Conduction heat transfer solutions

VanSant, J.H.

doi:10.2172/7035199

Cited by 21 publications

(12 citation statements)

References 3 publications

(7 reference statements)

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“…(16) and (17), the values of Nu c used are summarized in Table 4, wherein its analytical [43] and the present numerical values are in near prefect agreement. Overall, Eqs.…”

Section: E Average Nusselt Numbersupporting

confidence: 58%

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Patel

Chhabra

2016

Journal of Thermophysics and Heat Transfer

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Free convection from an isothermal elliptical cylinder in Bingham plastic fluids is studied numerically. This work spans a wide range of aspect ratios of the elliptical cylinder (0.1 ≤ E ≤ 10) to delineate the effect of shape on the flowfield close to the heated cylinder. The influence of the relevant parameters, namely, Rayleigh number (10 2 ≤ Ra ≤ 10 5 ), Prandtl number (10 ≤ Pr ≤ 100), and Bingham number (0.5 ≤ Bn ≤ 10 7 ), on the momentum and heat transfer characteristics is studied in terms of the yielded/unyielded regions, streamline, isotherm contours, and local Nusselt number for an elliptical cylinder of constant surface area in blunt (E > 1) and slender orientations (E < 1). The Nusselt number shows a positive dependence on the Rayleigh number, and it correlates negatively with Bingham and Prandtl numbers. The blunt orientations (E < 1) enhance heat transfer as compared to that for a circular cylinder (of equal surface area) while slender orientations (E > 1) impede it. Using the present numerical results, predictive correlations have been established in terms of the modified Rayleigh number (Ra ) and Prandtl number (Pr ), thereby enabling the prediction of Nusselt number in a new application. Nomenclature A = surface area of the cylinder, m 2 A p = projected area of the cylinder, m 2 a = semi-axis of the elliptical cylinder along the direction of flow, m Bn = τ o 2b∕μ B V c , Bingham number b = semi-axis of the elliptical cylinder normal to the direction of flow, m C = heat capacity of fluid, J∕kg ·of the outer boundary of the domain, m E = a∕b, aspect ratio of the elliptical cylinder e y = unit vector in y-direction F = total drag force per unit length of the cylinder, N∕m F DP = pressure component of drag force per unit length of the cylinder, N∕m GrGrashof number h = local heat transfer coefficient, W∕m 2 · K k = thermal conductivity of fluid, W∕m · K M = growth rate parameter in Papanastasiou model n s = unit vector normal to the surface of cylinder Nu = local Nusselt number Nu avg = average Nusselt number Nu c = Nusselt number in the conduction limit p = pressure p s = local pressure on the surface of cylinder, Pa p ∞ = reference pressure far away from the cylinder, Pa Pr = Cμ B ∕k, Prandtl number Pr = Pr1 Bn, modified Prandtl number Ra = ρ 2 ∞ CgβT w − T ∞ 2b 3 ∕μ B k, Rayleigh number Ra = Ra∕1 Bn, modified Rayleigh number T = temperature of fluid, K T w = constant wall temperature at the surface of the cylinder, K V = velocity vector V c = characteristic fluid velocity, m∕s β = −1∕ρ∂ρ∕∂Tj P , coefficient of volumetric expansion, 1∕K γ ij = components of the rate of deformation tensor δ = growth rate parameter in Bercovier and Engelman model η = effective fluid viscosity θ = position on the surface of cylinder (measured from the front stagnation point), deg μ B = Bingham plastic viscosity, Pa · s μ y = yielding viscosity, Pa · s ξ = T − T ∞ ∕T w − T ∞ , temperature of fluid ρ = fluid density, kg∕m 3 τ = extra stress tensor τ ij = components of the extra stress tensor τ 0 = Bingham yield stress, P...

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“…(16) and (17), the values of Nu c used are summarized in Table 4, wherein its analytical [43] and the present numerical values are in near prefect agreement. Overall, Eqs.…”

Section: E Average Nusselt Numbersupporting

confidence: 58%

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Patel

Chhabra

2016

Journal of Thermophysics and Heat Transfer

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“…The increase of the surface temperature of the plasma facing components under runaway impact can be approximately evaluated by the application of the one-dimensional solution of the heat diffusion equation in a semi-infinite solid [38] and taking into account that the runaway electrons, because of the high energies in the MeV range, have a nonnegligible penetration depth. Assuming an exponential decay of the runaway electron energy deposition into the plasma facing components, the heating at the plasma facing component surface under runaway impact can be evaluated by [39,19]:…”

Section: Runaway Heat Loads On the Plasma Facing Componentsmentioning

confidence: 99%

Inter-machine comparison of the termination phase and energy conversion in tokamak disruptions with runaway current plateau formation and implications for ITER

et al. 2014

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The termination of the current and the loss of runaway electrons following runaway current plateau formation during disruptions have been investigated in the JET, DIII-D and FTU tokamaks. Substantial conversion of magnetic energy into runaway kinetic energy, up to ~10 times the initial plateau runaway kinetic energy, has been inferred for the slowest current terminations. Both, modelling and experiment suggest that, in present devices, the efficiency of conversion into runaway kinetic energy is determined to a great extent by the characteristic runaway loss time, t diff , and the resistive time of the residual ohmic plasma after the disruption, t res , increasing with the ratio t diff /t res. It is predicted that, in large future devices such as ITER, the generation of runaways by the avalanche mechanism will play an important role, particularly for slow runaway discharge

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“…We woluld like also notice that various forms of solutions for the cylinder (roller) are showed, e.g. in works of Carslaw et al (1959) and VanSant (1983).…”

Section: Discussionmentioning

confidence: 92%

“…For example, the thermostatted vibrator roller in the machine Heidelberg XL105 (according to technical drawing) has a diameter and length , width of the contact zone , displacement of the roller along the axis , coolant flow diameter . We assume that:  the roller is made of steel (according to VanSant (1983): ( ), );  the cooling fluid is the water at a temperature ( ) under conditions of forced flow into the pipe ( ( ));  and the surrounding is the air at the temperature ( ) under conditions of forced flow near the surface of the roller ( ( )). The preliminary analysis was performed for the case when functions ( ) for are Heaviside step functions ( ) ( ( ) for and ( ) for ).…”

Section: Discussionmentioning

confidence: 99%

Analysis of Tribological Processes in the Inking Unit of the Offset Printing Machine

Pyryev¹,

Piętak²

2013

Acta Mechanica Et Automatica

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In this paper is proposed the mathematical description of the temperature distribution resulting from the friction between the two inking rollers (one of which is made off steel and the second one has elastic layer) in the offset printing machine. So-called in printing industry steel vibrator roller perform simultaneously rotary and reciprocating motion. This reciprocating motion is the main source of the heat generation. Using the Laplace transform method for heat conduction equations with boundary conditions taking into account the real processes taking place in the inking unit in contact area we obtained and analyzed the solution that could be useful for determination and regulation of parameters in order to decrease time of process stabilization

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Conduction heat transfer solutions

Abstract: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees.^ makes, any warranty, express ox impUed, Show more

Cited by 21 publications

References 3 publications

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Elliptic Cylinder

Inter-machine comparison of the termination phase and energy conversion in tokamak disruptions with runaway current plateau formation and implications for ITER

Analysis of Tribological Processes in the Inking Unit of the Offset Printing Machine

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