This study intends to investigate the influences of thermal radiation and variable electrical conductivity on the MHD peristaltic flow of Carreau nanofluids as the radiotherapy and thermotherapy are required for cancer treatment.Formulation of temperature-dependent electrical conductivity is introduced for the first time in the peristaltic literature. The related equations of momentum, mass, and concentration are reformulated using lubrication approximations (ie, tiny or zero Reynolds number and long wavelength). These simplified equations are solved numerically with the aid of Parameteric-NDSolve. Results for velocity, temperature, and concentration distributions are obtained in three-dimensional analytical forms. The streamline graphs are offered in the terminus, which elucidate the trapping bolus phenomenon. A "special case" of our results offered to get the solutions over certain contours for the behaviors of velocity, temperature, and nanoparticle concentration. It is found that the magnetic nanoparticles acquire more energy at high temperature, enabling them to destroy and damage tumors tissues (thermotherapy of oncology). Radiation is the reason for spreading the energy, that is, the energy of all the fluid nanoparticles does not continue with the same value.Heat Transfer-Asian Res. 2019;48:938-956. wileyonlinelibrary.com/journal/htj 938 |

Background: Cancer is deadly to most of its patients. Consequently, researchers and modelers studies show that there are many ways to cure and destroy it. One of the effective ways is to inject the blood vessel close to the tumor with magnetic nanoparticles. Another way called the radiation therapy or radiotherapy, which eradicates cancer cells through high doses of radiation. Objective: This paper opts to investigate the influences of thermal radiation and variable electrical conductivity on peristaltic flow of Carreau Nanofluids. First order chemical reaction, Dufour and Soret effects are taken into consideration. Methods: The resulting system of partial differential equations is solved numerically with the aid of Parametric-NDSolve. Results for velocity, temperature and concentration distributions are obtained in the analytical two-dimensional and three-dimensional forms. The streamlines graphs are offered in the terminus, elucidating the trapping bolus phenomenon. Results: It has been found that thermal radiation is a decreasing function in the temperature of the fluid. As the temperature decreases, the diameter of the nanoparticles increases i.e., the volume of nanoparticle and its concentration increases and become more effective near tumor tissues. Conclusion: Radiotherapy and Thermotherapy are effective methods to cure and damage the tumor tissues.

As conduction, convection, and radiation are fundamental modes of heat emitter and transfer, this paper looks at the influences of temperature-dependent thermal conductivity and thermal radiation on peristaltic flow of pseudoplastic nanofluids in an inclined non-uniform asymmetric channel. Inclined magnetic field is taken into consideration. As the Wiedemann–Franz law in metals, electrical conductivity has identical behavior as that of thermal conductivity; as freely animated evenness, electrons transfer not only electric current but also heat energy. Consequently, electrical conductivity should be depending on the temperature of nanoparticles. The related equations of momentum, mass, and concentration are reformulated using lubrication approximations (i.e., tiny or zero Reynolds number and long wavelength). The resulting system of nonlinear equations is solved semi-numerically with the aid of the parametric ND solve package using mathematica version 11. Results of velocity, temperature, and concentration distributions are obtained in the analytical three-dimensional forms. The streamline graphs are offered in the terminus, which elucidate the trapping bolus phenomenon. As a special case, a comparison is made and signified with the recently published results by Hayat et al. (2016, Soret and Dufour Effects in MHD Peristalsis of Pseudoplastic Nanofluid With Chemical Reaction,” J. Mol. Liq., 220, pp. 693–706). It's found that, the increases in thermal conductivity and electrical conductivity cause an increase in the temperature of nanofluid and the heat transfer rate gets induced so a better absorption of solar energy is gained.

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