Natural Convection in a Non-Uniformly Heated Vertical Annular Cavity

2017 ◽  
Vol 377 ◽  
pp. 189-199 ◽  
Author(s):  
M. Sankar ◽  
S. Kiran ◽  
G.K. Ramesh ◽  
Oluwole Daniel Makinde
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Outer Wall ◽  
Uniform Heating ◽  
Cylindrical Wall ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Model Equations

Natural convection from the linearly heated inner and/or outer walls of a vertical annular cavity has been numerically investigated. The bottom wall is uniformly heated and top cylindrical wall is thermally insulated. In this analysis, we considered two different thermal boundary conditions, namely case (I) and case (II) to understand the effect of non-uniform heating of inner and/or outer walls on the convective flow and subsequently the local and global heat transfer rate. For case (I), the inner and outer walls are heated linearly, while the linearly heated inner wall and cooled outer wall is considered in case (II). An implicit finite difference scheme is applied to solve the model equations of the problem. The numerical simulations in terms of streamlines and isotherms, local and global Nusselt numbers are presented to illustrate the effects of Rayleigh number and non-uniform thermal boundary conditions for a fixed Prandtl number of Pr = 0.7.

Effects of Thermal Boundary Conditions on Entropy Generation During Natural Convection in a Differentially Heated Square Cavity

2010 ◽  
Author(s):  
Ram Satish Kaluri ◽  
Tanmay Basak ◽  
A. R. Balakrishnan
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Entropy Generation ◽  
Bottom Wall ◽  
Convection Flow ◽  
Uniform Heating ◽  
Square Cavity ◽  
Fluid Friction ◽  
Thermal Boundary Conditions

Natural convection is a widely occurring phenomena which has important applications in material processing, energy storage devices, electronic cooling, building ventilation etc. The concept of ‘entropy generation minimization’, which is a thermodynamic approach for optimization, may be very useful in designing efficient thermal systems. In the current study, entropy generation in steady laminar natural convection flow in a square cavity is studied with following isothermal boundary conditions: (1) Bottom wall is uniformly heated (2) Bottom wall is sinusoidally heated. The side walls are maintained cold and the top wall is maintained adiabatic. The thermal boundary condition in non-uniform heating case (case 2) is such that the dimensionless average temperature of the bottom wall is equal to that of uniform heating case (case 1). The prime objective of this work is to investigate the influence of uniform and non-uniform heating on entropy generation. The governing mass, momentum and energy equations are solved using Galerkin finite element method. Streamlines, isotherms, contour maps of entropy generation due to heat transfer and fluid friction are studied for Pr = 0.01 (molten metals) and 7 (water) in range of Ra = 103–105. Detailed analysis on the effect of uniform and non-uniform thermal boundary conditions on entropy generation due to heat transfer and fluid friction has been presented. Also, the average Bejan’s number which indicates the relative dominance of entropy generation due to heat transfer or fluid friction and the total entropy generation are studied for each case.

scholarly journals Natural convection air flow in vertical upright-angled triangular cavities under realistic thermal boundary conditions

2016 ◽  
Vol 20 (5) ◽  
pp. 1407-1420 ◽  
Author(s):  
Jaime Sieres ◽  
Antonio Campo ◽  
José Martínez-Súarez
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Aperture Angle ◽  
Temperature Fields ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Horizontal Wall ◽  
Rayleigh Numbers

This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle ? is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles ? (= 15?, 30? and 45?) and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction) to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.

Effects of complex boundary conditions on natural convection of a viscoplastic fluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2792-2808 ◽  
Author(s):  
Behnam Rafiei ◽  
Hamed Masoumi ◽  
Mohammad Saeid Aghighi ◽  
Amine Ammar
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Heated Wall ◽  
Uniform Heating ◽  
Content Type ◽  
Yield Stress Fluids ◽  
Complex Boundary

