Pipe - heat flow calculation with varying fluid properties 1

[satu2]

I have the following problem: A pipe shall have a constant surface temperature, whereby it gets elevated (from mean sea level to 10km) such that the ambient temperature and the air density decrease. I need to know the rate of heat flux.

I tried to solve this problem by calculating the Prandtl, Rayleigh number and Nusselt number (Free convection & external flow). With the Nusselt Number I determined the convection coefficient. The formula Q=α×A×ΔT allowed me to obtain the rate of heat flow. With ΔT=Tsurface,pipe−Tambient, A being the surface area of the pipe and α the convection coefficient.

I calculated the Nusselt number the corresponding Q for different heights (in total 40), but not continuous because I did not know how to get height depending functions for viscosity, thermal conductivity etc.

Is Q now the rate of heat flow which I can apply so that the surface temperature of the pipe is not exceeded and is my approach correct?

 

[georgeverghese]

Your approach is approximately correct for convective component, but not complete, a few important additional heat transfer mechanisms also must be considered to get the total Q at any location:
a)Heat transfer by radiation
b)External htc is also affected by cross wind speed
c) In most cases, total convective component is not affected by internal htc, since internal htc is << combined external htc, but is that true in your case?

BTW, why do you need to maintain constant external surface temp? Note that these calcs for heat loss to ambient are approximate, especially for radiation component, which relies on grey body emissitivity factors. What process control mechanisms do you have in place to control actual surface temperature?