Velocity Boundary Layer – Thermal Boundary Layer

Velocity Boundary Layer

In general, when a fluid flows over a stationary surface, e.g. the flat plate, the bed of a river, or the wall of a pipe, the fluid touching the surface is brought to rest by the shear stress to at the wall. The region in which flow adjusts from zero velocity at the wall to a maximum in the main stream of the flow is termed the boundary layer. The concept of boundary layers is of importance in all of viscous fluid dynamics and also in the theory of heat transfer.

Basic characteristics of all laminar and turbulent boundary layers are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:

Boundary layer on flat plate

Boundary layers may be either laminar, or turbulent depending on the value of the Reynolds number.

See also: Boundary Layer

Thermal Boundary Layer

thermal boundary layer - convectionSimilarly as a velocity boundary layer develops when there is fluid flow over a surface, a thermal boundary layer must develop if the bulk temperature and surface temperature differ. Consider flow over an isothermal flat plate at a constant temperature of Twall. At the leading edge the temperature profile is uniform with Tbulk. Fluid particles that come into contact with the plate achieve thermal equilibrium at the plate’s surface temperature. At this point, energy flow occurs at the surface purely by conduction. These particles exchange energy with those in the adjoining fluid layer (by conduction and diffusion), and temperature gradients develop in the fluid. The region of the fluid in which these temperature gradients exist is the thermal boundary layer. Its thickness, δt, is typically defined as the distance from the body at which the temperature is 99% of the temperature found from an inviscid solution. With increasing distance from the leading edge, the effects of heat transfer penetrate farther into the stream and the thermal boundary layer grows.

Prandtl Number - materialsThe ratio of these two thicknesses (velocity and thermal boundary layers) is governed by the Prandtl number, which is defined as the ratio of momentum diffusivity to thermal diffusivity. A Prandtl number of unity indicates that momentum and thermal diffusivity are comparable, and velocity and thermal boundary layers almost coincide with each other. If the Prandtl number is less than 1, which is the case for air at standard conditions, the thermal boundary layer is thicker than the velocity boundary layer. If the Prandtl number is greater than 1, the thermal boundary layer is thinner than the velocity boundary layer. Air at room temperature has a Prandtl number of 0.71 and for water at 18°C it is around 7.56, which means that the thermal diffusivity is more dominant for air than for water.

Similarly as for Prandtl Number, the Lewis number physically relates the relative thickness of the thermal layer and mass-transfer (concentration) boundary layer. The Schmidt number physically relates the relative thickness of the velocity boundary layer and mass-transfer (concentration) boundary layer.

Lewis Number - Prandtl Number - Schmidt Number

where n = 1/3  for most applications in all three relations. These relations, in general, are applicable only for laminar flow and are not applicable to turbulent boundary layers since turbulent mixing in this case may dominate the diffusion processes.

 
References:
Heat Transfer:
  1. Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley & Sons, Incorporated, 2011. ISBN: 9781118137253.
  2. Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.
  3. Fundamentals of Heat and Mass Transfer. C. P. Kothandaraman. New Age International, 2006, ISBN: 9788122417722.
  4. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Boundary Layer