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Nusselt solution

Recently, Kasimov and Zigmund (K12) have published the first part of a new theoretical treatment of wavy film flow, extending their recent work on smooth laminar film flow (Section III, B, 5) to this case also. It is shown that, with appropriate assumptions, the new theory reduces to the Nusselt solution for smooth films, or to a result similar to the corrected Kapitsa solution. The most interesting conclusions to be drawn from the part of the theory so far published are ... [Pg.169]

A similarity solution is available for Eqs. 9.93 to 9.95 subject to negligible macroscopic inertial and viscous forces, that is, small permeabilities and constant DL [115,116]. The inertial and viscous forces are included by Kaviany [117] through the regular perturbation of the similarity solution for plain media, that is, the Nusselt solution [113]. The perturbation parameter used is... [Pg.698]

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... [Pg.559]

Navier-Stokes equations, 318, 386-387 Nitrocellulose, 31 Nitroglycerine, 31-32 Normalization binary solutions, 156-157 multicomponent solutions, 157-158 Nusselt number, 118... [Pg.412]

The average Nusselt number, Nu, is presented in Fig. 4.10a,b versus the shear Reynolds number, RCsh- This dependence is qualitatively similar to water behavior for all surfactant solutions used. At a given value of Reynolds number, RCsh, the Nusselt number, Nu, increases with an increase in the shear viscosity. As discussed in Chap. 3, the use of shear viscosity for the determination of drag reduction is not a good choice. The heat transfer results also illustrate the need for a more appropriate physical parameter. In particular. Fig. 4.10a shows different behavior of the Nusselt number for water and surfactants. Figure 4.10b shows the dependence of the Nusselt number on the Peclet number. The Nusselt numbers of all solutions are in agreement with heat transfer enhancement presented in Fig. 4.8. The data in Fig. 4.10b show... [Pg.160]

Fig. 4.10a,b The dependence of the Nusselt number on the Reynolds and Peclet numbers, (a) Dependence of the average Nusselt number on the solution Reynolds number, (b) Dependence of the Nusselt number on the Peclet number. Reprinted from Hetsroni et al. (2004) with permission... [Pg.160]

Chakraborty S (2006) Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed gradients. Int J Heat Mass Transfer 49 810-813... [Pg.188]

Because of nonlinear Interactions between buoyancy, viscous and Inertia terms multiple stable flow fields may exist for the same parameter values as also predicted by Kusumoto et al (M.). The bifurcations underlying this phenomenon may be computed by the techniques described In the numerical analysis section. The solution structure Is Illustrated In Figure 7 In terms of the Nusselt number (Nu, a measure of the growth rate) for varying Inlet flow rate and susceptor temperature. Here the Nusselt number Is defined as ... [Pg.367]

A number of authors have considered channel cross-sections other than rectangular [102-104]. Figure 2.17 shows some examples of cross-sections for which friction factors and Nusselt numbers were computed. In general, an analytical solution of the Navier-Stokes and the enthalpy equations in such channel geometries would be involved owing to the implementation of the wall boundary condition. For this reason, usually numerical methods are employed to study laminar flow and heat transfer in channels with arbitrary cross-sectional geometry. [Pg.171]

In the articles cited above, the studies were restricted to steady-state flows, and steady-state solutions could be determined for the range of Reynolds numbers considered. Experimental work on flow and heat transfer in sinusoidally curved channels was conducted by Rush et al. [121]. Their results indicate heat-transfer enhancement and do not show evidence of a Nusselt number reduction in any range... [Pg.186]

To obtain approximate solutions for convection heating problems, we only need to identify a heat transfer problem that has a given theoretical or empirical correlation for hc. This is usually given in the form of the Nusselt number (Nu),... [Pg.249]

Since the dimensionless equations and boundary conditions governing heat transfer and dilute-solution mass transfer are identical, the solutions to these equations in dimensionless form are also identical. Profiles of dimensionless concentration and temperature are therefore the same, while the dimensionless transfer rates, the Sherwood number (Sh = kL/ ) for mass transfer, and the Nusselt number (Nu = hL/K ) for heat transfer, are identical functions of Re, Sc or Pr, and dimensionless time. Most results in this book are given in terms of Sh and Sc the equivalent results for heat transfer may be found by simply replacing Sh by Nu and Sc by Pr. [Pg.12]

