Nusselt Number for Liquid Metal Reactors. See also: Nusselt Number for Liquid Metal Reactors For liquid metals the Prandtl number is very small, generally in the range from 0.01 to 0.001. This means that the thermal diffusivity, which is related to the rate of heat transfer by conduction, unambiguously dominates.This very high thermal diffusivity results from very high thermal conductivity of. * The new theory introduces a thermal history kernel and provides transient Nusselt (Nu) and Sherwood (Sh) numbers as a function of the Reynolds (Re), Prandtl (Pr), and Schmidt numbers (Sc)*. For the first time, these new correlations take into account the mixture properties due to the concentration of CoV particles in a saliva droplet

Generalmente il numero di Nusselt è valutato in funzione del numero di Prandtl e,se la convezione è naturale, del numero di Grashof o del numero di Reynolds (se la convenzione è forzata), a meno di un coefficiente C e degli esponenti n ed m a cui sono elevati gli altri due gruppi adimensionali Unknown coefficients x 1 , , x n appearing in the heat transfer correlation expressing the Nusselt number as a function of the Reynolds number and Prandtl number were determined by the method.

** Nombre de Nusselt pour les réacteurs à métal liquide**. Voir aussi:** Nombre de Nusselt pour les réacteurs à métal liquide** Pour les métaux liquides, le nombre de Prandtl est très faible, généralement compris entre 0,01 et 0,001. Cela signifie que la diffusivité thermique , qui est liée au taux de transfert de chaleur par conduction , domine sans ambiguïté Nusselt = F ( Reynolds , Prandtl ) F = Function. See: https://www several correlations relating the Nusselt number to the Reynolds and the Prandtl numbers are provided in the literature Nusselt, Reynolds, and Prandtl numbers. Only . µ w, which appears in the viscosity ratio, is evaluated at the wall temperature. The Reynolds and Prandtl numbers are raised to the same power in the laminar flow correlation. Therefore, we can write the correlation as ( ) ( ) 1/3 0.14 1/3 0.14 1.86 Re Pr 1/3bb 1.86 Pe ww DD Nu LL µµ µ Qualitatively, the Nusselt number development for other channel flows with heated walls is the same as for Poiseuille flow (regardless of geometry, turbulent flow, presence of scattering, nongrayness, etc.). The heat transfer behavior is somewhat different if a hot fluid enters a cold-walled duct (T w < T i).This is shown in Fig. 21-13 for turbulent tube flow of a gas seeded with small.

- Il numero di Nusselt è funzione dei numeri puri di Reynolds, di Grashof, di Prandtl, e del posizionatore. (13) La funzione che restituisce il numero di Nusselt a partire dai quattro numeri puri deve essere unica ed a coefficienti costanti, ed è chiamata soluzione del problema. Dato un certo campo di validità dei risultati ( es
- This paper presents new correlations between the Nusselt and Reynolds numbers for food products being subjected to water and/or air cooling applications. In the theoretical part, we assume that the problem of cooling a cylindrical or spherical product can be reduced to 1-D heat conduction in the radial direction, subject to convective cooling at the surface
- For fully developed (hydrodynamically and thermally) turbulent flow in a smooth circular tube, the local
**Nusselt**number may be obtained from the well-known Dittus Boelter equation. To calculate the**Nusselt**number, we have to know: the**Reynolds**number, which is Re Dh = 575600; the**Prandtl**number, which is Pr = 0.8

the different inlets and correlations to predict heat transfer in the transition re-gion of flow. All correlations are approximate and may possess errors as much as 25 percent or larger. In this paper, a new correlation for the Nusselt number Nu in terms of the friction factor ξ, Reynolds number Re and Prandtl numbe The larger the Nusselt number, the more effective the convection. A larger Nusselt number corresponds to more effective convection, with turbulent flow typically in the 100-1000 range. For turbulent flow, the Nusselt number is usually a function of the Reynolds number and the Prandtl number

