Over time, different approaches have been developed to calculate the heat-flow density in the subsurface. That are mainly:
- the interval method where heat flow is calculated for a specific depth interval as product of thermal conductivity and temperature gradient according to Fourier's law of heat conduction.
- the Bullard method for one dimensional, steady-state conductive heat flow in a layered medium, which is calculated as quotient from temperature gradient and the summed thermal resistance of n depth intervals.
What is your experience, what approach do you prefer (under which circumstances) and why? What are the advantages and disadvantages of the different approaches from your point of view?
Hi I prefer the second one it gives a more realistic calculation of the heat flow at the cost of an accurately knowlege of the thermal resistance of each layer.
best regards
Hi Ramon,
do you know studies that gives you evidence that Bullard gives you a more realistic calculation? Or is this your own experience?
Regards
If you have transient heat process you have to know not only thermal conductivity, also thermal diffusivity or volume specific heat. If you need I can measure these properties: [email protected]
- It is my own experience and I agree with Mr Litovsky that thermal conductance may represent an issue but in each case it can be measured.
Dear Efim and Ramon, Thanks for your remarks. Does anyone have specific experiences with the results (and its comparability) of the above mentioned heat-flow calculation methods (interval method and Bullard method)? Does anybody have knowledge of an experimental proof of both methods and, more specifically, something to say about advantages and disadvantages of the different approaches?
I think may be into the Numerical Recipes, but I'm not sure. Both techniques are good and in terms of speed are strong dependant of boundary conditions or accuracy of the
medium difusivity and /or thermal resistivity and integration volume topology.
Leaving transient and advective processes aside, not sure if this is obvious, but there is some equivalency. Assuming an interval with just 2 temperatures at the top and bottom T2 and T1. Within that interval assume a number of equally distributed conductivity measurements, the Bullard method gives T2-T1 = q 1/N*sum(dz/ki), using discrete integration. Further assuming equidistant dz, taking the sum over dz gives z2-z1, so you have (T2-T1)/(z2-z1) = q 1/Nsum(1/ki). The conductivity term really is the inverse of the harmonic average h and the left hand side is the gradient over the interval. So this is h grad T = q. So for this particular case the interval method is equivalent to the Bullard method, if the harmonic mean conductivity is used. Which is sensible anyway.
A point to consider for the Bullard method is the error in both variables, temperature and thermal resistance. Normal regression allows errors only in y. So one would need Total Least Squares or something similar to proporly handle errors.
The charme of the method to me is to work with temperatures rather than noisy gradients making it easier on graphs. That is a help to spot sections where the steady state conduction assumption may be violated.
Attached also Bullards paper where he describes his reasoning.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Thermodynamics