Heat transfer coefficients turbulent conduit flow

Laminar Flow Although heat-transfer coefficients for laminar flow are considerably smaller than for turbulent flow, it is sometimes necessary to accept lower heat transfer in order to reduce pumping costs. The heat-flow mechanism in purely laminar flow is conduction. The rate of heat flow between the walls of the conduit and the fluid flowing in it can be obtained analytically. But to obtain a solution it is necessary to know or assume the velocity distribution in the conduit. In fully developed laminar flow without heat transfer, the velocity distribution at any cross section has the shape of a parabola. The velocity profile in laminar flow usually becomes fully established much more rapidly than the temperature profile. Heat-transfer equations based on the assumption of a parabolic velocity distribution will therefore not introduce serious errors for viscous fluids flowing in long ducts, if they are modified to account for effects caused by the variation of the viscosity due to the temperature gradient. The equation below can be used to predict heat transfer in laminar flow. 

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... 

No published heat-transfer data appear to be available for turbulent flow of polymer systems through other geometries. If such situations are encountered, it is recommended that Eq. (4-33) be used with four times the hydraulic radius substituted for the circular conduit diameter. Based on Newtonian fluid results, this should give at least reasonable estimates of the heat-transfer coefficient. 

Certainly, the most important convective heat-transfer process industrially is that of cooling or heating a fluid flowing inside a closed circular conduit or pipe. Diflferent types of correlations for the convective coefficient are needed for laminar flow below 2100), for fully turbulent flow above 6000), and for the transition region (/Vr between 2100 and 6000). 

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