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The heat and mass transfer impacts on a steady 2-dimensional magnetohydrodynamic (MHD) natural convection boundary layer flow of viscous fluid surrounded by a porous vertical surface with heat source, Ohmic dissipation, chemical reaction and radiation effects are studied. The governing partial differential equations (PDE) are converted into a set of ordinary differential equations (ODE) employing non-dimensional quantities then we solved the ODE employing perturbation method. Most of the studies so far have presented the numerical and semi analytical solutions of flow and heat transfer because of porous vertical surface. Present analysis on analytical solution for the flow velocity and the temperature in the form of a series solution. It was found that increasing the permeability parameter and radiation parameter, the corresponding value of velocity increases and a reverse trend has seen in magnetic parameter.

The modeling and control of laser-irradiated tissue is a challenging problem due to the non-linear behavior of the tissue when heated. This is compounded by the fact that in-vivo tissue parameters are not well known. In order to properly model and design control methods for LITT, it is necessary to quantify the uncertainties in the model parameters and their effect on the variability of the final output. For this purpose, a non-linear LITT model has been developed and an uncertainty and sensitivity analysis of the model was performed. This was also done to identify the parameters which have the largest contribution to the uncertainty in the output. The uncertainty analysis revealed that uncertainties in the model parameters can result in a variance of up to 42 °C (40% of the mean) in the predicted temperature. The sensitivity analysis showed that thermal parameters have a larger effect on the predicted temperature and thermal dose than optical parameters. The analysis also showed that changes in the specific heat and mass density had the largest effect on the model output early in a treatment, while thermal conductivity had the largest effect later in the treatment. These results are being used to develop a framework for controlling LITT.

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