**4. Clinical potential of spray cooling by low GWP R1234yf**

The extremely high global warming potential (GWP = 1430) of commercially used cryogen R134a with boiling point of 26.1°C will cause severe environmental

Duhamel's theorem was improved to get the accurate results through the transformation of internal temperature into surface temperature, when the indirect surface temperature measurement (FTC) method is used. A hypothetical triangular pulse heat flux was employed to analyze the accuracy and sensitivity to noise of the algorithms under TFTC and FTC measurements. The estimated result of Duhamel's theorem and SFS method widely deviated from the given heat flux under the threelayer FTC measurement method, whereas the transfer function and improved

*The Fundamental and Application of Surface Heat Flux Estimation by Inverse Method…*

The 2D filter solution was proposed to solve a general 2D multilayer IHCP for the estimation of surface heat flux. An optimal comparison criterion was employed to optimize the key parameters, namely, *α<sup>t</sup>* and *αs*. Six hypothetical triangular heat fluxes and random temperature errors of 1°C were employed to analyze the accuracy and sensitivity of the filter solution for 2D three-layer IHCPs with FTC measurement. The *qMRE* values for FTC measurement with and without the random temperature errors were all within the acceptable range, which validates the good accuracy and stability of the filter solutions. The maximum heat flux calculated by the 1D method was underestimated by 60% than that calculated by 2D filter solution considering lateral heat transfer. The 2D filter solution was more accurate than the 1D method. Moreover, lateral heat transfer should not be ignored, especially

Duhamel's theorem all provided the exact estimated heat flux.

*DOI: http://dx.doi.org/10.5772/intechopen.89095*

when the heat conductivity coefficient of the material is large.

application of low GWP R1234yf in clinics.

The authors declare no conflict of interest.

**Acknowledgements**

**Conflict of interest**

**139**

The surface heat transfer characteristics of spray cooling with R134a and R1234yf were investigated based on 2D filter solution. The maximum effective heat fluxes *qe*,max were 262.1 and 225.8 kW/m2 for R134a and R1234yf at different spray distances of 25.6 and 25.1 mm. Through the cooling enhancement of reducing the nozzle diameter and decreasing the back pressure, *qe*,max of R1234yf was increased by 18.8% (*D* = 0.4 mm and *Pb* = 0.04 MPa). The enhanced *qe*,max is a bit higher than that of R134a in normal condition, which provides a theoretical basis for potential

This work was supported by the National Natural Science Foundation of China

(51727811) and Fundamental Research Funds for the Central Universities.

**Figure 11.**

*Variations of effective surface heat flux as a function of spray distance [39]. (a) effective surface heat flux with R134a and R1234yf and (b) effective surface heat flux before and after cooling enhancement with R1234yf.*

hazards, and the substitution of R134a in clinical application is urgent. R1234yf with boiling point of 29.5°C may be a potential candidate for environment protection due to its low GWP (<1). In this chapter, the clinical potential of R1234yf substitution for R134a was investigated.

Using the maximum surface heat flux correlation obtained by experimental spray characteristics (droplet temperature, velocity, and diameter) and surface heat transfer performance (surface heat flux calculated by 2D filter solution), **Figure 11(a)** shows the variations of effective surface heat flux with different R134a and R1234yf as a function of spray distance. The effective surface heat flux (*qe*) was obtained by multiplying the maximum surface heat flux, and cooling concentration within the radius of 2 mm is the interested area [39]. The effective surface heat flux by using R134a and R1234yf increased firstly due to the droplet temperature reduction as spray distance increased. Then, *qe* reaches their maximum value and finally decreases slowly. The maximum *qe* of R134a and R1234yf is 262.1 and 225.8 kW/m<sup>2</sup> at the optimal spray distances of 25.6 and 25.1 mm (see **Figure 11(a)**), respectively. The substitution of R1234yf for R134a can produce remarkable reduction of global warming potential to <1. However, the cooling capacity should be enhanced for the clinical application in laser treatment, owing to the 13.8% reduction in effective heat flux (from 262.1 to 225.8 kW/m<sup>2</sup> ). Therefore, the enhancement of cooling capacity is necessary for the implementation of R1234yf in clinical laser treatment of PWS.

According to our experience, two simple ways are available to enhance the cooling capacity, i.e., changing the nozzle diameter and decreasing the back pressure by decreasing the boiling point of cryogens [40, 41]. As shown in **Figure 11(b)**, the enhancement of effective surface heat flux at different spray distances was remarkable. After reducing the nozzle diameter and decreasing the back pressure, *qe* increases rapidly due to violent evaporation, and the peak value of the effective heat flux (268.3 kW/m<sup>2</sup> ) is increased by 18.8%. This result is comparable with that of R134a under 1 atm, which proves the potential of R1234yf in the clinic CSC for the laser treatment of PWS.

#### **5. Conclusions**

Several algorithms including the SFS, TF, and Duhamel's theorem methods were analyzed and compared in predicting time-varying surface heat flux during CSC.

### *The Fundamental and Application of Surface Heat Flux Estimation by Inverse Method… DOI: http://dx.doi.org/10.5772/intechopen.89095*

Duhamel's theorem was improved to get the accurate results through the transformation of internal temperature into surface temperature, when the indirect surface temperature measurement (FTC) method is used. A hypothetical triangular pulse heat flux was employed to analyze the accuracy and sensitivity to noise of the algorithms under TFTC and FTC measurements. The estimated result of Duhamel's theorem and SFS method widely deviated from the given heat flux under the threelayer FTC measurement method, whereas the transfer function and improved Duhamel's theorem all provided the exact estimated heat flux.

The 2D filter solution was proposed to solve a general 2D multilayer IHCP for the estimation of surface heat flux. An optimal comparison criterion was employed to optimize the key parameters, namely, *α<sup>t</sup>* and *αs*. Six hypothetical triangular heat fluxes and random temperature errors of 1°C were employed to analyze the accuracy and sensitivity of the filter solution for 2D three-layer IHCPs with FTC measurement. The *qMRE* values for FTC measurement with and without the random temperature errors were all within the acceptable range, which validates the good accuracy and stability of the filter solutions. The maximum heat flux calculated by the 1D method was underestimated by 60% than that calculated by 2D filter solution considering lateral heat transfer. The 2D filter solution was more accurate than the 1D method. Moreover, lateral heat transfer should not be ignored, especially when the heat conductivity coefficient of the material is large.

The surface heat transfer characteristics of spray cooling with R134a and R1234yf were investigated based on 2D filter solution. The maximum effective heat fluxes *qe*,max were 262.1 and 225.8 kW/m2 for R134a and R1234yf at different spray distances of 25.6 and 25.1 mm. Through the cooling enhancement of reducing the nozzle diameter and decreasing the back pressure, *qe*,max of R1234yf was increased by 18.8% (*D* = 0.4 mm and *Pb* = 0.04 MPa). The enhanced *qe*,max is a bit higher than that of R134a in normal condition, which provides a theoretical basis for potential application of low GWP R1234yf in clinics.
