Study of Steady Natural Convection With Laminar Flow in the Enclosures of Different Shapes

2016 ◽  
Author(s):  
Anuj Gupta ◽  
H. C. Thakur ◽  
Bhavyanidhi Vats
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Maximum Heat ◽  
Grashof Number ◽  
Maximum Heat Transfer ◽  
Convection Problem ◽  
Different Shapes ◽  
Natural Convection Problem

This paper deals with the results of a simulative study of free convective heat transfer in the enclosure having different shapes. Problem has been characterized with the constant temperature on lower and upper walls while side walls have been considered as adiabatic walls. This study has been conducted for finding the shape of enclosure having maximum heat transfer rate considering different values for the aspect ratio and the Grashof number. Steady state natural convection problem has been formulated for all enclosures having laminar flow of air (at Pr = 0.7). Values for the aspect ratio vary from 0.2 to 0.5 while for the Grashof number from 10e4 to 10e8. ANSYS 14.0 has been used for modelling and simulation and for concluding study in the terms of Nusselt Number.

Optimization of Finned Ducts in Laminar Flow

1984 ◽  
Vol 106 (3) ◽  
pp. 586-590 ◽  
Author(s):  
M. Kovarik
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Heat Exchanger ◽  
Laminar Flow ◽  
Unit Cost ◽  
Necessary Condition ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Necessary Condition Of Optimality

A simple necessary condition of optimality for a finned heat exchanger duct in laminar flow is derived. The criterion of optimality is maximum heat transfer from the fin per unit cost of the finned duct. The heat transfer is determined by the conjugate convection-conduction process rather than by the assumption of a given heat transfer coefficient on the fin surface. Both forced and natural convection are considered. Expressions comparing the performance of optimal assemblies of different materials are given. Approximate dimensions of optimal fins are derived. The relations between the present and earlier results are discussed.

The Effect of Thermal Wall Properties on Natural Convection in Inclined Rectangular Cells

1982 ◽  
Vol 104 (1) ◽  
pp. 111-117 ◽  
Author(s):  
B. A. Meyer ◽  
J. W. Mitchell ◽  
M. M. El-Wakil
Keyword(s):  
Heat Transfer ◽  
Cell Wall ◽  
Natural Convection ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Conductive Heat ◽  
Numerical Work ◽  
Aspect Ratios ◽  
Convection Problem ◽  
Natural Convection Problem

The effects of cell wall thickness and thermal conductivity on natural convective heat transfer within inclined rectangular cells was studied. The cell walls are thin, and the hot and cold surfaces are isothermal. The two-dimensional natural convection problem was solved using finite difference techniques. The parameters studied were cell aspect ratios (A) of 0.5 and 1, Rayleigh numbers (Ra) up to 105, a Prandtl number (Pr) of 0.72 and a tilt angle (φ) of 60 deg. These parameters are of interest in solar collectors. The numerical results are substantiated by experimental results. It was found that convection coefficients for cells with adiabatic walls are substantially higher than those for cells with conducting walls. Correlations are given for estimating the convective heat transfer across the cell and the conductive heat transfer across the cell wall. These correlations are compared with available experimental and numerical work of other authors.

Effect of Periodicity of Non-Uniform Sinusoidal Side Heating on Natural Convection in an Anisotropic Porous-Enclosure

2011 ◽  
Vol 110-116 ◽  
pp. 1613-1618 ◽  
Author(s):  
S. Kapoor ◽  
P. Bera
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Stream Function ◽  
Numerical Study ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Porous Enclosure

A comprehensive numerical study on the natural convection in a hydrodynamically anisotropic as well as isotropic porous enclosure is presented, flow is induced by non uniform sinusoidal heating of the right wall of the enclosure. The principal directions of the permeability tensor has been taken oblique to the gravity vector. The spectral Element method has been adopted to solve numerically the governing differential equations by using the vorticity-stream-function approach. The results are presented in terms of stream function, temperature profile and Nusselt number. The result show that the maximum heat transfer takes place at y = 1.5 when N is odd.. Also, increasing media permeability, by changing K* = 1 to K* = 0.2, increases heat transfer rate at below and above right corner of the enclosure. Furthermore, for the all values of N, profiles of local Nusselt number (Nuy) in isotropic as well as anisotropic media are similar, but for even values of N differ slightly at N = 2.. In particular the present analysis shows that, different periodicity (N) of temperature boundary condition has the significant effect on the flow pattern and consequently on the local heat transfer phenomena.

