Nusselt equation

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... 

Nusselt Equation for Various Geometries Natural-convection coefficients for various bodies may be predicted from Eq. (5-32). The various numerical values of 7 andm have been determined experimen-... 

Vertical Tubes For the following cases Reynolds number < 2100 and is calculated by using F = Wp/ KD. The Nusselt equation for the heat-transfer coefficient for condensate films may be written in the following ways (using liquid physical properties and where L is the cooled lengm and At is — t,) ... 

For liorizontal in-tube condensation at low flow rates Kern s modification (Process Heat Transfer, McGraw-Hill, New York, 1950) of the Nusselt equation is vahd ... 

Clements and Colver developed the modified Nusselt equation to correlate hydrocarbon and hydrocarbon mixtures in turbulent film condensation ... 

H = heat transfer coefficient ratio, h /hN h i = effective heat transfer film coefficient, Btu/hr-ff-°F hNu condensing film coefficient by Nusselt equation Btu/hr-ff-°F... 

Condensation on vertical and horizontal tubes The Nusselt equation... 

A high vapour velocity upwards tends to increase the thickness of the film and thus reduce h though the film may sometimes be disrupted mechanically as a result of the formation of small waves. For the downward flow of vapour, TEN Bosch<5 9 has shown that h increases considerably at high vapour velocities and may increase to two or three times the value given by the Nusselt equation. It must be remembered that when a large... 

The basic equations for filmwise condensation were derived by Nusselt (1916), and his equations form the basis for practical condenser design. The basic Nusselt equations are derived in Volume 1, Chapter 9. In the Nusselt model of condensation laminar flow is assumed in the film, and heat transfer is assumed to take place entirely by conduction through the film. In practical condensers the Nusselt model will strictly only apply at low liquid and vapour rates, and where the flowing condensate film is undisturbed. Turbulence can be induced in the liquid film at high liquid rates, and by shear at high vapour rates. This will generally increase the rate of heat transfer over that predicted using the Nusselt model. The effect of vapour shear and film turbulence are discussed in Volume 1, Chapter 9, see also Butterworth (1978) and Taborek (1974). 

Two flow models are used to estimate the mean condensation coefficient in horizontal tubes stratified flow, Figure 12.45a, and annular flow, Figure 12.45. The stratified flow model represents the limiting condition at low condensate and vapour rates, and the annular model the condition at high vapour and low condensate rates. For the stratified flow model, the condensate film coefficient can be estimated from the Nusselt equation, applying a suitable correction for the reduction in the coefficient caused by... 

The equation given by Bromley (1950) can be used to estimate the heat-transfer coefficient for film boiling on tubes. Heat transfer in the film-boiling region will be controlled by conduction through the film of vapour, and Bromley s equation is similar to the Nusselt equation for condensation, where conduction is occurring through the film of condensate. 

For condensation inside horizontal tubes, the Nusselt Equation can be applied with a correction for the reduction in condensing coefficient caused by the accumulation of condensation. The correction usually applied is 0.8. No correction for the number of tubes is required. Thus, for condensation inside horizontal tubes ... 

The Nusselt Equations apply to laminar flow of the condensing film. For horizontal condensation the equations... 

For condensation on a vertical surface, the Nusselt Equation takes the form1 ... 

Combining Equations 15.86 and 15.88 gives the Nusselt Equation for condensation inside vertical tubes ... 

For vertical condensation, the Nusselt Equations are valid for a laminar film according to ... 

A recent publication by Zhivaikin (Zl) has reviewed Soviet work on film thickness and entrainment from films, and has presented correlations both for the thickness and for critical entrainment velocities. The relationships, given in terms of dimensionless quantities for downward cocurrent flow, upward cocurrent flow, and gas-liquid counterflow, follow. For laminar flow of liquid alone vertically downward along a pipe wall, the Nusselt equation was found to apply. 

The usual Nusselt equations, Section III, B, 2, are strictly valid only in the second zone, which is usually only of short extent. 

In addition to the general treatments of wavy flow, a number of theories concerning the stability of film flow have been published in these the flow conditions under which waves can appear are determined. The general method of dealing with the problem is to set up the main equations of flow (usually the Navier-Stokes equations or the simplified Nusselt equations), on which small perturbations are imposed, leading to an equation of the Orr-Sommerfeld type, which is then solved by various approximate means to determine the conditions for stability to exist. The various treatments are lengthy, and only the briefest summaiy of the results can be given here. 

Labuntsov (L2), 1957 Heat transfer to condensate films on vertical and horizontal surfaces. In laminar region, Nusselt equations are corrected for (a) inertia effects, (b) variation of physical properties with temperature, (c) effects of waves. In turbulent region various universal velocity profiles are used. Results compared with experimental data. 

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. 

Related Calculations. For low values of Reynolds number (4T//x), the Nusselt equation can be used to predict condensing heat-transfer coefficients for vertical tubes ... 

At low flow rates, a vapor may be condensed inside a horizontal or nearly horizontal tube under the condition that the condensate flhn drains down the inside surface of the tube by gravity and in laminar flow into the liquid pool at the bottom of the tube and then out the tube outlet. Kern [38] proposed a simple modification of the Nusselt equation for condensation outside horizontal tubes (see next section) that can be used for this case ... 

---