Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Rectangular Channels

1987 ◽  
Vol 109 (4) ◽  
pp. 936-942 ◽  
Author(s):  
G. J. Hwang ◽  
F. C. Chou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Numerical Study ◽  
Fully Developed Flow ◽  
Rectangular Channels ◽  
Laminar Convection

This paper presents a numerical study of the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal rectangular channels with uniform heat input axially, In addition to the Prandtl number, the Grashof number Gr+, and the aspect ratio γ, a parameter Kp indicating the significance of wall conduction plays an important role in heat transfer. A finite-difference method utilizing a power-law scheme is employed to solve the system of governing partial differential equations coupled with the equation for wall conduction. The numerical solution covers the parameters: Pr = 7.2 and 0.73, γ = 0.5, 1, and 2, Kp = 10−4–104, and Gr+ = 0–1.37×105. The flow patterns and isotherms, the wall temperature distribution, the friction factor, and the Nusselt number are presented. The results show a significant effect of the conduction parameter Kp.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

Lattice Boltzmann Analysis of the Heat Transfer in Cubical Enclosures

2012 ◽  
Vol 326-328 ◽  
pp. 536-541
Author(s):  
Djamel Eddine Ameziani ◽  
Rachid Benacer ◽  
Mohamed Belmedani ◽  
Abdelkader Boutraa
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Lattice Boltzmann ◽  
Thermal Characteristics ◽  
Governing Equations ◽  
Boltzmann Method

The purpose of this work is to study hydrodynamic and thermal characteristics of air contended into a differentially heated cubic cavity. Due to their importance in the characterization of heat transfer in this kind of configuration, the effect of some parameters is analyzed. It consists in the Rayleigh number and the aspect ratio. In order to resolve the governing equations, the Lattice-Boltzmann method coupled with finite difference method is used.

Buoyancy Effects on Heat Transfer in Five Different Aspect-Ratio Rectangular Channels With Smooth Walls and 45-Degree Ribbed Walls

2005 ◽  
Author(s):  
Wen-Lung Fu ◽  
Lesley M. Wright ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Thermal Performance ◽  
Flow Direction ◽  
Aspect Ratios ◽  
Number Ratio ◽  
Buoyancy Parameter ◽  
Rectangular Channels ◽  
Channel Aspect Ratio

This paper experimentally studies the effects of the buoyancy force and channel aspect ratio on heat transfer in two-pass rotating rectangular channels with smooth walls and 45° ribbed walls. The channel aspect ratios include 4:1, 2:1, 1:1, 1:2 and 1:4. Four Reynolds numbers are studied: 5000, 10000, 25000 and 40000. The rotation speed is fixed at 550 rpm for all tests, and for each channel, two channel orientations are studied: 90° and 45° or 135°, with respect to the plane of rotation. Rib turbulators are placed on the leading and trailing walls of the channels at an angle of 45° to the flow direction. The ribs have a 1.59 by 1.59 mm square cross section, and the rib pitch-to-height ratio (P/e) is 10 for all tests. The effects of the local buoyancy parameter and channel aspect ratio on the regional Nusselt number ratio are presented. The results show that increasing the local buoyancy parameter increases the Nusselt number ratio on the trailing surface and decreases the Nusselt number ratio on the leading surface in the first pass for all channels. However, the trend of the Nusselt number ratio in the second pass is more complicated due to the strong effect of the 180° turn. Results are also presented for this critical turn region of the two-pass channels. In addition to these regions, the channel averaged heat transfer, friction factor, and thermal performance are determined for each channel. With the channels having comparable Nusselt number ratios, the 1:4 channel has the superior thermal performance because it incurs the least pressure penalty.

Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

2014 ◽  
Vol 24 (8) ◽  
pp. 1954-1978 ◽  
Author(s):  
M.A. Mansour ◽  
M.A. Bakeir ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Cu Nanoparticles ◽  
Content Type ◽  
The Finite Difference Method

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

Natural Convection From L-Shaped Corners With Adiabatic and Cold Isothermal Horizontal Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 149-157 ◽  
Author(s):  
D. Angirasa ◽  
R. L. Mahajan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Numerical Study ◽  
Outer Region ◽  
Vertical Side ◽  
Layer Flow ◽  
Horizontal Side

A numerical study of two-dimensional fluid flow and heat transfer by natural convection from L-shaped corners is reported. The vertical side is hot isothermal, and the horizontal side is either adiabatic or cold isothermal at the ambient temperature. The effect of changing the aspect ratio (length of the horizontal side/height of the vertical side) on the transport from the vertical side is studied in detail. It is shown that when the length of the horizontal wall is of the order of the boundary layer thickness on the vertical side, the entrainment flow as well as the boundary layer flow are influenced significantly by a change in the length of the horizontal surface. The heat transfer rate from the vertical side also decreases with increasing length. For values of the aspect ratio > 0.3 (Pr = 0.7), the Nusselt number for the vertical side of the L-shaped body is about 10 percent less than that for the vertical plate. As the length of the horizontal plate increases further, the flow in the outer region undergoes a significant change, but the heat transfer from the vertical heated leg remains unaffected. As the aspect ratio approaches = 2.0, increasing the length of the horizontal side ceases to have any further influence on the entire flow field. Comparison of Nusselt number with past experimental data for air shows good agreement. Finally, Nusselt number correlations in the range of Rayleigh number from 105 to 109 are presented.

