# formulation of convective term

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 June 25, 2000, 21:39 formulation of convective term #1 Zeng Guest   Posts: n/a Problem: vertor a=(ar,aq,az) and vector b=(br,bq,bz) ar,aq,az represent the component in radial(r), circumferential(q) and axial(z) direction, respetively. Delta is gradient operator in cylindrical coordinate What is (a·Delta)b ? I encounter it when I deal with a problem with linear stability analysis. I need a full form in r,q,z direction for coding. Your help is highly appreciated. Zeng fax:[81]22-215-2052

 June 25, 2000, 22:20 Re: formulation of convective term #2 John C. Chien Guest   Posts: n/a (1). Take a look at the convection term first. You may be able to get the expanded form there. I mean the conservation equations.

 June 26, 2000, 00:47 Re: formulation of convective term #3 Zeng Guest   Posts: n/a Yes, I have checked the expended form of convection term in N-S equation, and derived the expended term of (a·Delta)b by myself, but I have no confidence on its correction, and I failed to find the expended form in the reference books. Maybe the expended form of (a·Delta)b in cylindrical coodinate exist in reference, can you kindly help me to find them? Thanks in advance.

 June 26, 2000, 14:41 Re: formulation of convective term #4 Sergei Chernyshenko Guest   Posts: n/a Hi, Zeng, The formulae you are looking for can be found in G.K.Batchelor, An introduction to fluid dynamics, Cambridge University Press, 1970, Apendix 2. or G.A.Korn, T.M.Korn, Mathematical handbook for scientists and engineers, McGraw-Hill, 1961. Table 6.4.1 + Table 6.5.1 Rgds, Sergei

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