This problem deals with the thermo-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic orthotropic spherical shell in the context of a new consideration of heat conduction with fractional order generalized thermoelasticity. Using the Laplace transformation, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by eigen value approach and operator theory analysis. The inversion of the transformed solution is carried out by applying a method of Bellman et al (1966). Numerical estimates for thermophysical quantities are obtained for copper like material for weak, normal and strong conductivity and have been depicted graphically to estimate the effects of the fractional order parameter. Comparisons of the results for different theories (TEWED (GN-III), three-phase-lag model) have also been presented and the effect of viscosity is also shown. When the material is isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature.

Introduction To date, there is a paucity of literature offering practicing urologists a reference for the amount of radiation exposure received while surgically managing urolithiasis. This study examines the cumulative radiation exposure of an urologist over 9 months. Materials and Methods We present a case series of fluoroscopic exposures of an experienced stone surgeon operating at an academic comprehensive stone center between April and December 2011. Radiation exposure measurements were determined by a thermoluminescent dosimeter worn on the outside of the surgeon's thyroid shield. Estimations of radiation exposure (mrem) per month were charted with fluoroscopy times, using scatter plots to estimate Spearman's rank correlation coefficients. Results The total 9-month radiation exposure was 87 mrems for deep dose equivalent (DDE), 293 mrem for lens dose equivalent (LDE), and 282 mrem for shallow dose equivalent (SDE). Total fluoroscopy time was 252.44 minutes for 64 ureteroscopies (URSs), 29 percutaneous nephrolithtomies (PNLs), 20 cystoscopies with ureteral stent placements, 9 shock wave lithotripsies (SWLs), 9 retrograde pyelograms (RPGs), 2 endoureterotomies, and 1 ureteral balloon dilation. Spearman's rank correlation coefficients examining the association between fluoroscopy time and radiation exposure were not significant for DDE (p = 0.6, Spearman's rho = 0.2), LDE (p = 0.6, Spearman's rho = 0.2), or SDE (p = 0.6, Spearman's rho = 0.2). Conclusions Over a 9-month period, total radiation exposures were well below annual accepted limits (DDE 5000 mrem, LDE 15,000 mrem and SDE 50,000 mrem). Although fluoroscopy time did not correlate with radiation exposure, future prospective studies can account for co-variates such as patient obesity and urologist distance from radiation source.