On Some Laminar Forced-Convection Problems

1961 ◽  
Vol 83 (4) ◽  
pp. 466-472 ◽  
Author(s):  
L. N. Tao

The forced-connection problems in channels of fully developed laminar flow with heat sources and constant wall-temperature gradient are approached by the method of complex variables. It is shown that the stated problems are reduced to the determination of some analytic functions which satisfy the boundary conditions. Few basic problems, including flows in equilateral triangular ducts and in elliptical tubes, are studied. Also, it is shown that the cases of circular tubes and of parallel plates with a gap are directly deducible from that of elliptical tubes. All these solutions are expressed in closed forms by polynomials.

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
A. Baptista ◽  
M. A. Alves ◽  
P. M. Coelho

In this work, we present approximate and exact solutions for the temperature profile and Nusselt number under fully developed laminar flow of a power law fluid inside pipes and between parallel plates. Constant wall temperature and negligible axial heat conduction are considered, for both the cases with and without viscous dissipation. For completeness, the corresponding solutions for the related problem of constant heat flux at the wall are also presented. In the absence of viscous dissipation, the solutions obtained are semi-analytic, since they rely upon an iterative procedure. As a benchmark result, to allow comparison with the results obtained with the semi-analytical expressions, we also present highly accurate numerical solutions for the Nusselt number, Nu, based on numerical integration of the energy equation. Also based on these numerical results, simplified correlations for Nu are proposed, valid for a wide range of the power law index.


1991 ◽  
Vol 113 (3) ◽  
pp. 206-210 ◽  
Author(s):  
D. Yogi Goswami

This paper analyzes velocity profiles for flow through circular tubes in laminar, turbulent, and transition region flows and how they affect measurement by flow-meters. Experimental measurements of velocity profiles across the cross-section of straight circular tubes were made using laser doppler velocimetry. In addition, flow visualization was done using the hydrogen bubble technique. Velocity profiles in the laminar and the turbulent flow are quite predictable which allow the determination of meter factors for accurate flow measurement. However, the profiles can not be predicted at all in the transition region. Therefore, for the accuracy of the flowmeter, it must be ensured that the flow is completely in the laminar regime or completely in the turbulent regime. In the laminar flow a bend, even at a large distance, affects the meter factor. The paper also discusses some strategies to restructure the flow to avoid the transition region.


Author(s):  
Halil Tetik ◽  
Dong Lin

Abstract 3D freeze printing is a hybrid manufacturing method composed of freeze casting and inkjet-based printing. It is a facile method to fabricate lightweight, porous, and functional structures. Freeze casting is a well-known method for fabricating porous bodies and is capable of manipulating the micro-structure of the resulting product. Freeze casting simply involves solidification of a liquid suspension using low temperature and sublimation of the solvent using low temperature and pressure. After the sublimation of the solvent crystals, we obtain a porous structure where the pores are a replica of solvent crystal. Making use of the temperature gradient, as seen in unidirectional and bidirectional freeze casting, during the solidification with low temperature values, the solvent crystals grow along the temperature gradient. Furthermore, by manipulating the freezing kinetics during solidification, we can have a control on the average pore size distribution. For instance, when lower freezing temperatures result in finer pores with higher amount, higher freezing temperatures result in coarser pores with less amount. Also, the use of some additives inside the suspension leads to changes in the morphology of the solvent crystals as well as the resulting pores. However, the macro-structure of the fabricated body is highly dependent on the mold used during the process. In order to eliminate the dependency on the mold during the freeze casting process, our group recently combined this technique with inkjet-based 3D printing. With inkjet-based 3D printing, we fabricated uniform lines from single droplets, and complex 3D shapes from the lines. This provided us the ability of tailoring the macro structure of the final product without any dependency on a mold as seen in freeze casting. As a result of the 3D freeze printing process, we achieved fabricating lightweight, porous, and functional bodies with engineered micro and macro-structures. However, achieving fine droplets, and uniform lines by merging the droplets requires a good combination of fabrication parameters such as pressure adjustment inside the print head, print head speed, jetting frequency. Also, fabricating complex shapes from uniform lines requires well-adjusted parameters such as line thickness and layer height. In this study, we briefly explained the mechanics of the 3D freeze printing process. Following that we presented the development process of an open-source inkjet-based 3D printer. Finally, we explained the determination of inkjet dispensing and 3D printing parameters required for a high-quality 3D printing. During our experiments for the determination of fabrication parameters, we used a nanocellulose crystals-based ink due to its low cost and ease of preparation.


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