Heat exchange during flow of anomalously viscous fluids in cylindrical channels of simply connected cross section

1979 ◽  
Vol 37 (6) ◽  
pp. 1401-1405
Author(s):  
Yu. G. Nazmeev ◽  
L. I. Feifer ◽  
A. M. Yurist ◽  
K. D. Vachagin
Keyword(s):  
Heat Exchange ◽  
Cross Section ◽  
Viscous Fluids ◽  
Simply Connected

Streamlining an agitated vessel to intensify heat exchange with highly viscous fluids

1970 ◽  
Vol 6 (12) ◽  
pp. 1061-1062 ◽  
Author(s):  
G. S. Kozlov ◽  
�. A. Kramm ◽  
A. M. Lastovtsev ◽  
A. K. Nikitin
Keyword(s):  
Heat Exchange ◽  
Viscous Fluids ◽  
Agitated Vessel ◽  
Intensify Heat Exchange

Bounds for the Torsional Rigidity of Isotropic Beams

1962 ◽  
Vol 58 (2) ◽  
pp. 417-419 ◽  
Author(s):  
L. M. Milne-Thomson
Keyword(s):  
Cross Section ◽  
Isotropic Material ◽  
Torsional Rigidity ◽  
Connected Region ◽  
Closed Contour ◽  
Prismatic Beam ◽  
The Cross ◽  
Simply Connected Region ◽  
Simply Connected

Consider a cylindrical or prismatic beam of isotropic material. Let the cross-section of the beam be a simply-connected region S bounded by the closed contour C.

FLOW OF GAS THROUGH A TUBE OF CONSTANT CROSS-SECTION WITH HEAT EXCHANGE THROUGH THE TUBE WALLS

1945 ◽  
Vol 23a (1) ◽  
pp. 1-11 ◽  
Author(s):  
B. Szczeniowski
Keyword(s):  
Heat Exchange ◽  
Cross Section ◽  
Stream Velocity ◽  
Constant Cross Section ◽  
Velocity Of Sound ◽  
Heat Conductance ◽  
A Value ◽  
Maximum Value ◽  
Theoretical Investigations ◽  
Present View

The influence of the exchange of heat between a gas flowing through a tube and the outside atmosphere on the pressure in the gas stream is usually overlooked. Theoretical investigations show, however, that this influence is marked in the case of large stream velocities, approximating the velocity of sound. In addition, the theory permits us to state that the heat exchange is possible only when the stream velocity is maintained beyond certain limits. For stream velocities within these limits, heat exchange is not possible.The conclusion is reached that the velocity of flow in the tube, if the tube is heated or cooled, shows a natural and permanent tendency to reach the velocity of sound, after which the heat exchange is no longer possible.Finally, this theoretical investigation shows that the present view that the heat conductance coefficient increases continually with the stream velocity is wrong. This coefficient will be equal to zero when the stream velocity reaches the velocity of sound. This means that it will reach a certain maximum value corresponding to a value of stream velocity which is not exactly known but which will be less than that of sound.

scholarly journals Closed form solution in buckling optimization problem of twisted rod

2021 ◽  
Author(s):  
Vladimir Kobelev
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimal Shape ◽  
Actual Problem ◽  
The Cross ◽  
Simply Connected

Abstract The applications of this method for stability problems are illustrated in this manuscript. In the context of twisted rods, the counterpart for Euler’s buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under torsion (Greenhill, 1883). We search the optimal shape of the rod along its axis. A priori form of the cross-section remains unknown. For the solution of the actual problem the stability equations take into account all possible convex, simply connected shapes of the cross-section. Thus, we drop the assumption about the equality of principle moments of inertia for the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The distribution of material along the length of a twisted rod is optimized so that the rod is of the constant volume T and will support the maximal moment without spatial buckling. The cross section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. We demonstrate at the beginning the validity of static Euler’s approach for simply supported rod (hinged), twisted by the conservative moment. The applied method for integration of the optimization criteria delivers different length and volumes of the optimal twisted rods. Instead of the seeking for the twisted rods of the fixed length and volume, we directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for twisted rod is stated in closed form in terms of the higher transcendental functions. In the torsion stability problem, the optimal shape of cross-section is the equilateral triangle.

scholarly journals Theory of Heat Exchange in Pipes With Turbulators With d/D = 0.95 ÷ 0.90 And t/D = 0.25 ÷ 1.00, and Also in Rough Pipes, by Air With Great Reynold’s Numbers Re = 106

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Lobanov Igor Evgenjevich
Keyword(s):  
Heat Exchange ◽  
Cross Section ◽  
Energy Equation ◽  
Stress Transfer ◽  
Reynolds Numbers ◽  
Transfer Model ◽  
Computational Studies ◽  
Structured Grids ◽  
Multi Scale ◽  
Semicircular Cross Section

Mathematical modeling of heat exchange in air in pipes with turbulators with d / D = 0.95 ÷ 0.90 and t / D = 0.25 ÷ 1.00, as well as in rough pipes, with large Reynolds numbers (Re = 106). The solution of the heat exchange problem for semicircular cross-section flow turbulizers based on multi-block computing technologies based on the factorized Reynolds equations (closed using the Menter shear stress transfer model) and the energy equation (on multi-scale intersecting structured grids) was considered. This method was previously successfully applied and verified by experiment in [1-4] for lower Reynolds numbers. The article continues the computational studies initiated in [1-4,25-27].

Heat exchange in cylindrical pipes of complicated cross section with mixed boundary conditions

1975 ◽  
Vol 11 (6) ◽  
pp. 596-601
Author(s):  
V. L. Rvachev ◽  
A. P. Slesarenko ◽  
V. I. Popivshii
Keyword(s):  
Heat Exchange ◽  
Boundary Conditions ◽  
Cross Section ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions

Heat exchange in laminar flow through planar and quasiplanar channels of variable cross section

1976 ◽  
Vol 31 (2) ◽  
pp. 880-886
Author(s):  
I. V. Kabanova ◽  
A. I. Kaidanov ◽  
V. P. Morozov
Keyword(s):  
Heat Exchange ◽  
Laminar Flow ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Flow Through

scholarly journals Low-Reynolds Simulation of Heat Transfer in Turbulent Flow in a Flat Channel with Symmetrically Arranged Turbulators on Both Sides of the Channel

2020 ◽  
Vol 4 (1) ◽  
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Cross Section ◽  
Heat Exchangers ◽  
Thermal Loading ◽  
Flat Channel ◽  
Heat Transfer Intensification ◽  
Heat Flows ◽  
Heat Exchange Surface ◽  
Exchange Surface

Widespread use in modern heat exchangers and apparatus received heat exchangers, where the channels have a cross-section, different from the round tubes, in a particular case, flat channels, where heat is not produced by means of a full surface to be washed. The thermal loading of a flat channel can be asymmetric, since the heat flows on different surfaces can be unequal, namely: flat channels with one-way heating or with two-way heating with unequal heat flows. In order to ensure the compactness of heat exchange devices and heat exchange apparatuses, heat transfer intensification is used, which in flat channels is achievable by two main methods: the development of the heat exchange surface and turbulence of the flow in the channels.

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