The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal con

The one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow cylindrical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical
function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant the

Magnesium Phthalocyanine (MgPc) was deposited on a glass substrate by pulsed laser deposition (PLD) using Q-Switching Nd:YAG laser with wavelength 1064 nm, repetition rate 6 Hz, at room temperature (300K) and different annealing temperatures (373, 473, and 573)K under vacuum condition of 10-3 torr. All films were annealed for one hour to attain crystallinity. X-ray diffraction (XRD) of MgPc powder indicated that MgPc crystallizes in polycrystalline with a monoclinic structure. While comparing the MgPc films, it was observed that the intensity of the characteristic peak increases with temperature, and the crystallization exhibited a monoclinic structure typical of the β-form. The Miller indices, hkl, values for each diffraction peak

In this paper two modifications on Kuznetsov model namely on growth rate law and fractional cell kill term are given. Laplace Adomian decomposition method is used to get the solution (volume of the tumor) as a function of time .Stability analysis is applied. For lung cancer the tumor will continue in growing in spite of the treatment.