# Physical and Computational Aspects of Convective Heat by Tuncer Cebeci

By Tuncer Cebeci

**From the reviews:** "The booklet has a huge and normal assurance of either the math and the numerical tools well matched for graduate students." *Applied Mechanics Reviews* number 1 "This is a truly good written booklet. the themes are constructed with separate headings making the problem simply comprehensible. laptop courses also are incorporated for lots of difficulties including a separate bankruptcy facing the applying of machine courses to warmth move difficulties. This complements the software of the book." *Zentralblatt für * *Mathematik* no 1

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**Extra info for Physical and Computational Aspects of Convective Heat Transfer**

**Sample text**

In deriving the momentum equation, we adopted the usual convention that viscous effects are equivalent to stresses; however, they are in fact net rates of transport of momentum by molecular agencies and, so regarded, would appear on the left-hand side of Eq. 3) instead of in the force terms on the right. On the other hand, molecular transport of heat (the effect of thermal conductivity) is always regarded as transport and is therefore at first allocated to the second and third terms on the left-hand side of Eq.

6 If we multiply the x-component of the momentum equation, Eq. 9) by u, and use the definition of the substantial-derivative symbol d / dt given by Eq. 2) Adding the corresponding equation for d/dt (1/2v2), which can be most easily derived by changing the variables in Eq. 3) is known as the kinetic energy equation. Its left-hand side represents the rate of increase of kinetic energy per unit mass of the fluid, as the fluid moves along a streamline. The terms on the right-hand side which can be written in tensor notation as ap ao;},' ) -u; ( --+-+pj; p ax; ax} represent, respectively, the rates at which work is done on unit mass of the fluid by the pressure, by the viscous or turbulent o-stresses, and by the body force per unit mass, f.

It follows that i)t is of order V[(Jl/Pr)xtlu e] . 46 Boundary-Layer Equations Turbulent Flow In turbulent flow we can use exactly the same arguments as in laminar flow to show that the term p a2ulax 2 in the x-component momentum equation, Eq. 6), can be neglected compared with p a2ulay2. In the case of the turbulent-stress terms it is found from experiment that U,2 is of the same order as u'v', so that au,2I ax will be smaller than au 'v'I a y by a factor of order BI x. In the y-component equation, we can show that the terms on the left-hand side and the larger of the two viscous terms are again of order u;Blx2, and since U,2 and u'v' are of the same order, au'v'lax is of order (Blx)(av,2/ay).