Mean Nusselt number

Comparison between predicted and experimental mean Nusselt numbers. 

The mean Nusselt number for the whole plate Nui( = hUk) is, therefore, given by ... 

It should be noted that if the approximate expression for A given in Eq. (3.43) is utilized, the local and mean Nusselt numbers are given by ... 

These expressions give results that are in reasonably good agreement with experimental results, a comparison of some measurements of mean Nusselt number with the values predicted by Eq. (3.51) being shown in Fig. 3.7. 

Predicted variation of mean Nusselt number for a square cylinder with Reynolds number for Pr —... 

The variation of the mean Nusselt number with aspect ratio as given by this program is shown in Fig. 4.13. This Nusselt number is based on the duct height, W. Now, for a rectangular duct, the hydraulic diameter is given by ... 

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. 

The left-hand side of this equation is the mean Nusselt number up to dimensionless distance Z from the inlet considered. Hence, this equation can be written... 

Integrating Eq. (6.51) over the entire plate as was done w ith the Reynolds analogy equation and assuming that the flow is turbulent from the leading edge of the plate then gives the following expression for the mean Nusselt number... 

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. 

Variation of mean Nusselt number with Rayleigh number for an enclosure with an aspect ratio of 5 for Pr = 0.7. 

But the mean Nusselt number is conventionally defined in terms of the full duct width W( = 2w) so Eq. (10.161) is written as ... 

While this is rather small to apply the boundary layer assumptions it will, nevertheless, be assumed that the mean Nusselt number is given by ... 

Because uniform grid spacing has been used, the mean Nusselt numbers are given by ... 

Variation of mean Nusselt number with Raw for various A. 

The mean heat transfer coefficient am from (1.33) is also independent of x+ and z+. The mean Nusselt number Num, which contains am, is only a function of... 

The determination of heat transfer coefficients with the assistance of dimensionless numbers has already been explained in section 1.1.4. This method can also be used for mass transfer, and as an example we will take the mean Nusselt number Num = amL/ in forced flow, which can be represented by an expression of the form... 

The Nusselt number is equal to the dimensionless temperature gradient at the wall. It is a universal function of x+, Re and Pr for every fluid with a body of a given shape. The mean Nusselt number is independent of x+, as it is the integral mean value over the heat transfer surface... 

Example 3.8 Derive from the local Nusselt number (3.196), equations for the mean Nusselt numbers Num = amL/ with... 

The mean Nusselt number JV mjiam follows from (3.196a)... 

The mean Nusselt number comes from the mean heat transfer coefficient... 

For sufficiently large values of the length X+ —> oo the adiabatic mixing temperature (3.249) may be calculated using only the first term of the series. The mean Nusselt number according to (3.251) is then transformed into... 

In the same way as shown in the previous section, the heat transfer coefficient and from that the mean Nusselt number Nume = amed/A (the index e stands for entry flow) can be obtained from the temperature profile. The Nusselt number can be calculated from an empirical equation of the form... 

Fig. 3.35 illustrates the pattern of the mean Nusselt number over the dimensionless length A 1 = L/(dPe). All the lines are arranged between those for... 

Fig. 3.35 Mean Nusselt numbers in laminar tubular flow...

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