calculated using the best fitted values: h = 4150Wm2 K1 and
a = 39.62%. According to the procedure in Fig. 3, correct h and a
have to satisfy two conditions: 1. the temperature rises in the middle
of the fiber caused by laser heating and electric current heating
are equal; 2. the measured temperature rise and the calculated
temperature rise caused by laser heating are equal. The thermal
conductivity from inset (a) is taken as a known parameter in the
analysis. In order to increase the measurement accuracy, a series
of measured temperature rises induced by different laser powers
are used for searching h. Further, the best fitted heat transfer coefficient
is increased and decreased by 15% to check the measurement
sensitivity as shown in Fig. 9.
Fujii et al. [18] proposed an empirical formula to predict the
heat transfer coefficient around a long horizontal thin wire in air:
2
Nu¼ln 1:0þ
3:3
CðPrÞRan
;
CðPrÞ¼0:671=½1þð0:492=PrÞ9=16
4=9
; n¼0:25þ1:0=ð10þ5Ra0:175Þ;
ð4Þ
where the fiber diameter is chosen as a characteristic length. Eq. (4)
gives a theoretical prediction of h = 4117.8Wm2 K1, which agrees
well with the measured value.