The Nusselt number based on the local convective heat transfer coefficient is expressed as 1/ 2 NuX = fPr ReX The expression of ƒPr depend on the fluid Prandtl number For liquid metals with very low Prandtl number liquid metals (Pr ≤ 0.05) 1/ 2 fPr =0.564Pr For 0.6 < Pr < 50 1/ 3 fPr =0.332Pr For very large Prandtl number 1/ 3 fPr =0.339P $\begingroup$ I mean the Nusselt number for laminar flow inside a pipe is constant (4.364) which means however high is the velocity (of course to the point that flow stays laminar), the heat transfer rate is not affected furthermore the case for turbulent flow is different and Nusselt number is a function of reynolds and prandtl number. $\endgroup$ - moeinSj Apr 20 at 17:3

- Convection Heat Transfer Reading Problems 19-1 → 19-8 19-15, 19-24, 19-35, 19-47, 19-53, 19-69, 19-77 20-1 → 20-6 20-21, 20-28, 20-44, 20-57, 20-79 Introduction • in convective heat transfer, the bulk ﬂuid motion of the ﬂuid plays a major role in the over- all energy transfer process. Therefore, knowledge of the velocity distribution near a soli
- ar Für Re<2300: 2
- The theory involves an unknown constant exponent s and two unknown functions of the Prandtl number. For either s = ½ or s = 1/3, corresponding to two different theories of thermal convection, and for a given Prandtl number, constants can be chosen to give excellent agreement with existing data over nearly the whole explored range of Rayleigh numbers in the turbulent case

La relazion pussée doprada a l'è chèsta chì: = ⋅ ⋅ che la var per 0,6<Pr<60 e la var per 'na piastra isotèrma. indoe el numer del Nusselt l'è correlàa cont el numer del Reynolds e 'l numer del Prandtl, indoe C, m e n hinn di coefficient che varien second la geometria e del tipo de mòto ( regimm laminà e regimm turborent).Per capì se el regìmm l'è laminà o turborent a. JRB, ASR MEAM333 - Convection Correlations 3.8 Impinging Jets Heat and mass transfer is measured against the uid properties at the nozzle exit q00= h(T s T e) The Reynolds and Nusselt numbers are measured using the hydraulic diameter of the nozzle D h= A c;e P The Reynolds number uses the nozzle exit velocity. All correlations use the target. Il numero di Prandtl (abbreviato spesso con Pr) è un numero adimensionale che esprime il rapporto della diffusività cinematica rispetto alla diffusività termica per un fluido viscoso. Il suo analogo per lo scambio materiale è il numero di Schmidt Convection Coefficient using Reynolds and Nusselt numbers RE-Lecture. Loading... Unsubscribe from RE-Lecture? Cancel Unsubscribe. Working... Subscribe Subscribed Unsubscribe 1.33K. Loading.

A 5th order 2D polynomial in terms of Reynolds and Prandtl numbers is then used to provide a correlation for each of the 13 coefficients. A very high resolution database consisting of 25 Reynolds numbers from 10 to 250 in increments of 10, and 24 Prandtl numbers from 0.1 to 40 comprising a total of 600 simulations is used for the modeling The average Nusselt number. (Nu) Plot the Nusselt number versus the Reynolds Number. What does the graph suggests? Finally plot the correlation for turbulent flow given in the book (Nu = 0.23*Re^(4/5)*Pr^n). Find a value for n that fits the experimental data the closest Nusselt number calculator Sweepstakes. Follow us. Nusselt number calculator. * For Reynolds numbers smaller than 10,000 and Prandtl numbers between 0*.6 and 2000, the average Nusselt number for a laminar flow around a flat plate which is isothermally heated or cooled can be calculated using the following formula A model for the internal structure of the turbulent eddy is developed using the approach of Tennekes (1968) and used to derive analytically the Colburn analogy St (Pr exp 2/3) = 0.5 f, where St is the Stanton number, Pr is the Prandtl number, and f is the coefficient of friction. The momentum and thermal microscales are reviewed, the model of a kinetic turbulon is constructed, thermal scales.

