Rayleigh and modified rayleigh number

[philus]

Hi all,

I have some doubt about the Rayleigh number: when it is computed in case of a constant wall temperature it is in the form

Ra=g*beta/(nu*alpha)*(Tw-Tinf)L^3

while in case of a constant heat flux it is

Ra*=g*beta/(nu*alpha)*q/k*L^4

But if I suppose only convective the heat exchange I can say that q=h*(Tw-Tinf), then

Ra*=g*beta/(nu*alpha)*h*(Tw-Tinf)/k*L^4 = g*beta/(nu*alpha)*(Tw-Tinf)L^3 * h*L/k = Ra * Nu

I should then conclude that the Rayleigh number is completly another thing respect the modified Rayleigh number? They are not comparable?

I have to simulate the heat exchange of a real tube, I am neither in the case of a constant wall temperature, nor in the case of a constant wall heat flux. I have found a good correlation for my case (Misumi 2003) and they use the modified Rayleigh number. Should I absolutely use the modified form? Because I have a difference of order 100 (the Nusselt) and the flow is just transitory...

Can anyone help me in that?

Thanks in advance
philus