Unformatted text preview: 1) 2) 3) EML 6155 Homework 8 Write down the appropriate differential equations and boundary conditions
required to solve for free convection heat transfer between two horizontal plates,
each maintained at a constant temperature. Using the approximate integral solution for turbulent free convection over a
vertical, constant temperature surface, give an expression for (Six. Compare and
discuss how the boundary layer thickness varies with x for laminar and turbulent
free and forced convection for Pr~1. An integral method is to be appIicd to free convection from a vertical
plate, immersed in a constantproperty ﬂuid. whose surface heat ﬂux
qw is constant [19]. (a) Show that use of the assumed proﬁles
qW a 2 2
TTm= ktla}, u=uin(1n) where n = y/S, 5 is the common thermal and velocity
boundarylayer thickness. and u, is a reference velocity to be
determined in Eq. (1014) gives («WED/105) _ D2 w d(WDz/30] _ 2 ax 5 D' 0!)! _ E
Here W=u,{g,6ng2/k)‘”“, D = 6(gﬁqw/kv2P/4, and X=
xl'giBGw/ki’zilﬂ {h} Solve these two differential equations to achieve 6000 ”5 4 ”/5
W=( ) (pH—i xm Pr 5
350 1/5 4 1/5
D= iri il’rtgi X'” (cl From the result of part b show that T T 1 6:2qu;: Pr + 0.8 1/5
W a _ I k Pr2 Gr:
qw k Pr2Gr: "’5
a; = = 0.62— ——
T» — 1; .1: Fr + 0.8 where Gr: = (gﬁx3/v2Xqu/k) is a modiﬁed Grashof number.
Note that T“. varies as xlt’s as predicted by the exact solution. ...
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 Spring '10
 Dr.JamesKlausner
 Heat Transfer

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