Heat and Mass Transfer
In 1928, the French engineer André Lévêque observed that convective heat transfer in a flowing fluid is affected only by the velocity values very close to the surface. For flows of large Prandtl number, the temperature/mass transition from surface to freestream temperature takes place across a very thin region close to the surface. Therefore, the most important fluid velocities are those inside this very thin region in which the change in velocity can be considered linear with normal distance from the surface. In this way, for
when, then
- ,
where θ is the tangent of the Poiseuille parabola intersecting the wall. Although Lévêque's solution was specific to heat transfer into a Poiseuille flow, his insight helped lead other scientists to an exact solution of the thermal boundary-layer problem. Schuh observed that in a boundary-layer, u is again a linear function of y, but that in this case, the wall tangent is a function of x. He expressed this with a modified version of Lévêque's profile,
- .
This results in a very good approximation, even for low numbers, so that only liquid metals with much less than 1 cannot be treated this way. In 1962, Kestin and Persen published a paper describing solutions for heat transfer when the thermal boundary layer is contained entirely within the momentum layer and for various wall temperature distributions. For the problem of a flat plate with a temperature jump at, they propose a substitution that reduces the parabolic thermal boundary-layer equation to an ordinary differential equation. The solution to this equation, the temperature at any point in the fluid, can be expressed as an incomplete gamma function. Schlichting proposed an equivalent substitution that reduces the thermal boundary-layer equation to an ordinary differential equation whose solution is the same incomplete gamma function.
Read more about this topic: Boundary Layer
Famous quotes containing the words heat, mass and/or transfer:
“Glories, like glow-worms, afar off shine bright,
But looked to near, have neither heat nor light.”
—John Webster (1580–1625)
“... the mass migrations now habitual in our nation are disastrous to the family and to the formation of individual character. It is impossible to create a stable society if something like a third of our people are constantly moving about. We cannot grow fine human beings, any more than we can grow fine trees, if they are constantly torn up by the roots and transplanted ...”
—Agnes E. Meyer (1887–1970)
“If it had not been for storytelling, the black family would not have survived. It was the responsibility of the Uncle Remus types to transfer philosophies, attitudes, values, and advice, by way of storytelling using creatures in the woods as symbols.”
—Jackie Torrence (b. 1944)