# br We have extracted the parameter of lung

We have extracted the parameter of lung and tumor tissue for numerical computation from Table 1(Kumar et al., 2018; Katiyar et al., 2017; Bischof et al., 1992) given below:

Stage I:

Fig .4 exhibits the graph between temperature distribution and time for the generalized boundary condition in Stage I. In this stage, we see the temperature distribution at 200 s. In this figure(Fig. 4) we see the difference in the temperature distribution by keeping it Pertussis Toxin at a constant temperature(I kind), a constant heat flux(II kind) and a constant heat

transfer coefficient(III kind). We see how much temperature distribu-tion vary by imposing boundary condition of I, II and III kind. In this stage, temperature decreases rapidly as the time increases. Here the lung tumor is cooled from initial temperature T0(370C) to liquidus temperature Tl ( 10C), and also the temperature (Tu ) decreases as space coordinate x, y increases. We obtained the non-dimensional tempera-ture u by applying Modified Legendre wavelet Galerkin Method and then obtained Tu .

Fig. 12. Temperature distribution of frozen region in Stage3 at 900 s (a) I kind

Stage II:

In this stage, Figs. 5 and 6 exhibits the graph between temperature distribution and time for the generalized boundary condition. In this stage, we see the temperature distribution at 500 s. In these figures (Figs. 5 and 6) we see the difference in the temperature distribution by keeping it at a constant temperature(I kind), a constant heat flux(II
Journal of Thermal Biology 84 (2019) 53–73

kind) and a constant heat transfer coefficient(III kind). We see how much temperature distribution vary by imposing boundary condition of I, II and III kind. As observed the temperature of unfrozen region di-minishes slowly as compared to the mushy region. In this stage, the lung tumor is cooled from the liquidus temperature Tl ( 10C) to solidus temperature Ts( 80C). We obtained the dimensionless temperature m and u by applying Modified wavelet Galerkin Method and then ob-tained Tm and Tu . We see that the temperature distribution in unfrozen (Tu ) and mushy region(Tm) decreases as space coordinate x, y increases. We also see that there is slight variation not too much in temperature distribution by imposing generalized boundary condition (I, II and III kind). Fig. 7 shows the comparison of dimensionless moving layer thickness 2 ( Fo2) in the mushy-liquid region of boundary condition I, II and III kind and moving layer thickness 2 ( Fo2) increases as the di-mensionless time Fo2 increases. The effect of Stefan number on moving layer thickness is also observed in Fig. 13.

Stage III:

Here, the solidus moving front 1 and the liquidus moving front 2 are calculated. Fig. 8 exhibits the dimensionless moving layer thickness 1 (Fo3) in solid-mush region and Fig. 9 exhibits the moving layer thickness 2 ( Fo3) in the mush-liquid region by imposing on Sporulation boundary condition of I, II and III kind. We see that 1 (Fo3) and 2 ( Fo3) increases as the dimensionless time Fo3 increases. Also, the effect of Stefan number is observed on moving layer thickness 1 and 2 in Figs. 14 and 15 respectively. We obtained the non-dimensional temperature f , m and u by applying Modified wavelet Galerkin Method and then ob-tained Tf , Tm and Tu . The temperature distribution in frozen region(Tf ), mushy region(Tm) and unfrozen region(Tu) decreases as space co-ordinate x, y increases. Figs. 10–12 shows the graph between tem-perature distribution and time by keeping it at a constant temperature(I kind), a constant heat flux(II kind) and a constant heat transfer coef-ficient(III kind). In this stage, we see the temperature distribution at 900 s. In these figures, we see the difference in the temperature dis-tribution of boundary condition I, II and III kind. We see how much temperature distribution vary with different boundary condition. As observed the temperature of the frozen region decreases rapidly as compared to the mushy region and the unfrozen region.