Purpose The purpose of this paper is to analyze the effects of complex boundary conditions on natural convection of a yield stress fluid in a square enclosure heated from below (uniformly and non-uniformly) and symmetrically cooled from the sides. Design/methodology/approach The governing equations are solved numerically subject to continuous and discontinuous Dirichlet boundary conditions by Galerkin’s weighted residuals scheme of finite element method and using a non-uniform unstructured triangular grid. Findings Results show that the overall heat transfer from the heated wall decreases in the case of non-uniform heating for both Newtonian and yield stress fluids. It is found that the effect of yield stress on heat transfer is almost similar in both uniform and non-uniform heating cases. The yield stress has a stabilizing effect, reducing the convection intensity in both cases. Above a certain value of yield number Y, heat transfer is only due to conduction. It is found that a transition of different modes of stability may occur as Rayleigh number changes; this fact gives rise to a discontinuity in the variation of critical yield number. Originality/value Besides the new numerical method based on the finite element and using a non-uniform unstructured grid for analyzing natural convection of viscoplastic materials with complex boundary conditions, the originality of the present work concerns the treatment of the yield stress fluids under the influence of complex boundary conditions.

Natural convection flow in a vertical micro-annulus with time-periodic thermal boundary conditions

2018 ◽  
Vol 14 (5) ◽  
pp. 1064-1081
Author(s):  
Basant Kumar Jha ◽  
Michael O. Oni
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Content Type ◽  
Thermal Boundary Conditions ◽  
The Impact ◽  
Time Periodic

PurposeThe purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.Design/methodology/approachAnalytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.FindingsIt is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.Research limitations/implicationsNo laboratory practical or experiment was conducted.Practical implicationsCooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.Originality/valueIn view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

scholarly journals Numerical simulation of natural convection in an inclined porous cavity under time-periodic boundary conditions with a partially active thermal side wall

RSC Advances ◽  
2017 ◽  
Vol 7 (28) ◽  
pp. 17519-17530 ◽  
Author(s):  
Feng Wu ◽  
Gang Wang
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Side Wall ◽  
Periodic Boundary Conditions ◽  
Porous Cavity ◽  
Thermal Boundary Conditions ◽  
The Right ◽  
Time Periodic

Natural convection in an inclined porous cavity with positively or negatively inclined angles is studied numerically for time-periodic boundary conditions on the left side wall and partially active thermal boundary conditions on the right wall.

Natural Convection in an Inclined Rectangular Cavity With Different Thermal Boundary Conditions at the Top Plate

1988 ◽  
Vol 110 (2) ◽  
pp. 350-357 ◽  
Author(s):  
T. G. Karayiannis ◽  
J. D. Tarasuk
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Forced Convection ◽  
Rectangular Cavity ◽  
Forced Flow ◽  
Cold Plate ◽  
Transfer Rates ◽  
Average Heat ◽  
Thermal Boundary Conditions

Natural convection inside a rectangular cavity with different temperature boundary conditions on the cold top plate was studied using a Mach-Zehnder interferometer for θ = 15, 45, and 60 deg to the horizontal. At θ = 60 deg coupling with external forced convection and non-coupled heat transfer from a cavity with an isothermal top plate was studied. In all experiments the bottom hot plate was isothermal. The Rayleigh number Ra was varied from subcritical to 6×105 and the cavity aspect ratio ARx, from 6.68 to 33.4. The Reynolds number of the external forced flow Redh was constant and approximately equal to 5.8×104. It was found that for Ra ≲ 3×104 the differing thermal boundary conditions at the top plate did not affect the local or average heat transfer rates from the cavity. For Ra ≳ 3×104 coupling at the top plate compared to the non-coupled case resulted not only in a reduction in the variation of the local heat transfer rates at the cold plate, but also in a significant reduction in the variation of the average transfer rates from hot and cold plates of the cavity. Forced convection at the top plate as compared to natural convection resulted only in a small reduction in the heat transfer coefficient at the cold plate. Correlation equations for coupled and noncoupled average heat transfer rates are presented.

Natural Convection Inside a Square Cavity Heated From Below and Symmetrically Cooled at Both Sides: Effects of Various Dirichlet Boundary Conditions at the Bottom Wall

2005 ◽  
Author(s):  
Satyajit Roy ◽  
Tanmay Basak
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Transfer Rate ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Bottom Wall ◽  
Uniform Heating ◽  
Square Cavity ◽  
Rayleigh Numbers

A numerical study is performed to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over the range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 105 and Prandtl number Pr, 0.7 ≤ Pr ≤ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained.

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