Thermally developing laminar flow inside rectangular ducts

Aparecido, J. B.; Cotta, Renato M.

doi:10.1016/0017-9310(90)90103-2

Cited by 54 publications

(14 citation statements)

References 7 publications

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“…Aparecido and Cotta [6] solved the problem of thermally developing flow in square ducts for the T boundary condition. However, both these sets of results were limited to a small range of channel aspect ratios ( = 1 to 4), and were also restricted by the available computational resources of the time.…”

Section: Introductionmentioning

confidence: 99%

“…It is important for the design of microchannel heat sinks to be able to accurately predict the heat transfer coefficients under different flow and thermal conditions, especially in developing laminar flow. In contrast to ducts with cross sections defined by a single coordinate, such as circular tubes and parallel plates, where analytical solutions may be readily 4 obtained, the analysis of heat transfer in a rectangular duct is more complicated and most studies have employed numerical approaches [5,6].…”

Section: Introductionmentioning

confidence: 99%

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Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Lee

Garimella

2006

International Journal of Heat and Mass Transfer

380

141

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Laminar convective heat transfer in the entrance region of microchannels of rectangular cross section is investigated under circumferentially uniform wall temperature and axially uniform wall heat flux thermal boundary conditions. Three-dimensional numerical simulations were performed for laminar thermally developing flow in microchannels of different aspect ratios. Based on the temperature and heat flux distributions obtained, both the local and average Nusselt numbers are presented graphically as a function of the dimensionless axial distance and channel aspect ratio. Generalized correlations, useful for the design and optimization of microchannel heat sinks and other microfluidic devices, are proposed for predicting Nusselt numbers. The proposed correlations are compared with other conventional correlations and with available experimental data, and show very good agreement.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Lee

Garimella

2006

International Journal of Heat and Mass Transfer

380

141

View full text Add to dashboard Cite

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“…An algebraic solution of this kind has been applied to three-dimensional steady-state laminar forced convection inside rectangular ducts after integral transforming along two spatial coordinates, leaving the remaining one as the independent variable of the transformed ODE system [3]. Later on, Almeida and Cotta [1] applied the same approach to solve a transient twodimensional advection-diffusion problem in petroleum reservoirs.…”

Section: Problem Formulationmentioning

confidence: 98%

Integral transform solutions for atmospheric pollutant dispersion

Almeida

Pimentel

Cotta

2007

Environ Model Assess

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A transient two-dimensional advection-diffusion model describing the turbulent dispersion of pollutants in the atmosphere has been solved via the Generalized Integral Transform Technique (GITT), by two different schemes. The first approach performs numerical integration of the transformed system using available routines for initial value problems with automatic error control. In spite of the timeconsuming character of such a scheme, its flexibility allows the handling of problems involving time-dependent meteorological parameters such as wind speed and eddy diffusivities. The second approach works fully analytically being thus intrinsically more robust and economic, although not directly applicable in dealing with time-dependent parameters. For the test problem used in this work, both methods agree very well with each other, as well as with a known analytical solution for a simpler formulation used as benchmark. The impact of the longitudinal diffusivity on the stiffness of the ordinary differential equation (ODE) system arising from the integral transformation has been assessed through the processing time demanded to solve it when the numerical approach is used. The observed CPU times show that the analytical approach is clearly preferable unless the problem involves time-dependent parameters.

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“…The flow and heat transfer characteristics of fluids flowing in micro-channels could not be adequately predicted by the theories. The studies (Aparecido and Cotta 1990;Wei 2002) showed that the performance of a micro channel heat exchanger depends on the aspect ratio (AR) of the channels. Bau (1998) conducted optimization studies to minimize temperature gradient and overall thermal resistance in micro channels and concluded that reduction in overall thermal resistance could be achieved by varying the cross-sectional dimensions of a micro channel.…”

Section: Introductionmentioning

confidence: 99%