In fluid dynamics , the Nusselt number Nu is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection fluid motion and diffusion conduction. The conductive component is measured under the same conditions as the convective but for a hypothetically motionless fluid. It is a dimensionless number , closely related to the fluid's Rayleigh number. A Nusselt number of value one represents heat transfer by pure conduction. A similar non-dimensional property is the Biot number , which concerns thermal conductivity for a solid body rather than a fluid.

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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. Different geometries, boiling, and condensation will be covered in later lectures. Frictional heating viscous dissipation is not included in these correlations. This should not be a problem, since this phenomena is typically neglected except for highly viscous flows or gases at high mach numbers.

Unless otherwise specified, fluid properties should be evaluated at the "bulk average" temperature -- the arithmetic mean of the inlet and outlet temperatures:. When choosing a correlation, begin by asking: What is the geometry? Flow through a pipe, around an object, over a plane, etc. Is there a phase change? What is the flow regime? Check the Reynolds number to decide on laminar, transition, or turbulent flow.

If the flow is laminar, is natural convection important? The Grashof number will be used for this. Different values are needed because of the variation of viscosity with temperature. Heating and cooling effect the velocity profile of a flowing fluid differently because of the temperature dependence of viscosity. Heating usually makes the fluid near the wall less viscous, so the flow profile becomes more "plug-like. The effect is most pronounced for viscous flows with large wall -- bulk temperature differences.

Instead of using different exponents for heating and cooling, a direct correction for viscosity can be used. This takes the form of the ratio of the viscosity at the bulk fluid temperature to the viscosity at the wall temperature. The ratio is then raised to the 0. Levenspiel recommends the following correlation for transition flow. The entrance effect correction may be omitted for "long" conduits. Many of the laminar flow correlations are set up in terms of the Graetz Number.

McCabe et al. Consequently, you must be very careful to use the form that matches the correlation you are using. Two correlations are provided for laminar flow, depending on the magnitude of the Graetz number. For Gz which approaches a limiting value of 3. Heat usually causes the density of a fluid to change. Less dense fluid tends to rise, while the more dense fluid falls.

The result is circulation -- "natural" or "free" convection. This movement raises h values in slow moving fluids near surfaces, but is rarely significant in turbulent flow. Thus, it is necessary to check and compensate for free convection only in laminar flow problems. This will require determining an additional set of property values.

The Grashof Number provides a measure of the significance of natural convection. When the Grashof Number is greater than , heat transfer coefficients should be corrected to reflect the increase due to free circulation.

Multiplicative correction factors are available to apply to the Nusselt Number or the heat transfer coefficient do NOT use both. These are: References: Brodkey, R. Levenspiel, O. McCabe, W. Smith, and P.

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## Dittus-Boelter Equation

In heat transfer at a boundary surface within a fluid, the Nusselt number Nu is the ratio of convective to conductive heat transfer across normal to the boundary. In this context, convection includes both advection and diffusion. Named after Wilhelm Nusselt, it is a dimensionless number. The conductive component is measured under the same conditions as the heat convection but with a hypothetically stagnant or motionless fluid. A similar non-dimensional parameter is Biot number, with the difference that the thermal conductivity is of the solid body and not the fluid. This number gives an idea that how heat transfer rate in convection is related to the resulting of heat transfer rates in conduction. The Dittus-Boelter equation for turbulent flow is an explicit function for calculating the Nusselt number.

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## Dittus-Boelter equation - Nusselt number

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. Different geometries, boiling, and condensation will be covered in later lectures. Frictional heating viscous dissipation is not included in these correlations. This should not be a problem, since this phenomena is typically neglected except for highly viscous flows or gases at high mach numbers.

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## Nusselt number

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## DITTUS-BOELTER EQUATION

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