The Dittus-Boelter equation gives the heat transfer coefficient h for heat transfer from the fluid flowing through a pipe to the pipe walls. It was determined by. DITTUS-BOELTER EQUATION. (see Supercritical heat transfer; Tubes, single phase heat transfer in). Number of views: Article added: 8 February Thus the Dittus-Boelter equation (eq) should be used,. Thus h can be calculated for the known values of k, and d, which comes out to be. Energy balance is.
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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.
RMP Lecture Notes
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 dittuss 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 eqaution 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 equatioj, transition, or turbulent flow. If the flow is laminar, is natural convection important? The Grashof number will be used for this. The exponent on the Prandtl number depends on the service — wquation. 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.
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.
It makes use of the coefficient of volume expansion: The fluid properties used to calculate the Grashof number should be evaluated at the equuation temperaturethe arithmetic mean between the bulk and wall temperatures. 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 thanheat 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.