The currently accepted Nusselt number correlation for the transition regime, due to Gnielinski, is restricted to the high-Reynolds-number end of that regime. This limitation results from the need for a valid friction factor - Reynolds correlation for input to the Gnielinski equation Tabella 2: formule sperimentali per il calcolo del numero di Nusselt in convezione naturale Tabella 3- Formule sperimentali per il calcolo del numero di Nusselt: convezione mista. Situazione Nu = C.Rea.Grb.Prc geometrica Campo di Validità C a b c Autori Note Condotto verticale Re > 1600 0.525 0 0.25 0.2

Bharti et al. [7] investigated the effects of Reynolds number, Prandtl number and thermal boundary conditions (uniform heat flux and constant wall temperature) around the cylinder for the range 10 Re 45dd and 0.7 Pr 400dd in the steady regime. The rate of heat transfer is found to increase with an increase in Reynolds and/or Prandtl numbers various flow rates and temperatures in order to develop a correlation via modified Wilson plot technique corresponding to a maximum Reynolds number (Re) of 4500 and Prandtl number (Pr) in the range of 5.6 to 8. Key-Words: - Plate heat exchanger, Single phase, Nusselt number, Chevron plates, Modified Wilson plot 1 Introductio Correlations for Heat Transfer Coefficients. Each flow geometry requires different correlations be used to obtain heat transfer coefficients. Initially, we will look at correlations for fluids flowing in conduits. Most correlations will take the Nusselt form: The correlations that follow are limited to conduit flow without phase change Nu Nombre de Nusselt Gr Nombre de Grashof Ra Nombre de Rayleigh Pr Nombre de Prandtl Pe Nombre de P´eclet Ri Nombre de Richardson ϕ~ densit´e de ﬂux de chaleur (W.m−2) Φ Flux de chaleur (W) λ conductivit´e thermique (W.m−1.K−1) ∇2 = ∆ operateur laplacien ρ masse volumique (kg.m−3) α = λ ρC diﬀusivite thermique (m 2.s−1

Otherwise, for forced convection, the Nusselt number is generally a function of the Reynolds number and the Prandtl number, or. Empirical correlations for a wide variety of geometries are available that express the Nusselt number in the aforementioned forms. Free convection Free convection at a vertical wall. Cited as coming from Churchill and Chu determined Nusselt numbers, new correlations for Nusselt number as a function of Reynolds and Prandtl numbers have been proposed for various models for the turbulent Prandtl number. Engineering correlations developed in the paper can be used for the proper design and operation of thermal systems, in which liquid metals are the heat transfer. In this thesis we present the results of an extensive campaign of direct numerical simulations of Rayleigh-B\'enard convection at high Prandtl numbers ($10^{-1}\leq Pr \leq 10^4$) and moderate Rayleigh numbers ($10^{5}\leq Pr \leq 10^9$)

Else, for forced convection, the Nusselt number is generally a function of the Reynolds number and the Prandtl number, or Nu = f(Re, Pr). Empirical correlations for a wide variety of geometries are available that express the Nusselt number in the aforementioned forms. The mass transfer analog of the Nusselt number is the Sherwood number obtain a correlation for the determination of friction factor versus Reynolds number. Khan et al. [25] has been carried out experimental heat transfer studies with water-water in PHE for symmetric 30/30, 60/60, and mixed 30/60 chevron angle plates and a correlation to estimate Nusselt number as a function of Reynolds number, Prandtl number and. Prandtl correlation, 4000 £ Re £ 106 Figure 1: Equation 3 captures smooth pipe friction factor as a function of Reynolds number over the entire Reynolds-number range (Morrison, 2013) Последние твиты от ʀ⎊ᴜ ʀᴇʏɴ⎊ (@RouReynolds). songwriter, producer & composer. @entershikari

- Combined Internal/External Flow Correlations (Average) Note: For tube banks with fewer than 20 rows, multiply the average Nusselt number from the table at left by the correction factor C 2 in Table 7.6. This correction is valid if Re D,max is > 1,000. Average Nusselt Number Restrictions 20 · Tube Bank Correlation 1/ 4 0.36,max Pr Pr Re Pr.
- e a unique Nusselt correlation for the turbulent regime of Reynolds numbers (2000 <Re <7500), Prandtl number from 3 <Pr <5, and chevron angle of 60 degrees
- Numerical solutions for the Nusselt number during the direct contact evaporation of a moving drop in a stagnant column of immiscible liquid are presented. The effect of bubble growth rate on the radial component of drop velocity is taken into account in the analysis and the Nusselt number is found to be a function of Peclet number, Jakob number and vapour open angle

