Computational Analysis of Natural Convection in Inclined Rectangular Enclosures of Different Aspect Ratios

2002 ◽  
Author(s):  
Mosfequr Rahman ◽  
Muhammad A. R. Sharif
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Heat Generation ◽  
Internal Heat ◽  
Local Heat ◽  
Internal Heat Generation ◽  
Cold Wall ◽  
Aspect Ratios ◽  
Significant Difference ◽  
Local Heat Flux

Numerical investigations are conducted for free convective flow of a fluid with or without internal heat generation in rectangular enclosures of different aspect ratios and at various angles of inclination. Two principal parameters for this problem are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the sidewalls and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. Results are obtained for a fixed external Rayleigh number, RaE = 2×105 with internal Rayleigh number, RaI = 0 (without internal heat generation) and also with RaI = 2×105 (with internal heat generation). Flow patterns and isotherms do not show any significant difference between the cases with and without internal heat generation other than slight shift and changes in stream function and isotherm values as long as the internal Rayleigh number RaI is less than or equal to the external Rayleigh number RaE. Local heat flux ratios along the hot and the cold wall decrease monotonically in the flow direction for a major downstream portion. At certain inclinations the local heat flux ratios increase initially and then decrease. The variation of average heat flux ratio is similar for cases with and without internal heat source situation but the corresponding amount of heat transfer is higher through the hot wall and lower through the cold wall with internal heat generation. On the other hand, the convection strength increases as the enclosure shape changes from slender through square to shallow at any particular inclination but does not vary significantly with inclination at a particular aspect ratio.

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).

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

Effects of spatially varying roof cooling on thermal convection at high Rayleigh number in a fluid with a strongly temperature-dependent viscosity

2009 ◽  
Vol 629 ◽  
pp. 109-137 ◽  
Author(s):  
A. M. JELLINEK ◽  
A. LENARDIC
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Surface Area ◽  
Large Scale ◽  
Local Heat ◽  
Temperature Gradients ◽  
Local Heat Flux ◽  
Transfer Properties ◽  
Lateral Temperature

We investigate the effects of an insulating lid of variable spatial extent on convection in the stagnant-lid regime under thermally steady-state conditions. Using a combination of laboratory experiments, numerical simulations and scaling analyses we characterize the qualitative structure and quantitative heat transfer properties of flows in terms of the fractional extent L of an insulating lid applied at the cold boundary, the thermal resistance of the lid, the magnitude of the temperature dependence of the fluid viscosity Λ and the effective Rayleigh number Rae for the composite system. A partial insulating lid has two main effects: (i) To increase the mean interior temperature and reduce the average viscosity of the system, which enhances fluid motions, and (ii) to impart a lateral asymmetry to the thermal structure of the cold boundary that leads, in turn, to lateral temperature gradients that drive an overturning flow. Consequently, whereas flow in the uninsulated stagnant-lid regime is in the form of ‘small-scale’ rising and sinking thermals, there is an additional ‘large-scale’ circulation in the presence of partial insulation. The structure, wavelength and heat transfer properties of this large-scale stirring depends on L, Λ and Rae. For given Rae – Λ conditions we find optimal values of L at which there occur well-defined maxima in the rate of overturn, the local heat flux carried into the uninsulated part of the cold boundary and in the global average heat flux Nu carried across the system. Whereas both the rate of overturning and local heat flux are associated with the largest lateral temperature gradients, the optimal basal heat flux depends also on a tradeoff with the fractional surface area of the lid. Remarkably, maximal values of the global heat flux can significantly exceed that of the uninsulated stagnant-lid case. The occurrence of such maxima is insensitive to the mechanical boundary conditions applied and is not strongly influenced by lid shape. However, the magnitude and location of optimal heat fluxes depends in a complicated way on the lid surface area and shape, as well as the structure of the hot and cold boundary layers and the wavelength of the large-scale flow.

Numerical Solution for Variable Viscosity and Internal Heat Generation Effects on Boundary Layer Flow Over an Exponentially Stretching Porous Sheet with Constant Heat Flux and Thermal Radiation

2014 ◽  
Vol 30 (4) ◽  
pp. 395-402 ◽  
Author(s):  
A. M. Megahed
Keyword(s):  
Heat Flux ◽  
Heat Generation ◽  
Variable Viscosity ◽  
Internal Heat ◽  
Constant Heat Flux ◽  
Internal Heat Generation ◽  
Constant Heat ◽  
Suction Parameter ◽  
Viscosity Parameter ◽  
Exponentially Stretching

AbstractA numerical study has been carried out to analyze the constant heat flux, internal heat generation, variable viscosity and thermal radiation effects on the flow and heat transfer of a Newtonian fluid over an exponentially stretching porous sheet. Using a similarity transformation, the governing partial differential equations are transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by using an efficient Chebyshev spectral method. The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl number on velocity and temperature are discussed by using graphical approach. Moreover, numerical results indicate that in the presence of constant heat flux, the skin-friction coefficient as well as Nusselt number is strongly affected by the viscosity parameter, suction parameter, radiation parameter and the internal heat generation parameter.

On the Stefan Problem With Internal Heat Generation and Prescribed Heat Flux Conditions at the Boundary

2019 ◽  
Author(s):  
Lyudmyla Barannyk ◽  
Sidney D. V. Williams ◽  
Olufolahan Irene Ogidan ◽  
John C. Crepeau ◽  
Alexey Sakhnov
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Phase Change ◽  
Heat Generation ◽  
Separation Of Variables ◽  
Outer Boundary ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
The Difference ◽  
Solid Liquid Interface

Abstract We study the evolution of the solid-liquid interface during melting and solidification of a material with constant internal heat generation and prescribed heat flux at the boundary for a plane wall and a cylinder. The equations are solved by splitting them into transient and steady-state components and then using separation of variables. This results in an ordinary differential equation for the interface that involves infinite series. The initial value problem is solved numerically, and solutions are compared to the previously published quasi-static solutions. We show that when the internal heat generation and the heat flux at the boundary are close in value to each other, the motion of the phase change front takes longer to reach steady-state than when the values are farther apart. As the difference between the internal heat generation and the heat flux increases, the transient solutions become more dominant and the numerical solution of the phase change front does not reach steady-state before the outer boundary or centerline is reached. The difference between the internal heat generation and the heat flux at the boundary can be used to control the motion and speed of the interface. The problem has applications for a nuclear fuel rod during meltdown.

scholarly journals Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 124
Author(s):  
Saneshan Govender
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Heat Generation ◽  
Critical Rayleigh Number ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Onset Of Convection ◽  
Vadasz Number ◽  
The Impact

Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.

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