Heat exchange on the initial thermal section in stabilized turbulent air flow in circular pipes and rectangular channels

Legkii, V. M.; Макаров, А. С.

doi:10.1007/bf00825418

Cited by 5 publications

(1 citation statement)

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“…In the range 10 4 ≤ Re ≤ 1.5⋅10 5 , the deviation of the calculated curve from the empirical points does not exceed 4%; for Re > 1.5⋅10 5 it is already considerable. Figure 3 compares the ratio Nu/Nu ∞ obtained by calculation from formula (25) for Re = 50,000 and R = 50 mm on the initial thermal portion to the empirical formulas of [13] and [10], respectively: …”

Section: (19)mentioning

confidence: 99%

Heat exchange in a circular pipe in modeling of turbulent air flow by oriented-fluid flow

Бабкин

2006

J Eng Phys Thermophys

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536.244Based on the anisotropic-turbulence model, the velocity profile and the temperature distribution in the flow in the case of steady-state air flow in a circular pipe have been obtained.In the model of [1-3], a viscous fluid in the regime of turbulent flow in the wall region is considered as an oriented fluid, one kinematic parameter of which -the director -prescribes its local anisotropy. Within the framework of the model, the problem of determination of the velocity profile in the case of steady-state flow is formulated just as an ordinary boundary-value problem. A fairly good coincidence of the calculated velocity profiles in the case of confined flow between parallel planes [2] and in plane turbulent Couette flow [3] stimulates solution of other problems associated with turbulent flow.In the present work, we investigate the problem on stationary heat exchange in the case of steady-state flow of a viscous incompressible fluid in a straight circular pipe at a constant wall temperature. First we consider the issues associated with finding the velocity profile and determining the parameters of a medium as functions of the parameters of flow; thereafter we approximately (by the Galerkin method) solve the equation of propagation of heat. The resulting regularities of variation in the local Nusselt number on the portion of stabilized heat exchange and on the initial thermal portion are compared to the experimental data for air.Velocity Profile. A detailed solution of the problem (analogous to that considered in [2]) on determination of the velocity profile in confined flow between parallel planes enables us to restrict ourselves here only to a brief presentation.Let a viscous incompressible fluid flow in the regime of steady-state turbulent flow in a straight circular pipe of radius R (the pipe is infinite and the walls are smooth). The direction of the x axis of the cylindrical coordinate system r, ϕ, x coincides with the direction of flow. Disregarding the mass forces, we find the velocity u m and the director n m in the form u x = u (r) , u r = u ϕ = 0 , n x = cos θ (r) , n r = sin θ (r) , n ϕ = 0 .(1)The functions u(r) and θ(r) sought must satisfy the equations [2] sin θ cos θand the boundary conditions θ (R) = 0 , u (R) = 0 .The derivatives with respect to r in (2), (3), and in what follows are primed.

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Section: (19)mentioning

confidence: 99%