- pronounced for driven cavity of length higher values of Prandtl number and also derived a correlation for the average Nusselt number in terms of the Prandtl number, Reynolds number and Richardson number. Aydin and Yang (2000) numerically studied mixed convection heat transfer in a two-dimensiona
- In the case of granular flows (where ), ANSYS FLUENT uses a Nusselt number correlation by Gunn [ 117], applicable to a porosity range of 0.35-1.0 and a Reynolds number of up to : (16.5-106) The Prandtl number is defined as above with
- ar flow. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100-1000 range
- ar thermal boundary layer, Prandtl Number - Duration: Heat Transfer L29 p2 - Condensation - Nusselt's Correlation - Duration: 8:35. Ron Hugo 5,744 views
- e) for the Nusselt number (Nu) in terms of the Reynolds number (Re) and the Prandtl number (Pr) can be used as a mass transfer correlation by replacing the Prandtl number with the analogous.

Nusselt number (dimensionless) Re D: Reynolds number on the hydraulic diameter (dimensionless) Pr: Prandtl number (dimensionless) n: n= 0.4 for the fluid being heated, and n = 0.3 for the fluid being cooled (dimensionless The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 10 4 < Ra < 10 7 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated * The Nusselt number depends on the amount of turbulence in the flow*. The Reynolds number indicates whether the flow is laminar or turbulent, and for high Reynolds numbers can be a measure of the amount of turbulence - e.g. in the Dittus-Boelter equation and the Sieder-Tate correlation

One likely reason for the discrepancy shown in Figure 2 is that the Nusselt number or friction factor correlation used by the model is inaccurate or unsuitable for the range of Reynolds number (Re) and Prandtl number (Pr) that is used to produce the data (i.e., low Reynolds number and high Prandtl number). The Nusselt number is defined accordin * Prandtl Number: It describes the For each experimental set, we calculate the dimensionless numbers and using a log-log plot, we plot Nusselt Number vs Reynolds number for different values of Prandtl number*. By substituting experimentally obtained coefficients in above equation, we obtain empirical correlations and the plasma gas. This correlation can be written; . Re Prp mn d Nu h a c k (1) Where Nu the Nusselt number for the transfer plasma/particle, Re the Reynolds number of the particle given by equation(2), Pr the Prandtl number of surrounding gases given by equation(3). h the heat coeﬃcient and κ is the thermal conductivity of the gas Heat Transfer at the Pipe Wall. You can model heat transfer to and from the pipe walls in multiple ways. There are two analytical models: the Gnielinski correlation, which models the Nusselt number as a function of the Reynolds and Prandtl numbers with predefined coefficients, and the Dittus-Boelter correlation - Nusselt = a*Re^b*Pr^c, which models the Nusselt number as a function of the. The e ects of mass ﬂow rate of air on the outlet temperature, Nusselt Number, Reynolds Number, Prandtl Number, heat transfer in the thickness of the solar collector and thermal e ciency were studied. Experiments were performed for the mass ﬂow rates of 0.0108, 0.0145 and 0.0184 kg/s. For this e ect was have created

Forced Convection Correlations Experiments have shown a relationship between the Nusselt, Reynolds, and Prandtlnumbers to find h. 17 Fluid Velocity Characteristic Length Kinematic Viscosity Prandtl - Typically taken as 0.7 for ai The mean **Nusselt** number for turbulent flow over a plate of length l is Nu=0.037 Re^0.8 Pr/(1+2.44 3Re^-0.1(P r^2/3 -1)) , 5x10^5<Re< 10^7,0.6<P r<2000' where Re is the **Reynolds** number and Pr is the **Prandtl** number. Plot log10(Nu) as a surface that is a f Nusselt number correlations for simultaneously developing laminar duct ows of liquids with the local Prandtl number Pr = c=kand the local P eclet the ratio =kand of k, respectively. Therefore we have = e = Re e=Re and k=k e = Pe e=Pe, where Re e and Pe e are the Reynolds and P eclet numbers evaluated at t e. Moreover,. The Nusselt number is derived from empirical correlations with the Reynolds and Prandtl numbers. Use the Heat transfer parametrization parameter to select the most appropriate formulation for your simulation Also these correlations are a quick way to estimate the convective heat transfer. Several dimensionless numbers will be used to calculate h. These are the Grashof number (Gr), Nusselt number (Nu), Prandtl number (Pr), Reynolds number (Re) and the Rayleigh number (Ra)