For Gr = 0, the Sherwood or Nusselt number is given by Eq. (3-44). For Gr 0, neither perturbation nor asymptotic expansion methods have proved capable of yielding solutions for Sh comparable to Eq. (3-55). At larger Gr... [Pg.251]

In the examples treated in Section II, expressions for the rate of transfer in coupled processes have been derived by using scaling arguments and by interpolating between two limiting cases. Although the method is very simple, its results are generally within 10% of the more exact (and more complicated) solutions, As expected, the form of the interpolation equation depends on the particular physical problem. Indeed, in terms of the Nusselt (Sherwood) numbers for the two extreme cases between which the interpolation is carried... [Pg.53]

The above self-similar velocity profiles exists only for a Re number smaller than a critical value (e.g. 4.6 for a circular pipe). The self-similar velocity profiles must be found from the solution of the Navier-Stokes equations. Then they have to be substituted in Eq. (25) which must be solved to compute the local Nusselt number Nu z). The asymptotic Nusselt number 7Vm is for a pipe flow and constant temperature boundary condition is given by Kinney (1968) as a function of Rew and Prandtl (Pr) numbers. The complete Nu(z) curve for the pipe and slit geometries and constant temperature or constant flux boundary conditions were given by Raithby (1971). This author gave /Vm is as a function of Rew and fluid thermal Peclet (PeT) number. Both authors solved Eq. (25) via an eigenfunction expansion. [Pg.252]

The analytical solution to this problem provides an asymptotic value of Nu = 3.66. Notice that far downstream (i.e., at large values of z), both Tm and dT/dr approach zero. Thus at some sufficiently long downstream position the numerical solution is unable to compute the Nusselt number. The analytic solution can be used to find the limiting result of Nu = 3.66. The solution presented in Fig. 4.17 was computed on auniformly spaced mesh of 16 points, and returned an asymptotic value of Nu = 3.7, which represents about a 1% error. It returned the Nu = 3.7 result until about z = 1.0, before the zero-over-zero situation caused to evaluation to lose accuracy and eventually fail. [Pg.190]

The Sherwood number is a nondimensional mass-transfer coefficient that is analogous to the Nusselt number for heat transfer. For the situation of A being dilute in B, the mass transfer at the stagnation surface is derived from the solution to the species equation by... [Pg.276]

Write the Nusselt number in terms of the nondimensional solution profiles. [Pg.308]

Theoretical treatment of smooth laminar film flow on vertical surface, with and without gas flow, including inertia effects. Nusselt equations (N6, N7) are shown to be special cases of the present solutions. [Pg.226]

Portalski (P4), 1963 Theories of film flow and methods of measuring film thickness are reviewed. Film thicknesses on vertical plate (zero gas flow) reported for glycerol solutions, methanol, isopropanol, water, and aqueous solutions of surfactants. Results compared with values calculated by Nusselt, Kapitsa, and corrected Dukler and Bergelin treatments. [Pg.228]

Once 6 has been determined, the heat flux at the wall and the mean temperature can be found and the mean Nusselt number can then be found. Exact solutions for values of n up to 4 can be relatively easily obtained and approximate solutions for higher values of n can be obtained. The variation of the mean Nusselt number with Z given by these solutions is shown in Fig. 4.IS. [Pg.193]

The so-called Taylor-Prandtl analogy was applied to boundary layer flow in Chapter 6. Use this analogy solution to derive an expression for the Nusselt number in fully developed turbulent pipe flow. [Pg.338]

Nuh and Nuc being the mean Nusselt numbers, based on VV for the hot and the cold walls, respectively. With adiabatic end walls, because a steady state situation is being considered, these two values should have the same numerical value, i.e., the rate at which heat is transferred from the hot wall to the fluid should be equal to the rate at which heat is transferred from the fluid to thi cold wall. Small differences usually exist between the values of Nuh and Nuc given by the numerical solution due to the small numerical round-off errors and due to the finite convergence criterion used in the numerical solution. [Pg.398]


See other pages where Nusselt solution is mentioned: [Pg.162]    [Pg.525]    [Pg.237]    [Pg.162]    [Pg.525]    [Pg.237]    [Pg.155]    [Pg.174]    [Pg.331]    [Pg.184]    [Pg.72]    [Pg.374]    [Pg.109]    [Pg.153]    [Pg.112]    [Pg.322]    [Pg.305]   
See also in sourсe #XX -- [ Pg.237 ]




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