Enhancement of Natural Convection Heat Transfer by a Staggered Array of Discrete Vertical Plates

1980 ◽  
Vol 102 (2) ◽  
pp. 215-220 ◽  
Author(s):  
E. M. Sparrow ◽  
C. Prakash
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Parallel Plate ◽  
Convection Heat Transfer ◽  
Transfer Enhancement ◽  
Enhanced Heat Transfer ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Parameter Ranges

An analysis has been performed to determine whether, in natural convection, a staggered array of discrete vertical plates yields enhanced heat transfer compared with an array of continuous parallel vertical plates having the same surface area. The heat transfer results were obtained by numerically solving the equations of mass, momentum, and energy for the two types of configurations. It was found that the use of discrete plates gives rise to heat transfer enhancement when the parameter (Dh/H)Ra > ∼2 × 103 (Dh = hydraulic diameter of flow passage, H = overall system height). The extent of the enhancement is increased by use of numerous shorter plates, by larger transverse interplate spacing, and by relatively short system heights. For the parameter ranges investigated, the maximum heat transfer enhancement, relative to the parallel plate case, was a factor of two. The general degree of enhancement compares favorably with that which has been obtained in forced convection systems.

Natural Convection Heat Transfer Characteristics of Flat Plate Enclosures

1979 ◽  
Vol 101 (1) ◽  
pp. 120-125 ◽  
Author(s):  
K. R. Randall ◽  
J. W. Mitchell ◽  
M. M. El-Wakil
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Tilt Angle ◽  
Convection Heat Transfer ◽  
Transfer Coefficients ◽  
Number Range ◽  
Grashof Number ◽  
Average Heat ◽  
Plate Spacing

Heat transfer by natural convection in rectangular enclosures has been experimentally studied using interferometric techniques. The effects of Grashof number, tilt angle, and aspect ratio on both the local and average heat transfer coefficients have been determined. The Grashof number range tested was 4 × 103 to 3.1 × 105, and the aspect ratio (ratio of enclosure length to plate spacing) varied between 9 and 36. The angles of tilt of the enclosure with respect to the horizontal were 45, 60, 75 and 90 deg. Correlations are developed for both local and average Nusselt number over the range of test variables. The effect of tilt angle is found to reduce the average heat transfer by about 18 percent from the value of 45 deg to that at 90 deg. No significant effect of aspect ratio over the range tested was found. A method for characterizing the flow regimes that is based on heat transfer mechanisms is proposed.

Entropy Generation in Laminar and Turbulent Natural Convection Heat Transfer From Vertical Cylinder With Annular Fins

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Jnana Ranjan Senapati ◽  
Sukanta Kumar Dash ◽  
Subhransu Roy
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Entropy Generation ◽  
Vertical Cylinder ◽  
Turbulent Regime ◽  
Maximum Heat ◽  
Turbulent Natural Convection ◽  
Maximum Heat Transfer ◽  
Wide Range ◽  
Annular Fins

Entropy generation due to natural convection has been calculated for a wide range of Rayleigh number (Ra) in both laminar (104 ≤ Ra ≤ 108) and turbulent (1010 ≤ Ra ≤ 1012) flow regimes, for diameter ratio of 2 ≤ D/d ≤ 5, for an isothermal vertical cylinder fitted with annular fins. In the laminar regime, the entropy generation was predominantly caused by heat transfer (conduction and convection) and the viscous contribution was negligible with respect to heat transfer. But in the turbulent regime, entropy generation due to fluid friction is significant enough although heat transfer entropy generation is still dominant. The results demonstrate that the degree of irreversibility is higher in case of finned configuration when compared with unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to delineate the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)finned/(I/Q)unfinned. The ratio (I/Q)finned/(I/Q)unfinned gets its minimum value at optimum fin spacing where maximum heat transfer occurs in turbulent flow, whereas in laminar flow the ratio (I/Q)finned/(I/Q)unfinned decreases continuously with the increase in number of fins.

Heat Transfer Due to Natural Convection in a Periodically Heated Slot

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
M. Z. Hossain ◽  
J. M. Floryan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Field ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Horizontal Direction ◽  
Wave Number ◽  
Lower Wall ◽  
Maximum Heat ◽  
Maximum Heat Transfer

Heat transfer resulting from the natural convection in a fluid layer contained in an infinite horizontal slot bounded by solid walls and subject to a spatially periodic heating at the lower wall has been investigated. The heating produces sinusoidal temperature variations along one horizontal direction characterized by the wave number α with the amplitude expressed in terms of a suitably defined Rayleigh number Rap. The maximum heat transfer takes place for the heating with the wave numbers α = 0(1) as this leads to the most intense convection. The intensity of convection decreases proportionally to α when α→0, resulting in the temperature field being dominated by periodic conduction with the average Nusselt number decreasing proportionally to α2. When α→∞, the convection is confined to a thin layer adjacent to the lower wall with its intensity decreasing proportionally to α−3. The temperature field above the convection layer looses dependence on the horizontal direction. The bulk of the fluid sees the thin convective layer as a “hot wall.” The heat transfer between the walls becomes dominated by conduction driven by a uniform vertical temperature gradient which decreases proportionally to the intensity of convection resulting in the average Nusselt number decreasing as α−3. It is shown that processes described above occur for Prandtl numbers 0.001 < Pr < 10 considered in this study.

