The Prandtl number modifies the hydrodynamic entrance length to determine thermal entrance length. The shape of the fully developed temperature profile is determined by temperature and heat flux conditions along the inside wall of the pipe, as well as fluid properties. The thermal entrance length describes the distance for incoming flow in a pipe to form a temperature profile of the stable shape. For turbulent flow, entry length is approximately independent of the Reynolds Number. The hydrodynamic entry length is a function of Reynold's and Prandtl’s numbers. The thermal entry length is the point at which the temperature profile is fully developed from the point at which the tube wall is heated or cooled. The hydrodynamic entry length is the point at which the velocity profile is fully developed in the tube from the point of entry for the fluid. This develops a velocity gradient across the cross section of the pipe. For the conservation of mass to hold true, the velocity of layers of the fluid in the center of the pipe increases to compensate for the reduced velocities of the layers of fluid near the pipe surface. Due to viscous forces within the fluid, the layer in contact with the pipe surface resists the motion of adjacent layers and slows adjacent layers of fluid down gradually, forming a velocity profile. The fluid enters a pipe at a uniform velocity, then fluid particles in the layer in contact with the surface of the pipe come to a complete stop due to the no-slip condition. This region is characterized by a non-uniform flow. The hydrodynamic entrance region refers to the area of a pipe where fluid entering a pipe develops a velocity profile due to viscous forces propagating from the interior wall of a pipe. Hydrodynamic entrance length vs thermal entrance length on fluid flow and temperature In the case of turbulent flow, it gets a little flatter due to vigorous mixing in radial direction and eddy motion. The velocity of layers of the fluid in the center of the pipe increases to compensate for the reduced velocities of the layers of fluid near the pipe. If the flow in a pipe is laminar, the velocity distribution at a cross-section will be parabolic in shape with the maximum velocity at the center being about twice the average velocity in the pipe. Why velocity profile of laminar flow is parabolic and flat for turbulent flow? When the boundary layer expands to fill the entire pipe, the developing flow becomes a fully developed flow, where flow characteristics no longer change with increased distance along the pipe. The area following the pipe entrance where effects originating from the interior wall of the pipe propagate into the flow as an expanding boundary layer. The distance a fluid travels before becoming fully developed is called the entrance length The first question is how flow develops in a pipe? Why does the velocity profile of laminar flow is parabolic and turbulent flow flat?Ī fluid travels a distance in a pipe before it becomes fully developed. We assume fully developed incompressible, Newtonian, steady flow conditions. We classify the flow of a fluid in a straight circular pipe into either laminar or turbulent flow. The calculation of heat transfer coefficient, typically by convection or phase transition between a fluid and a solid is one of the major exercises we do in our heat transfer calculations. Heat transfer between the fluid and the pipe’s surroundings is an important aspect in heat exchangers, boilers, condensers, evaporators, and many other process equipment. Eddy transport in turbulent flow Laminar and turbulent heat transfer correlations Hydrodynamic and Thermal entrance’s role on fluid flow and temperature Nusselt number Prandtl number Sieder-Tate equation Dittus-Boelter correlation
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