enclosure is joined to a larger square enclosure, the vertical dividing wall between these two enclosures also being impermeable and offering no resistance to heat transfer. The vertical wall of the square main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. There is a uniform rate of heat generation in the dividing wall between the inner side enclosure and the main enclosure. The situation considered is an approximate model of a double-paned window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. In some such cases there can be significant heat generation in the blind due to the absorbtion of solar energy, this being modeled by the heat generation in the one dividing wall. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number, dimensionless width of the side enclosures and dimensionless heat generation rate in the blind on the Nusselt number have been investigated. The results show that for a fixed Rayleigh number and for a given dimensionless first (i.e., outer) side enclosure width, there is a minimum in the Nusselt number variation with the dimensionless width of the second side enclosure. An approximate solution for the Nusselt number variation with the dimensionless width of the second side enclosure for small values of this dimensionless width has also been derived.

Computational Analysis of Laminar Natural Convection in Rectangular Enclosures of Different Aspect Ratios With Different Heating Conditions

2012 ◽  
Author(s):  
Mosfequr Rahman ◽  
Charles Walker ◽  
Gustavo Molina ◽  
Valentin Soloiu
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Aspect Ratio ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
External Temperature ◽  
Aspect Ratios

Natural convection in rectangular enclosures is found in many real-world engineering applications. Included in these applications are the energy efficient design of buildings, operation and safety of nuclear reactors, solar collector design, passive energy storage, heat transfer across multi-pane windows, thermo-electric refrigeration and heating devices, and the design-for-mitigation of optical distortion in large-scale laser systems. A common industrial application of natural convection is free air cooling without the aid of fans and can happen on small scales such as computer chips to large scale process equipment. The enclosure phenomena can loosely be organized into two large classes: (1) horizontal enclosures heated from below and (2) vertical enclosures heated from the side. In addition to temperature gradient convection strength within the enclosure can vary due to the existence of heat sources with different strength. Numerical simulations are conducted for free convective flow of air with or without internal heat generation in two-dimensional rectangular enclosures of different aspect ratios. The objective of this numerical study is to investigate the effects of external temperature gradient, internal heat generation and aspect ratio (AR) of enclosure (ratio of the length of the isothermal walls to their separation distance), in free convective laminar flow of a fluid. Two-dimensional rectangular enclosures of different aspect ratio (1, 2, 4, 6, 8, and 10) with two adiabatic side walls and isothermal bottom (hot) and top (cold) walls are considered for the first configuration. Whereas for the second configuration, two adiabatic top and bottom walls, isothermal left side (cold) and right side (hot) walls are considered. Two principal parameters considered for the flow of fluid are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the isothermal walls, and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. The effect of external temperature gradient and aspect ratio on natural convection has been observed by varying the value of external Rayleigh number (RaE) equal to 2×104, 2×105, and 2×106 and keeping the internal Rayleigh number constant (RaI = 2×105). Similarly, the effect of internal heat generation and aspect ratio on natural convection has been observed by varying the value of internal Rayleigh number (RaI) equal to 2×104, 2×105, and 2×106 and keeping the external Rayleigh number constant (RaE = 2×105). Significant changes in flow patterns and isotherms have been observed for all cases. Also the variation of average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot and cold walls, and the convection strength have been calculated for all cases. It is found that the aspect ratio has a significant effect in fluid flow and heat transfer in the enclosures. The average heat flux ratio and the strength of convection increase with aspect ratio as the enclosure shape changes square (AR = 1) to shallow (AR > 1).

Lattice Boltzmann Method for Combined Natural Convection Surface Radiation in Open Cavity

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Ayoub Msaddak ◽  
Mohieddine Ben Salah ◽  
Ezeddine Sediki
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Lattice Boltzmann Method ◽  
Inclination Angle ◽  
Lattice Boltzmann ◽  
Surface Radiation ◽  
Surface Emissivity ◽  
Boltzmann Method

Lattice Boltzmann method (LBM) is performed to study numerically combined natural convection and surface radiation inside an inclined two-dimensional open square cavity. The cavity is heated by a constant temperature at the wall facing the opening. The walls normal to the heated surface are assumed to be adiabatic, diffuse, gray, and opaque while the open boundary is assumed to be black at ambient temperature. A Bathnagar, Gross and Krook (BGK) collision model with double distribution function (D2Q9-D2Q4) is adopted. Effects of surface radiation, inclination angle, and Rayleigh number on the heat transfer are analyzed and discussed. Results are presented in terms of isotherms, streamlines, and Nusselt number. It was found that the presence of surface radiation enhances the heat transfer. The convective Nusselt number decreases with increasing surface emissivity as well as with Rayleigh number, while the total Nusselt number increases with increasing surface emissivity and Rayleigh number. The inclination angle has also a significant effect on flow and heat transfer inside the cavity. However, the magnitude of total heat transfer decreases considerably when open cavity is tilted downward.

scholarly journals An Efficient Numerical Simulation of 2D Natural Convection in an Inclined Cavity with Internal Heat Generation Using Differential Quadrature Method