Magnetohydrodynamic Natural Convection Heat Transfer of Hybrid Nanofluid in a Square Enclosure in the Presence of a Wavy Circular Conductive Cylinder

2019 ◽  
Vol 12 (3) ◽  
Author(s):  
Tahar Tayebi ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Flow Characteristics ◽  
Hybrid Nanofluid ◽  
Square Enclosure ◽  
Convection Problem ◽  
Laminar Natural Convection ◽  
Natural Convection Problem ◽  
Volume Method

Abstract In this paper, steady natural convective heat transfer and flow characteristics of Al2O3-Cu/water hybrid nanofluid filled square enclosure in the presence of magnetic field has been investigated numerically. The enclosure is equipped with a wavy circular conductive cylinder. The natural convection in the cavity is induced by a temperature difference between the vertical left hot wall and the other right cold wall. The steady 2-D equations of laminar natural convection problem for Newtonian and incompressible mixture are discretized using the finite volume method. The effective thermal conductivity and viscosity of the hybrid nanofluid are calculated using Corcione correlations taking into consideration the Brownian motion of the nanoparticles. A numerical parametric investigation is carried out for different values of the nanoparticles volumic concentration, Hartmann number, Rayleigh number, and the ratio of fluid to solid thermal conductivities. According to the results, the corrugated conductive block plays an important role in controlling the convective flow characteristic and the heat transfer rate within the system.

Reduced Basis Methods and a Posteriori Error Estimators for Heat Transfer Problems

2009 ◽  
Author(s):  
G. Rozza ◽  
C. N. Nguyen ◽  
A. T. Patera ◽  
S. Deparis
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Element Discretization ◽  
Convection Problem ◽  
Prandtl Numbers ◽  
Basis Method ◽  
Two Parameters ◽  
Natural Convection Problem

This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — material properties, boundary conditions and sources, and geometry — we would like to compute certain outputs of engineering interest — heat fluxes and average temperatures. The certified reduced basis method provides both (i) a very inexpensive yet accurate output prediction, and (ii) a rigorous bound for the error in the reduced basis prediction relative to an underlying expensive high-fidelity finite element discretization. The feasibility and efficiency of the method is demonstrated for three natural convection model problems: a scalar steady forced convection problem in a rectangular channel is characterized by two parameters — Pe´clet number and the aspect ratio of the channel — and an output — the average temperature over the domain; a steady natural convection problem in a laterally heated cavity is characterized by three parameters — Grashof and Prandtl numbers, and the aspect ratio of the cavity — and an output — the inverse of the Nusselt number; and an unsteady natural convection problem in a laterally heated cavity is characterized by two parameters — Grashof and Prandtl numbers — and a time-dependent output — the average of the horizontal velocity over a specified area of the cavity.

Compounded Heat Transfer Enhancement in Enclosure Natural Convection by Changing the Cold Wall Shape and the Gas Composition

2006 ◽  
Vol 129 (7) ◽  
pp. 827-834 ◽  
Author(s):  
El Hassan Ridouane ◽  
Antonio Campo
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Gas Mixtures ◽  
Gas Mixture ◽  
Transfer Enhancement ◽  
Maximum Enhancement ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Triangular Enclosure

This article addresses compound heat transfer enhancement for gaseous natural convection in closed enclosures; that is, the simultaneous use of two passive techniques to obtain heat transfer enhancement, which is greater than that produced by only one technique itself. The compounded heat transfer enhancement comes from two sources: (1) reshaping the bounded space and (2) the adequacy of the gas. The sizing of enclosures is of great interest in the miniaturization of electronic packaging that is severely constrained by space and∕or weight. The gases consist in a subset of binary gas mixtures formed with helium (He) as the primary gas. The secondary gases are nitrogen (N2), oxygen (O2), carbon dioxide (CO2), methane (CH4), and xenon (Xe). The steady-state flow is governed by a system of 2-D coupled mass, momentum, and energy conservation equations, in conjunction with the ideal gas equation of state. The set of partial differential equations is solved using the finite volume method, for a square and a right-angled isosceles triangular enclosure, accounting for the second-order accurate QUICK and SIMPLE schemes. The grid layouts rendered reliable velocities and temperatures for air and the five gas mixtures at high Ra=106, producing errors within 1% were 18,500 and 47,300 elements for the square and triangle enclosures, respectively. In terms of heat transfer enhancement, helium is better than air for the square and the isosceles triangle. It was found that the maximum heat transfer conditions are obtained filling the isosceles triangular enclosure with a He–Xe gas mixture. This gives a good trade-off between maximizing the heat transfer rate while reducing the enclosure space in half; the maximum enhancement of triangle∕square went up from 19% when filled with air into 46% when filled with He–Xe gas mixture at high Ra=106.

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