* The Nusselt number in the annular section was estimated based on the modified Wilson plot method solved by an ANN*. This model included the Reynolds and Prandtl numbers as input variables and three neurons in their hidden layer. The Nusselt number in the inner section was estimated based on the Rohsenow equation, solved by an ANN Theoretical expressions for the Nusselt modulus and radial temperature distribution in terms of Reynolds number, Prandtl number, the ratio k of the eddy diffusivities for heat and momentum, and the friction factor are developed for the case of heat transfer from a tube of circular section to a fluid flowing turbulently through it. The results, appropriate to fluids with Prandtl numbers greater. Correlations are then formed for these two sections, which are assumed to be separated by a distinct transition Reynolds number. An example is the correlation for average heat transfer coefficient proposed by Whitaker : the heat transfer coefficient is averaged over the length, using results from laminar theory and correlation for turbulent flow

The **Nusselt** number is a function of the **Reynolds** number and the **Prandtl** and can from CHEMICAL E 350 at Tuskegee Universit The Prandtl numbers of fluids range from less than 0.01 for liquid metals to more than 100,000 for heavy oils. Note that the Prandtl number is in the order of 10 for water. The Prandtl numbers of gases are about 1, which indicates that both momentum and heat dissipate through the fluid at about the same rate Correlations of average Nusselt number were deduced from experimental data in terms of Reynolds number, Prandtl number and coil hydraulic diameter. Correlations prediction was compared with experimental data and the comparison was fair enough. Nomenclatur proposed correlations available is given in Table 1. These equations are discussed in detail in Appendix A. Most of the proposed equations for calculating the Nusselt number are functions of the annular diameter ratio (a = D2/D1), the Reynolds number (Re) and the Prandtl (Pr) number and corresponds with the Dittus-Boelter type from

NUSSELT, ERNST KRAFT WILHELM (b.Nuremberg, Germany, 25 November 1882; d.Munich, Germany, 1 September 1957), heat transfer, thermodynamics. Nusselt was the first significant contributor to the subject of analytical convective heat transfer (ii) Reynolds number must not be less than 40 000 (iii) Pr must be more than 0.6 . For a plate of length l, an average value of Nusselt number or convection coefficient may be obtained by integration. (b) The following correlation has been proposed for liquid metals - Nu x = 0.565 (Re x × Pr) (10.23 Condensation Nusselt number correlation for R32/ 152a.. 26 iv. ABSTRACT Average Nusselt numbers were measured for R22, R290, R290/600a, and R32/152a often expressed as a function of the Reynolds and Prandtl numbers, the distance from the entrance, and the tube diameter (Incropera and DeWitt, 1990) Solution(By Examveda Team) The ratio of Nusselt number and the product of Reynold's number and Prandtl number is equal to Stanton number The Stanton number is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of fluid The Nusselt number in each region strongly depends on the Reynolds number and the Prandtl number with different power indices. An empirical correlation for predicting the overall heat transfer from the cylinder is developed from the contributions of heat transfer in these three regions.

Nusselt number: | In |heat transfer| at a |boundary| (surface) within a |fluid|, the |Nusselt number| (|Nu|... World Heritage Encyclopedia, the aggregation of the. DETERMINING HEAT TRANSFER CORRELATIONS FOR TRANSITION AND TURBULENT FLOW IN DUCTS The objective of the paper is to develop correlations for the Nusselt number Nu in terms of the friction factor ξ (Re) and also Reynolds number Re and Prandtl num-ber Re, which is valid for transitional and fully developed turbulent flow ht.conv_internal.Nu_conv_internal (Re, Pr, eD=0.0, Di=None, x=None, fd=None, Method=None) [source] ¶. This function calculates the heat transfer coefficient for internal convection inside a circular pipe. Requires at a minimum a flow's Reynolds and Prandtl numbers Re and Pr.Relative roughness eD can be specified to include the enhancement of heat transfer from the added turbulence First of all, Stanton number is a non dimensionless quantity. So if you can find the corresponding Stanton number the calculations for the convection problems will be easy. You may be thinking how.. Right.. For most of the convection problems, t.. 6.4 × 104), Nusselt number (37.75 - 226.98) and for vertical tubes are obtained for the range of Reynolds number (4 × 104 to 6.9 × 104), Nusselt number (41.45 - 245.56). A correlation for the convective heat transfer coefficients is obtained. The present experimental correlation is compared with available correlation

