Diffusion term, convective term and time double derivative

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SUMMARY

The discussion centers on the Green Naghdi heat transport equation, specifically the terms representing convection and diffusion. The convective term is denoted as U_i,i, while the diffusive term is represented by U_i,ii. The confusion arises from the representation of the time double derivative T'' and its relationship to the single derivative in convection. The equation illustrates the interplay between these terms in heat transport dynamics.

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adnan jahan
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_{}Dear Fellows,
I am just using a Green Naghdi heat transport equation which is represented as,

ρ\timesC\timesT''+aT_0\timesU'_i,i=K\timesT'_i,i+K*\timesT_i,i

where (')=derivative with respect to time
(,i)= derivative with respect to space.

I am being informed that
U_i,i= is a convetive term
U_i,ii= diffusive term


I am very confused in this concept of diffusivity and convetion and specially T'' what it is representing??


Why diffusive term is represented by double derivative and single referred to convetion of heat ??
 
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