Newton’s second law of motion, Fx = d(mV )/dt
The rate of mass flow rate ?? ? = ??????
????= ?? ?? ????
Continuity equation for the boundary layer
?u
?x
+
?v
?y
= 0
The momentum equation of the laminar boundary layer with constant properties
? (u ?u/?x + v ?u/?y) = ? (?
2
u/?y
2
) – (?p/?x)
The velocity profiles at various x positions are similar; that is, they have the same
functional dependence on the y coordinate. There are four conditions to satisfy.
The simplest function that we can choose to satisfy these conditions is a
polynomial with four arbitrary constants.
u = C1 + C2y + C3 y
2
+ C4y
3
To obtain an expression for the boundary-layer thickness. For our approximate
analysis the conditions that the velocity function must satisfy:
u = 0 at y = 0 ………………… . [ a]
u = u ? at y = ? ………………. [ b]
?u/?y= 0 at y = ? …………… [ c]
For a constant-pressure condition
?
2
u/?y
2
= 0 at y = 0 …………… .[e]
Applying the four conditions (a) to (d )
??
???
=
3
2
??
??
?
1
2
(
??
??
)
3
Where (??) boundary ? layer thickness
u? the free-stream velocity outside the boundary layer
ENERGY EQUATION OF THEBOUNDARY LAYER
?T/?x<the energy balance may be written : Energy convected in left face + energy
convected in bottom face+ heat conducted in bottom face+ net viscous work
done on element= energy convected out right face + energy convected out top
face+ heat conducted out top face
where Pr is called the Prandtl number
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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