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

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).

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.

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.

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.

Numerical Study of Natural Convection in a Ferrofluid-Filled Corrugated Cavity With Internal Heat Generation

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Öztop
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Magnetic Dipole ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Dipole Source ◽  
Internal Heating ◽  
Dipole Strength

In this paper, numerical simulations for the natural convection in a ferrofluid-filled corrugated cavity with internal heat generation under the influence of a magnetic dipole source were performed. The cavity is heated from below and cooled from above while vertical side walls are assumed to be adiabatic. A magnetic dipole source was located under the bottom heated wall. The governing equations were solved by Galerkin weighted residual finite-element formulation. The influence of external Rayleigh number (between 104 and 5 × 105), internal Rayleigh number (between 104 and 5 × 106), magnetic dipole strength (between 0 and 4), horizontal (between 0.2 and 0.8) and vertical (between −5 and −2) locations of the magnetic dipole source on fluid flow, and heat transfer are numerically investigated. It was observed that depending on heating mechanism (the external or internal heating), the presence of corrugation of the bottom wall either enhances or deteriorates the absolute value of the averaged heat transfer. The strength and locations of the magnetic dipole source affect the distribution of the flow and thermal patterns within the cavity for both flat and corrugated wall cavity. The net effect of the complicated interaction of the internal heating, external heating, and ferroconvection of magnetic source results in heat transfer enhancement with increasing values of magnetic dipole strength. Wall corrugation causes more enhancement of averaged heat transfer and this is more pronounced for low values of vertical location of magnetic source.

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