Laminar Heat Transfer in Rectangular Channels

1959 ◽  
Vol 81 (2) ◽  
pp. 121-127 ◽  
Author(s):  
L. S. Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Boundary Conditions ◽  
Heat Input ◽  
Combined Effects ◽  
The Third ◽  
Rectangular Channels ◽  
Free And Forced Convection ◽  
Extended Surfaces ◽  
Rectangular Tubes

Three cases of laminar heat transfer with linear heat input in long rectangular channels have been treated by the method of orthogonal trigonometric series. The boundary conditions of the first two problems are those of laminar and slug flows with two opposite faces as secondary extended surfaces. A new fin parameter K defined as (wkm/bkf) has been shown to be the important factor in governing the Nusselt number. The third case discussed is the combined effects of free and forced-convection in vertical rectangular tubes.

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.

Roughness Effects on Flow and Heat Transfer for Additively Manufactured Channels

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Curtis K. Stimpson ◽  
Jacob C. Snyder ◽  
Karen A. Thole ◽  
Dominic Mongillo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Flow Conditions ◽  
Roughness Effects ◽  
Flow And Heat Transfer ◽  
Technological Advances ◽  
Rectangular Channels ◽  
Significant Augmentation ◽  
Flow Through

Recent technological advances in the field of additive manufacturing (AM), particularly with direct metal laser sintering (DMLS), have increased the potential for building gas turbine components with AM. Using the DMLS for turbine components broadens the design space and allows for increasingly small and complex geometries to be fabricated with little increase in time or cost. Challenges arise when attempting to evaluate the advantages of the DMLS for specific applications, particularly because of how little is known regarding the effects of surface roughness. This paper presents pressure drop and heat transfer results of flow through small, as produced channels that have been manufactured using the DMLS in an effort to better understand roughness. Ten different coupons made with the DMLS all having multiple rectangular channels were evaluated in this study. Measurements were collected at various flow conditions and reduced to a friction factor and a Nusselt number. Results showed significant augmentation of these parameters compared to smooth channels, particularly with the friction factor for minichannels with small hydraulic diameters. However, augmentation of Nusselt number did not increase proportionally with the augmentation of the friction factor.

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Pamela Vocale ◽  
Gian Luca Morini ◽  
Marco Spiga
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Slip Flow ◽  
The Cross ◽  
Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

Nusselt Number as Composite Functions of Aspect Ratio and Wall Inclination in Parallelogram Microchannels with Three Types of Thermal Boundary Conditions

2016 ◽  
Vol 33 (4) ◽  
pp. 521-533 ◽  
Author(s):  
T.-M. Liou ◽  
H. Wang ◽  
S.-P. Chan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Boundary Conditions ◽  
Simple Algorithm ◽  
Working Fluid ◽  
Constant Wall Temperature ◽  
Time Saving ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
New Findings

AbstractIn this study, attention is focused on the numerical simulations of laminar fluid flow and heat transfer in straight smooth-walled parallelogram channels with various aspect ratios (α) and inclined angles (θ). The Reynolds number (Re), characterized by the channel hydraulic diameter and the working fluid of water, is fixed at 100. The examinedαandθrange from 1 to 10 and 45° to 90°, respectively. Their effects on the thermal fluid features are explored under three thermal boundary conditions: constant wall temperature (TBC), constant axial heat transfer rate with constant peripheral temperature (H1BC), and constant wall heat flux (H2BC). The SIMPLE algorithm is employed for velocity–pressure coupling with the algebraic multigrid method, while the second-order upwind scheme is utilized for spatial discretization in pressure term; the momentum and energy equations are solved with a QUICK scheme; Least Squares Cell-Based Gradient Evaluation is applied for predicting scalar values at the cell faces and for computing secondary diffusion terms and velocity derivatives. One of the new findings is that there exists a critical value ofθ= 70° below which the Nusselt number under H2BC increases with increasingαwhereas beyond which the trend reverses, a result distinct from those computed with TBC and H1BC. Moreover, TBC is found to be a time-saving alternative to H1BC. Furthermore, both Nusselt numbers under the three thermal boundary conditions and friction factor timesReare successfully and compactly correlated with α andθto offer useful reference for designing micro-cooling channels.

scholarly journals Optimization of heat transfer at the surface of parabolic fins by genetic Algorithm

2017 ◽  
Vol 52 (4) ◽  
pp. 325-330
Author(s):  
A Gholami ◽  
H Mehrjou
Keyword(s):  
Heat Transfer ◽  
Genetic Algorithm ◽  
Nusselt Number ◽  
Hydraulic Resistance ◽  
Economic Efficiency ◽  
Heat Exchangers ◽  
Air Conditioning ◽  
Energy Exchanges ◽  
Extended Surfaces ◽  
Library Method

Thermal fins are extended surfaces like longitudinal, radial, and cylindrical fins. They are used for the improvement of heat transfer between an object and fluid. Fins can be applied in many processes of objects cooling such as electrical appliances, many types of engines, transformers, chemical industry, air conditioning, heat exchangers and the industries of energy exchanges. This matter is one of the main results of paying attention to this issue. Therefore, this study examined the optimization of fin heat transfer by using a genetic algorithm and consideration of Nusselt number and hydraulic resistance as the objective function. In this paper, we investigated the optimization of the fin to maximize the heat transfer and also to minimize the hydraulic resistance. The results of this study can be effective in term of technical and economic efficiency in the industry of fin transformer. The stimulation and library method has been used to collect data. The results indicated that if the hydraulic resistance was limited to a specific value, using wavy fins will not improve the device heat.Bangladesh J. Sci. Ind. Res. 52(4), 325-330, 2017

Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

2019 ◽  
Vol 29 (5) ◽  
pp. 1786-1814 ◽  
Author(s):  
A.A. Avramenko ◽  
N.P. Dmitrenko ◽  
I.V. Shevchuk ◽  
A.I. Tyrinov ◽  
V.I. Shevchuk
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Rotation Rate ◽  
Second Order ◽  
Temperature Profiles ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Slip Boundary

Purpose The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions. Design/methodology/approach The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other. Findings The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions. Originality/value The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

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.

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