+Forced Convection: Inside Pipe

HANNA ILYANI ZULHAIMI

+OUTLINE

u Introduction and Dimensionless Numbers

u Heat Transfer Coefficient for Laminar Flow inside a Pipe

u Heat Transfer Coefficient for Turbulent flow inside a Pipe

u Heat transfer coefficient for transition flow inside a pipe

u Heat transfer coefficient: Entrance-Region Effect

+Introduction and Dimensionless Numbers

Where we’ve been ……

u Introduction to internal flow, basic concepts.

Where we’re going:

u Developing heat transfer coefficient relationships and correlations for internal flow

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+Introduction and Dimensionless Numbers

u As with all external flows, the boundary layers develop freely without constraint.

u The convective coefficient for heat transfer through a fluid is given by:

u Boundary layer conditions may be entirely laminar, laminar and turbulent, or entirely turbulent.

u To determine the conditions, compute:

+ Introduction and Dimensionless Numbers u Value of Re depends on free stream turbulence and surface

roughness.

u Surface thermal conditions are commonly idealized as being of uniform temperature T or uniform heat flux q.

u We see there are two important dimensionless similarity parameters associated with the heat transfer in this case. These are the Reynolds, Pradatl and Nusselt numbers. Ø  The Reynolds number represents the ratio of the inertia to the

viscous forces Ø  The Nusselt number to relate data for the heat transfer

coefficient h to the thermal conductivity k of the fluid and con a characteristic dimension D

Ø  The Pradatl number is the ratio of the shear component of diffusivity of momentum to the diffusivity for heat and physically relates the relative thickness of hydrodynamic layer and thermal boundary layer

+Introduction and Dimensionless Numbers

u Reynolds number:

u Nusselt number:

u Pradatl number:

+Heat coefficient inside a pipe: Laminar Flow

u Different types of correlation for the convective coefficient are needed such that: Ø  Laminar flow: NRe< 2100 Ø  Transition region: 2100<NRe<6100 Ø  Turbulent region: Nre> 6000

u For Laminar Flow inside a pipe:

Where D= diameter of pipe (m); L=length of pipe before mixing occurs (m); μb=fluid viscocity at bulk temperature; μw= viscocity at the wall temperature, cp= heat capacity; k= thermal conductivity, ha= average heat transfer coefficient, NNu== Nusselt number

+Heat coefficient inside a pipe: Laminar Flow

u In laminar flow the average coefficient ha depends strongly on heated length. The average temperature drop ∧Ta is used to calculate the heat transfer q:

Where Tw= wall temperature; Tbi inlet bulk fluid temperature, Tbo outlet bulk fluid temperature

+Heat coefficient inside a pipe: Turbulent flow

u When Reynold’s number is above 6000, the flow is fully turbulent.

u The following equation has been found to hold for tubes but is also used for pipes. It holds Nre > 6000, NPr of 0.7 and 16 000 and L/D>60.

u For an L/D< 60, where the entry has sudden contraction, approximate correction is provided (in next section)

+Heat coefficient inside a pipe: Turbulent flow

u For air at 1 atm total pressure, the simplified equation holds for turbulent flow:

u For Water temperature range T= 4- 105°C (40-220°F)

+Heat coefficient inside a pipe: Turbulent flow

u For organic liquids:

u For flow inside helical coils and Nre above 104, the predicted film coefficient for straight pipes should be increased by the factor (1+3.5D/Dcoil)

+Heat coefficient inside a pipe: Transition flow

u In transition region between 2100 and 6000, the empirical equation are not well defined. No simple equation exist for accomplishing a smooth transition from heat transfer in laminar and in turbulent flow

u Graph represent an approximate relationship to use between the various heat transfer parameters and the reynolds number between 2100 and 6000.

+Heat coefficient inside a pipe: Transition flow

+Entrance-Region Effect on Heat Transfer Coefficient

u Near the entrance of a pipe where fluid is being heated, temperature profile is not fully developed and the local coefficient h is greater than the fully developed heat-transfer coefficient hL for turbulent flow.

u At the entrance, no temperature gradient has been established, thus creating infinite h.

u The value of h drops rapidly and is approximately the same as hL at L/D≅60, where L is the entrance length. These relation for turbulent flow inside pipe are as follow:

+Entrance-Region Effect on Heat Transfer Coefficient

Where h is the average value for tube of infinite length L and hL is the value for a very long tube.

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THANK YOU J