scholarly journals Free convection in a vertical cylindrical annulus filled with anisotropic porous medium

2009 ◽  
Vol 13 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Rathinam Thansekhar ◽  
Babu Mahesh ◽  
Sekhar Chandra
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Temperature Distribution ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Free Convection ◽  
Numerical Study ◽  
Radius Ratio ◽  
Permeability Ratio ◽  
Cylindrical Annulus

A numerical study has been carried out for free convection in a vertical cylindrical annulus filled with a porous medium and whose inner wall is isothermally heated and the outer wall is isothermally cooled, the horizontal walls being insulated. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. Numerical results are reported for 0.1 ? K*? 10, 0.1 ? ? ? 10,1 ? A ? 20,2 ? Rr ? 20, and Ra*? 10000. Anisotropy of the porous medium is found to affect fluid flow, temperature distribution and heat transfer significantly. Higher permeability in the vertical direction enhances convective flow intensity and heat transfer inside the annulus. Average Nusselt number on the inner hot wall increases with increase in Rayleigh number or radius ratio, while it decreases with increase in aspect ratio or permeability ratio. The influence of thermal anisotropy is not so significant as that of hydrodynamic anisotropy. The numerically predicted temperature distribution at various locations inside the annulus shows reasonable agreement with experimental results available for isotropic porous medium. Based on a parametric study, correlation for heat transfer is presented in terms of Rayleigh number, aspect ratio, radius ratio, and permeability ratio.

Rotational Buoyancy Effects on Heat Transfer in Five Different Aspect-Ratio Rectangular Channels With Smooth Walls and 45Degree Ribbed Walls

2006 ◽  
Vol 128 (11) ◽  
pp. 1130-1141 ◽  
Author(s):  
Wen-Lung Fu ◽  
Lesley M. Wright ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Rotation Speed ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Number Ratio ◽  
Buoyancy Parameter ◽  
Rectangular Channels ◽  
Channel Aspect Ratio

This paper experimentally studies the effects of the buoyancy force and channel aspect ratio (W:H) on heat transfer in two-pass rotating rectangular channels with smooth walls and 45deg ribbed walls. The channel aspect ratios include 4:1, 2:1, 1:1, 1:2, and 1:4. Four Reynolds numbers are studied: 5000, 10,000, 25,000, and 40,000. The rotation speed is fixed at 550rpm for all tests, and for each channel, two channel orientations are studied: 90deg and 45 or 135deg, with respect to the plane of rotation. The maximum inlet coolant-to-wall density ratio (Δρ∕ρ)inlet is maintained around 0.12. Rib turbulators are placed on the leading and trailing walls of the channels at an angle of 45deg to the flow direction. The ribs have a 1.59 by 1.59mm square cross section, and the rib pitch-to-height ratio (P∕e) is 10 for all tests. Under the fixed rotation speed (550rpm) and fixed inlet coolant-to-wall density ratio (0.12), the local buoyancy parameter is varied with different Reynolds numbers, local rotating radius, local coolant-to-wall density ratio, and channel hydraulic diameter. The effects of the local buoyancy parameter and channel aspect ratio on the regional Nusselt number ratio are presented. The results show that increasing the local buoyancy parameter increases the Nusselt number ratio on the trailing surface and decreases the Nusselt number ratio on the leading surface in the first pass for all channels. However, the trend of the Nusselt number ratio in the second pass is more complicated due to the strong effect of the 180deg turn. Results are also presented for this critical turn region of the two-pass channels. In addition to these regions, the channel averaged heat transfer, friction factor, and thermal performance are determined for each channel. With the channels having comparable Nusselt number ratios, the 1:4 channel has the superior thermal performance because it incurs the least pressure penalty.

Study on Model of Thermal Crown of Single-Stand Irreversible Foil Mill

2011 ◽  
Vol 117-119 ◽  
pp. 303-309
Author(s):  
Liang Hao ◽  
Hong Shuang Di ◽  
Dian Yao Gong
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Surface Temperature ◽  
Difference Method ◽  
Rolling Schedule ◽  
Thermal Crown ◽  
The Law ◽  
Develop Program

Based on the principles of heat transfer, finite difference method was adopted to develop program of calculating thermal crown of single-stand irreversible foil mill. The temperature distribution and thermal crown of roll were calculated for one rolling schedule. The temperature of each layer calculated was analyzed. The computed and measured surface temperature was compared, which shows good consistence with each other. The law of thermal crown changes with time conformed to practical account.

HEAT TRANSFER IN LARGE RUBBER ELEMENTS THROUGH OF MODELING BY FINITE DIFFERENCE METHOD

2019 ◽  
Author(s):  
Lucas Peixoto ◽  
Ane Lis Marocki ◽  
Celso Vieira Junior ◽  
Viviana Mariani
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method
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