Forced Convection Heat Transfer From an Isothermal Sphere to Water

Vliet, G. C.; Leppert, G.

doi:10.1115/1.3680504

Cited by 78 publications

(11 citation statements)

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“…/ -: where J I (~I P ) and Yt(alP) are Bessel functions of the first and second kinds of order one. Subsequently Drake [14] provided the simple correlation equation: NUD = 2 + 0.459RevsPro.sss .I <_ ReD 5 ~OO,OOO (18) which agrees to within *l% with the values predicted by the complex expression, Eq. (17).…”

Section: Sphere Correlation Equation Based On Diffusive Bodysupporting

confidence: 54%

General expression for forced convection heat and mass transfer fromisopotential spheroids

Yovanovich

1988

26th Aerospace Sciences Meeting

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A single, semi-empirical, correlation equation for laminar forced convection heat and mass transfer from isopotential spheroids is presented. It is based on blending Pec Peclet number [Ret Pr] two correlation equations of Yuge developed for isothermal spheres in air streams, and the diffusive body length, square root of the total body surface area, of Yovanovich recently proposed for laminar natural convection from complex bodies. The proposed correlation equation is in very good to excellent agreement over the full range of the Reynolds number 0 <_ Rec 5 lo6 with several other correlation equations developed for spheres and spheroids, s shape factor but over limited ranges of the Reynolds number. 5 P P r 6 Q Q; Rec I S C Schmidt number [./Dl Shc Nomenclature T temperature of extensive fluid To uniform body temperature dimensionless outward 'body normal [n/C] maximum (equatorial) body perimeter Prandtl number [ . / a i dimensionless pressure heat Bow rate dimensionless heat flow rate [QC/A(To -Tm)kl Reynolds number [ U m L / v ] spherical coordinate Sherwood number [She = h,L/D] U A surface area of the body [Cad] T, Buid temperature remote from the body Cartesian coordinates J;i diffusive characteristic body length of % Y , Z A l p Yovanovich UW uniform free stream velocity Pasternak-Gauvin characteristic body length 9 dimensionless surface area [AIL'] -AR aspect ratio of oblate and prolate spheroids velocity vector A a sphere radius 26 spheroid equatorial diameter [ P / r ]C , , C t , C a correlation coefficients C concentration in the extensive fluid Greek Letters eo uniform body concentration a thermal diffusivity of the extensive fluid Cm concentration remote from body a1 Drake-Backer parameter [Jm] D sphere diameter 11 dummy variable in Eq. (17) D molecular d i h i v i t y 9 spherical coordinate e eccentricity of spheroids P*,Pm fluid viscosity at surface and free stream h heat transfer coefficient temperatures h, mass transfer coefficient U kinematic viscosity of the extensive fluid z unit vector along flow direction P mass density of the extensive fluid k thermal conductivity of the extensive fluid 4 C arbitrary characteristic body length m mass flaw rate V del operator dimensionless velocity vector [V/Um] Bessel function of second kind of order one Yd.1 Bessel function of first kind of order one pm density of fluid remote from the body dimensionless temperature or concentration potential [ ( T -Tm)/(To -T,)] JI(.) m Reynolds number correlation parameter or [(c -cm)/(co -Cm)l dimensionless mass flow rate 9 dimensionless del operator [ L VI [hC/A(co -cm)DI VZ Laplacian operator N u c Nusselt number [ N u t = hC/kl ea dimensionless Laplacian operator [ L'2Q2\ n Prandlt number correlation parameter; W outward body normal 'Professor, Associate Fellow AIAA 'copyright @M.M. Yovanovich 1 Downloaded by KUNGLIGA TEKNISKA HOGSKOLEN KTH on July 30, 2015 | http://arc.aiaa.org |

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Section: Sphere Correlation Equation Based On Diffusive Bodysupporting

confidence: 54%

General expression for forced convection heat and mass transfer fromisopotential spheroids

Yovanovich

1988

26th Aerospace Sciences Meeting

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“…6.7-21 is compared with the experimental data of three investigators [39][40][41] in Fig. 6.7-21 is compared with the experimental data of three investigators [39][40][41] in Fig.…”

Section: Nusselt Numbers By An Equation Of the Formmentioning

confidence: 99%

Macroscopic Balances

Whitaker

1976

Elementary Heat Transfer Analysis

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“…For the forced convection correlations, he divided the correlations into two ranges with Re " 1800 as the point where the slope of the correlations changed. Later, Vliet and Leppert [18] carried out an experimental study with water, for Reynolds numbers in the range between 940 and 5ˆ10 4 , considering the effect of the variation of water properties and natural convection. Galloway and Sage [19] reviewed previous works measuring Nusselt and Sherwood numbers and highlighted the importance of turbulence level and sphere diameter.…”

Section: Introductionmentioning

confidence: 99%

Fluid dynamics and heat transfer in the wake of a sphere

Rodríguez

Lehmkuhl

Sòria

et al. 2019

International Journal of Heat and Fluid Flow

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Direct numerical simulation and large-eddy simulation have been performed for a heated sphere at Reynolds numbers of Re " 1000 and Re " 10 4 , respectively.The Prandtl number for both simulations has been P r " 0.7. Measurements of the local and average Nusselt number are performed and compared with literature available experimental results. Average and front stagnation point Nusselt numbers increase with the Reynolds number, while the minimum value moves towards the sphere apex as the flow enters the sub-critical regime. Differences in both viscous and thermal boundary layers are observed, while the shape factor at Reynolds number Re " 10 4 behaves similarly to that observed in circular cylinders at comparable Reynolds numbers. It is shown that as the Reynolds number increases, the increase in turbulent kinetic energy promotes the entrainment of irrotational flow thus enhancing the temperature mixing in the zone.The near wake, between 5 ď x{D ď 15, spreads at a faster rate at Re " 1000 with a slope close to x{D 1{2 , while at Re " 10 4 it follows a trend close to x{D 1{3 .

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Forced Convection Heat Transfer From an Isothermal Sphere to Water

Cited by 78 publications

References 0 publications

General expression for forced convection heat and mass transfer fromisopotential spheroids

General expression for forced convection heat and mass transfer fromisopotential spheroids

Macroscopic Balances

Fluid dynamics and heat transfer in the wake of a sphere

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