Temperature profiles in liquid metals and the effect of superimposed free convection in turbulent flow

Buhr, H. O.; Carr, A.D.; Balzhiser, Richard E.

doi:10.1016/0017-9310(68)90067-7

Cited by 47 publications

(13 citation statements)

References 9 publications

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“…The eddy diffusivities V T and a T for momentum and heat transfer, respectively, appearing in Eqs. (1) and (2) are given as where S lv = (3) -exp( -0.016tf r )], with C D = 0.09 and (4) The turbulent Prandtl number G T is assumed to be constant with the value of 0.85 according to the suggestion by Kader and Yaglom. 12 The fully developed turbulent kinetic energy equation is modeled phenomenologically by Ng and Spalding 13 as (5) In the current case of fully developed flow, dT/dx = 0.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Brown and Gauvin 1 ' 2 investigated the influence of buoyancy force on the heat-transfer rates and temperature fluctuations in aiding and opposing flows in a vertical heated tube. Buhr et al 3 studied the temperature profiles in liquid metals and the effect of superimposed free convection in turbulent flow. Hall and Price 4 presented the solution of combined forced and free convection from a vertical heated plate to air.…”

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Turbulent mixed flow of free and forced convection between vertical parallel plates

Chen

Chiu

Lee

1989

Journal of Thermophysics and Heat Transfer

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In predicting the fully developed turbulent mixed flow of forced and natural convection, the one-equation model of turbulence for low Reynolds number flows is adopted. Finite-element solutions are carried out in the upward turbulent flow between vertical parallel plates at different wall temperatures. In this condition, the aiding and opposing flows arise simultaneously on the heated and cooled sides, respectively, and a fully developed condition is established. The solutions with and without the effect of buoyancy force are predicted and the comparisons are discussed. In these two situations, the mean velocity and temperature profiles, the locations of the maximum velocity, eddy diffusivities of momentum, Nusselt number, friction factor, and turbulence kinetic energy are presented. The substantial effects of the buoyancy force are also confirmed.eddy diffusivity for heat 8 = global source vector b = distance between parallel plates bj = element of global source vector b + = dimensionless distance between parallel plates = bu*/v c p = specific heat at constant pressure f c -friction factor = 2 t c \/p (u >? f H = friction factor = 2 i; H \/p <« >Ĝ + = buoyancy parameter = gf$(T H -T c )v/u* 3 Gr -Grashof number based on temperature difference = *gp(T H -T c )b 3 /v 2 g = gravitational acceleration K = turbulence kinetic energy K + = dimensionless turbulence kinetic energy = K/u* 2 k = von Karman constant / = element length / 1Z) = mixing length in dissipation ID -dimensionless mixing length in dissipation = /i jD w*/v £ lv = mixing length in diffusivity £i~v = dimensionless mixing length in diffusivity = £ lv u*/v N f = shape function Nu c = Nusselt number = 4|#|<5/«r> c -rjM Nu H = Nusselt number = 4\q\(b -d)/(T H -P = turbulence production P u = viscous production P 0 = buoyancy production Pr = Prandtl number p = real pressure p s = static pressure p + = dimensionless pressure =

/pw* 2 q = heat flux -Reynolds number = 2£/v = local turbulent Reynolds number = dimensionless local turbulent Reynolds number = temperature = dimensionless temperature normalized by the cooled-wall parameter = (T -T c )pc p u*/\q\ = dimensionless temperature normalized by the heated-wall parameter = (T H -T)pc p Uff/\q\ = time-averaged velocity in the x direction = dimensionless velocity = u/u* = friction velocity = ^/\r c \/p = velocity in y direction = coordinate in the flow direction = dimensionless coordinate in the flow direction = xu*/v = distance from the cooled wall = dimensionless distance from the cooled = correction factor defined by Eq. (40) = thermal expansion coefficient = distance from the cooled wall to the maximum velocity location = dimensionless distance = du*/v = turbulent dissipation = dimensionless temperature = (r -T c )j(T H -T c ) = thermal conductivity = kinematic viscosity = eddy diffusivity for momentum = dimensionless eddy diffusivity for momentum = V T /V = density = turbulent Prandtl number = shear stress Subscripts c H m o = at the cooled wall = at the heated wall = momentum = forced convection < )...

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Section: Governing Equationsmentioning

confidence: 99%

mentioning

confidence: 99%

Turbulent mixed flow of free and forced convection between vertical parallel plates

Chen

Chiu

Lee

1989

Journal of Thermophysics and Heat Transfer

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“…Mixed convection can arise in fast reactors during fault or shutdown conditions, and it can also be the normal mode of heat transfer in components such as cold traps, where mean velocities are low. Previous experimental investigators have used NaK [2][3][4], mercury [4][5][6][7][8] (which has a similar Prandtl number to that of NaK), and sodium [3,[9][10][11], in pipes [2][3][4][5][6][7][8], a rectangular channel [9], and heat exchangers [10,11]. In assessing the data the considerable difficulties inherent in the measurement of liquid metal heat transfer should be noted.…”

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“…All of the experiments with mercury [4][5][6][7][8] have involved the study of turbulent upward flow in passages that were heated electrically. In each case the primary objective appears to have been to obtain information on the distortion of velocity and temperature profiles by buoyancy forces, although some heat transfer .…”

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Mixed-Convection Heat Transfer to Sodium in a Vertical Pipe

Jackson

Axcell

Walton

1994

Experimental Heat Transfer

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Heat and mass transfer for turbulent pipe flow

Hughmark¹

1971

AIChE Journal

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NOTATION a, b = constants, Equation ( 3 ) H o = enthalpy of ideal gas, B.t.u./lb.-mole H = enthalpy, B.t.u./lb.-mole P = pressure, Ib./sq. in. abs. R = gas constant T = absolute temperature, O R . D = molar volume z = compressibility factor Greek Letters K = constant, Equation ( 3 ) T Su brcripts c = critical = internal pressure, lb./sq. in. abs. T = constant temperature z, = constant volume LITERATURE CITED 1. 2. 3. 4. 5. 6.Beattie, J. A., and 0. C. Bridgeman, Proc. Am. Acad. ArtsHeat and mass transfer coefficients for turbulent flow in smooth circular pipes have been represented by empirical equations of the form N N u = a ( N R e ) (NPr)'(1)with various values of the constants a, b, and c to correlate experimental data. EARLY RESEARCHThe equations of Colburn (1 ) , Dittus and Boelter ( 2 ) , ( 3 ) , and Sieder and Tate ( 4 ) are representative of the significant differences in the constants for Equation ( 1). These constants represent data for fluids with Prandtl numbers with the approximate range of 1 to 100. Interest in liquid metals as heat transfer media resulted in experimental data which showed that these data for very low Prandtl number fluids could not be predicted by correlations of the form of Equation (1). This difference occurs because the wall region, with characteristics of laminar flow, provides the resistance for heat transfer with Prandtl numbers greater than one, but the fully turbulent core region represents much of the resistance for the liquid metals. Drexel and McAdams

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Temperature profiles in liquid metals and the effect of superimposed free convection in turbulent flow

Cited by 47 publications

References 9 publications

Turbulent mixed flow of free and forced convection between vertical parallel plates

Turbulent mixed flow of free and forced convection between vertical parallel plates

Mixed-Convection Heat Transfer to Sodium in a Vertical Pipe

Heat and mass transfer for turbulent pipe flow

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