- It can also be represented in terms of the fluid's Nusselt, Reynolds, and Prandtl numbers: = where Nu is the Nusselt number; Re is the Reynolds number; Pr is the Prandtl number. The Stanton number arises in the consideration of the Correlations using Reynolds-Colburn analogy
- Reynolds number, Prandtl number, Nusselt number and conductivity of the outer tube stream corresponding to the operating conditions listed in Table 2. Table 5. Outer tube heat transfer properties The outer tube heat transfer coefficients evaluated according to the Hausen correlation and using the data listed in Table 5 are included in Table 6. Th
- Nu = Nusselt number = => Dittus-Boelter correlation Pr = Prandtl number = Re = Reynolds number = = mass flow rate μ = fluid viscosity C p = heat capacity at constant pressure A = cross-sectional area of flow n = 0.4 for heating (wall hotter than the bulk fluid) and 0.3 for cooling (wall cooler than the bulk fluid)
- turbulent-flow Reynolds numbers of 4000 to 23000, and orifice to heat-source spacings of 1 to 5 jet diameters. Generalized correlations for heat transfer rates are proposed based on these results, and are valid over the range of coolant Prandtl numbers from 0.7 to 25.2
- [Trasmissione del calore] Prandtl - Reynolds - Péclet Il Forum di Matematicamente.it, comunità di studenti, insegnanti e appassionati di matematica 03/01/2010, 15:0

- Nusselt number. Share. Important role in analyzing the behavior of fluids. Common examples include the Reynolds or the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound,.
- ar equivalent diameter, is utilized
- imum a flow's Reynolds and Prandtl numbers Re and Pr. L and x are not used by any correlations presently, but are included for future support. If no correlation's name is provided as Method, the most accurate applicable correlation is selected

Nusselt number: non‐dimensional The Reynolds number at which the flow becomes turbulent is called the critical Reynolds number. For flat plate the critical Re is experimentally determined to be approximately Re critical = 5 x105. Prandtl number: is a measure of relative. The Prandtl number is dependent only on fluid properties; the Reynolds number is a ratio of inertial to viscous forces and is relevant throughout the subject of fluid mechanics and convection; the Stanton number is a combination of Nu, Pr, and Re; and the Grashof number characterizes natural convection with the gravitational acceleration, g, and β, the coefficient of volumetric thermal.

Fig. 1: (a) The Nusselt number and (b) the Reynolds number as a function of Pr for Ra = 10 5. Nu increases with increasing Pr for small Prandtl numbers, and does not vary much for moderate Pr . The Reynolds number decreases with increasing Pr . Dashed curve in panel (b) is the t given by the model of Pandey and Verma [20] The convection equations relating the Nusselt, Reynolds, and Prandtl numbers can be rearranged to show that for gases the heat transfer coefficient h c depends on the absolute temperature T and the group for the condition 0.5 . Pr 5.0.. State restrictions as necessary Nusselt prandtl and reynolds numbers. The Nusselt, Reynolds and Prandtl numbers are dimensionless numbers presented in the form of a ratio that compares two phenomena. - The Nusselt number (Nu=h*L / kf) is the ratio of convection to pure conduction heat transfer, where kf is the conductivity of the fluid. - The Reynolds number (Re=v.

The local heat-transfer coefficient depends on the position of M, the Reynolds and the Prandtl numbers. The local Nusselt number is proportional to hx(): Nu = h(x)D k [4.2] A B U φ u∞(x) x M Figure 4.3. Circular cylinder in a uniform stream. Definitions In the upstream region close to the cylinder, the flow is characterized by lamina experimental/numerical correlations developed by many authors (including Zˇukauskas and Ulinskas [10,13] and Grimison [14]) for speciﬁc values/ranges of longitudinal and transverse pitches, Reynolds and Prandtl numbers. In designing a tube bank, these correlations cannot be used due to many unknown design variables including D, N, L, and U app