A quick and clean method to measure thermal conductivity

A quick and clean method to measure thermal conductivity Application: QA and QC of spines Standard Method: DT between heat source and heat sink Disadvatage: depends on thermal coupling of heaters, sensors etc.... H.-G. Moser MPI, Munich

Ballistic Method heater pt100 pt100 T T t t Measure reponse T(t): time constant depends on c/ck (c: specific heat, ck: thermal conductivity) H.-G. Moser MPI, Munich

Ballistic Method heater pt100 pt100 X=0 L t=0: T0 t>0: Tr T(t,x)=Tr-(Tr-T0)Sciexp(-ei²at/L²)cos[ei(x-L)/L] ei=p/2, 3/2 p , 5/2 p ci=4 sin(ei)/[2ei sin(2ei)] a=ck/cr H.-G. Moser MPI, Munich

TPG bar 12 cm Theoretical solution for T=const boundary condition! H.-G. Moser MPI, Munich

Measurements In practice: use heater (constant power) instead of constant temperature bath Spine is a composite object => Calibration necessary H.-G. Moser MPI, Munich

TPG/Cu Ln[(T-Tmin)/(Tmin-Tmax)] Copper bar TPG bar H.-G. Moser MPI, Munich

Effect of different power One practical problem is bad reproducibility of the coupling heater/sample (and sensor/sample) Can be checked by varying the heater power 1.7, 3.2, 6.6 W Ln[(T-Tmax)/(Tmin-Tmax)] H.-G. Moser MPI, Munich

Conclusions Time constant (almost) independent of heater power, coupling of heaters and sensors Fast response: small effect of ambient temperature Robust and reproducible measurement of Ck -> develop a simple QC setup for spine H.-G. Moser MPI, Munich

A quick and clean method to measure thermal conductivity