2021 ◽  
Vol 18 (13) ◽  
Author(s):  
Israa ALESBE ◽  
Sattar ALJABAIR ◽  
Jalal M. JALIL
Keyword(s):  
Rayleigh Number ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Internal Source ◽  
Cpu Time ◽  
Aspect Ratios ◽  
Inclination Angles ◽  
Grid Points ◽  
Convective Fluid

Natural laminar convective fluid flow has been simulated inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles. The most important basic dimensionless parameters for this problem are the external Rayleigh number (RaE) and the internal Rayleigh number (RaI), where RaE refers to the effects of the differential heating of the side walls and RaI refers to the amount of heat produced internally. Results were obtained for 4 cases with 192 tests: case (1), RaI = 0 without internal source generation, and cases (2, 3, and 4) with internal source generation for RaI = RaE, 10 RaE, and 100 RaE, respectively. In all cases, the parameters of study changed as 103 ≤ RaE ≤106, 0 ≤ RaI ≤ 107, inclination angle from 0 to 60 deg., and aspect ratios of the enclosure from 0.5 to 2. Results were represented graphically for flow and thermal fields as a streamline, isothermal contours, and Nusselt number. The computed results show that the strength of convection currents is measured by the internal energy. Finally, it is illustrated that by using a few grid points and a shorter CPU time for calculation, the present method can produce accurate numerical results. Also, increase in RaI leads to increasing heat transfer rate and its direction out from the cavity at both hot and cold walls. For lower values of RaI, heat transfer diffusion is more prominent, while for higher values of RaI, convection outweighs diffusion. HIGHLIGHTS Natural laminar convective fluid flow inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles has been simulated The most important basic dimensionless parameters, the external Rayleigh number (RaE) and the internal Rayleigh number (RaI) are studied DQ method performance was excellent The obtained computational results indicate that the strength of the convection currents depends on the internal energy Accurate numerical results can be obtained by the present method using a few grid points and shorter CPU time for calculation GRAPHICAL ABSTRACT

Combined Natural Convection and Radiation in a Volumetrically Heated Fluid Layer

1980 ◽  
Vol 102 (1) ◽  
pp. 81-85 ◽  
Author(s):  
T. C. Chawla ◽  
S. H. Chan ◽  
F. B. Cheung ◽  
D. H. Cho
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Radiation Parameter ◽  
Turbulent Natural Convection ◽  
Heated Fluid ◽  
Rosseland Approximation

The effect of radiation in combination with turbulent natural convection on the rates of heat transfer in volumetrically heated fluid layers characterized by high temperatures has been considered in this study. It is demonstrated that even at high Rayleigh numbers the radiation mode is as effective as the turbulent natural convection mode in removing the heat from the upper surface of the molten pools with adiabatic lower boundary. As a result of this improved heat transfer, it is shown that considerably thicker molten pools with internal heat generation can be supported without boiling inception. The total Nusselt number at a moderate but fixed value of conduction-radiation parameter, can be represented as a function of Rayleigh number in a simple power-law form. As a consequence of this relationship it is shown that maximum nonboiling pool thicknesses vary approximately inversely as the 0.9 power of internal heat generation rate. A comparison between exact analysis using the integral formulation of radiation flux and Rosseland approximation shows that the latter approximation bears out very adequately for optically thick pools with conduction-radiation parameter ≳ 0.4 inspite of the fact that individual components of Nusselt number due to radiation and convection, respectively, are grossly in error. These errors in component heat fluxes are compensating due to the total heat balance constraint. However, the comparison between Rosseland approximation and exact formulation gets poorer as the value of conduction-radiation parameter decreases. This increase in error is principally incurred due to the error in estimating wall temperature differences.

A Study on Natural Convection in a Cold Square Enclosure With Two Vertical Eccentric Square Heat Sources Using the IB–LBM Scheme

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
S. M. Dash ◽  
S. Sahoo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Lattice Boltzmann Model ◽  
Immersed Boundary ◽  
Heat Sources ◽  
Square Enclosure ◽  
Thermal Lattice Boltzmann

In this article, the natural convection process in a two-dimensional cold square enclosure is numerically investigated in the presence of two inline square heat sources. Two different heat source boundary conditions are analyzed, namely, case 1 (when one heat source is hot) and case 2 (when two heat sources are hot), using the in-house developed flexible forcing immersed boundary–thermal lattice Boltzmann model. The isotherms, streamlines, local, and surface-averaged Nusselt number distributions are analyzed at ten different vertical eccentric locations of the heat sources for Rayleigh number between 103 and 106. Distinct flow regimes including primary, secondary, tertiary, quaternary, and Rayleigh–Benard cells are observed when the mode of heat transfer is changed from conduction to convection and heat sources eccentricity is varied. For Rayleigh number up to 104, the heat transfer from the enclosure is symmetric for the upward and downward eccentricity of the heat sources. At Rayleigh number greater than 104, the heat transfer from the enclosure is better for downward eccentricity cases that attain a maximum when the heat sources are near the bottom enclosure wall. Moreover, the heat transfer rate from the enclosure in case 2 is nearly twice that of case 1 at all Rayleigh numbers and eccentric locations. The correlations for heat transfer are developed by relating Nusselt number, Rayleigh number, and eccentricity of the heat sources.

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