Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Single-function approach to calibrating whatman n.º 42 filter paper based on suction versus water content relationships

Several suction–water-content (s-w) calibrations for the filter paper method (FPM) used for soil-suction measurement have been published. Most of the calibrations involve a bilinear function (i.e., two different equations) with an inflection point occurring at 60 kPawith a smooth transition between the high and low suctions based on a regression analysis of various previously published calibrations obtained for filter paper Whatman No. 42 (W42) is presented and discussed. The approach is applied herein to data obtained from three establish bilinear calibrations (six equations) for W42 filter paper to determine the two fitting parameters of the continuous function. An experimental evaluation of the new calibration show that the suctions estimated by the contact FPM test using the proposed function compare well with suctions measured by other laboratory techniques for two different soils for the suction range of 50 kPa