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Conv_hw8 - 1 2 3 EML 6155 Homework 8 Write down the...

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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 constant-property fluid. whose surface heat flux qw is constant [19]. (a) Show that use of the assumed profiles qW a 2 2 T-Tm= ktl-a}, u=uin(1-n) where n = y/S, 5 is the common thermal and velocity boundary-layer thickness. and u, is a reference velocity to be determined in Eq. (10-14) 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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