Genva, January 23, 2001H.-G. Moser MPI, Munich A quick and clean method to measure thermal conductivity Application: QA and QC of spines Standard Method:  T between heat source and heat sink Disadvatage: depends on thermal coupling of heaters, sensors etc....

Genva, January 23, 2001H.-G. Moser MPI, Munich Ballistic Method heater pt100 T t T t Measure reponse T(t): time constant depends on c/ck (c: specific heat, ck: thermal conductivity)

Genva, January 23, 2001H.-G. Moser MPI, Munich Ballistic Method heater pt100 t=0: T 0 t>0: T r T(t,x)=T r -(T r -T 0 )  c i exp(-   ²  t/L²)cos[   (x-L)/L]  i =  /2, 3/2 , 5/2  c i =4 sin(  i )/[2  i sin(2  i )]  =c k /c  L X=0

Genva, January 23, 2001H.-G. Moser MPI, Munich TPG bar 12 cm Theoretical solution for T=const boundary condition!

Genva, January 23, 2001H.-G. Moser MPI, Munich Measurements In practice: use heater (constant power) instead of constant temperature bath Spine is a composite object => Calibration necessary

Genva, January 23, 2001H.-G. Moser MPI, Munich TPG/Cu TPG bar Copper bar Ln[(T-Tmin)/(Tmin-Tmax)]

Genva, January 23, 2001H.-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)]

Genva, January 23, 2001H.-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 C k -> develop a simple QC setup for spine