Internal Convection - CHAPTER 8 INTERNAL CONVECTION In...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
C HAPTER 8: I NTERNAL C ONVECTION In internal convection, boundary layer development may be restricted by the diameter of the pipe or conduit within which the fluid flows barb4right Possible that u is never reached External convection: Internal convection: δ u u u u max < u u Midline Laminar or turbulent? Laminar or turbulent? Fully developed or not? Thus, to calculate h for internal flow cases, we need to evaluate the effect of constraining the fluid flow on the development of the thermal and velocity boundary layers.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
NOTE: A flow is considered internal if the fluid is completely contained within a conduit (for any boundary layer development) OR if fluid flows externally between two bodies (i.e. two parallel plates) and incomplete boundary layer development occurs between those two bodies. For the latter case, you should check the boundary layer thicknesses: Laminar flow between plates: Turbulent flow between plates: If 2 δ < plate spacing barb2right external, plate If 2 δ > spacing barb2right internal,square duct Evaluate Re x at the end of the plate ( maximum δ development barb2right point of highest likelihood of boundary layer overlap) 2 . 0 Re 37 . 0 x x = δ 5 . 0 Re 5 x x = δ
Image of page 2
Velocity Boundary Layer Development in a Circular Tube Two regions of flow exist in this case: Entrance Region (0 < x < x fd,h ): Frictional drag induces boundary layer development Velocity profile, boundary layer thickness vary with x Fully Developed Region ( x > x fd,h ) “Steady-state” flow occurs Velocity profile, Re , boundary layer thickness do not change with x o Compare to external flow– Re=f(x) at all x values Hydrodynamic Entrance Region Fully Developed Region x fd,h x u Inviscid flow region Boundary layer region u(r,x) δ δ r o r
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The length of the entrance region x fd,h depends on the nature of the flow Generally, for internal flow, μ ρ D u m D = Re u m = mean velocity of fluid within pipe For incompressible fluids, c m A Q u = Q = volumetric flow rate of fluid through conduit A c = cross-sectional area of conduit Flow is LAMINAR if Re D 2300 In this case, D h fd D x Re 05 . 0 , and 2 D = δ Flow is TURBULENT if Re D > 2300 (although full turbulent flow does not occur until Re D > 10000) In this case, 60 10 , < < D x h fd and 2 D < δ barb4right assume fully developed turbulent flow at x fd,h /D >10
Image of page 4
The velocity profile within the pipe can be derived based on the definition of the mass flow rate through the pipe. c m A u m ρ = & On this basis, for a cylindrical pipe, The mass flow rate m can also be expressed as the integral of the mass flux ( ρ u ) over the cross-section: c A dA x r u m c ) , ( = ρ & Thus, the mean velocity u m can also be written as: Or, for an incompressible fluid in a circular tube: m = mass flow rate through tube A c = cross-sectional area of tube ρ = fluid density ( T- dependent) c c A m A dA x r u u c ρ ρ ) , ( = = o r o m rdr x r u r u 0 2 ) , ( 2 .
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern