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Some solutions are presented to show the ability of the spectral line-based weighted sum of gray gases approach to solve the radiative transfer equation in absorbing-emitting non-gray media. The medium contains heat sources and is atradiative equilibrium state which occurs in high temperature systems. The non-gray gaseous medium is divided into a number of gray gases, and the radiative transfer equation is solved for each gray gas by the discrete ordinate method. The intensities are found by a summation over all gray gases, and the temperature field is updated by an iterative procedure. The updated coefficients obtained from high-temperature molecular spectroscopic database (2010thedition) are employed in the spectral line-based weighted sum of gray gases model. The method is verified through comparison with a benchmark problem for the case of a specified temperature distribution, and also for thecase of a variable temperature distribution (radiative equilibrium). Several examples are taken into account to show the ability and performance of proposed procedure for the radiative equilibrium calculations in media with heat sources and different boundary conditions (constant temperature and insulated walls).

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In this study, numerically investigated effect of magnetic heat sources (residual and hysteresis) that can be useful in hyperthermia and their effects on cancerous tissue. The governing equations of continuty, momentum, concentration, energy and Arrhenius tissue destruction equation in the form of couplings are defined, solved and investigated in the finite-element COMSOL software. For blood flow inside the cancerous capillary, non-newtonian and temperature dependent model is used. The geometric model is simulated in three dimensions, including the capillary and cancerous tissue. Thermophysical properties of blood and tissue are also temperature dependent. Results indicated that the residual heat source plays a major role in increasing the temperature of the blood and tissue and can be ignored the effect of hysteresis heat source. The residual heat source has an inverse relation to the particle size and is ineffective in the particle size above 100 nm but hysteresis heat source is directly related to the size of the nanoparticles, and for particles with a size of 150 nm, it will result in a 1 degree increase in temperature for the tissue. The increase in blood temperature for 25 nm magnetic nanoparticles with the residual heat source can lead to the most destruction in cancerous tissue. Also, the viscosity of blood has an inverse relation with the concentration of magnetic nanoparticles in the capillary wall and blood temperature.