It is generally accepted that tumour cells can be eliminated by M1 anti-tumour macrophages and CD8 T cells. However, experimental results over the past 10-15 years have shown that B16 mouse melanoma cells can be eliminated by the CD4 T cells alone (either Th1 or Th2 sub-types), in the absence of CD8 T cells. In some studies, elimination of B16 melanoma was associated with a Th1 immune response (i.e., elimination occurred in the presence of cytokines produced by Th1 cells), while in other studies melanoma elimination was associated with a Th2 immune response (i.e., elimination occurred in the presence of cytokines produced by Th2 cells). Moreover, macrophages have been shown to be present inside the tumours, during both Th1 and Th2 immune responses. To investigate the possible biological mechanisms behind these apparently contradictory results, we develop a class of mathematical models for the dynamics of Th1 and Th2 cells, and M1 and M2 macrophages in the presence/absence of tumour cells. Using this mathematical model, we show that depending on the re-polarisation rates between M1 and M2 macrophages, we obtain tumour elimination in the presence of a type-I immune response (i.e., more Th1 and M1 cells, compared to the Th2 and M2 cells), or in the presence of a type-II immune response (i.e., more Th2 and M2 cells). Moreover, tumour elimination is also possible in the presence of a mixed type-I/type-II immune response. Tumour growth always occurs in the presence of a type-II immune response, as observed experimentally. Finally, tumour dormancy is the result of a delicate balance between the pro-tumour effects of M2 cells and the anti-tumour effects of M1 and Th1 cells.

Ethylene glycol is commonly used as a cooling agent in the engine, therefore the study associated with EG has great importance in engineering and mechanical fields. The hybrid nanofluid has been synthesized by adding copper and graphene nanoparticles into the Ethylene glycol, which obeys the power-law rheological model and exhibits shear rate-dependent viscosity. As a result of these features, the power-law model is utilized in conjunction with thermophysical characteristics and basic rules of heat transport in the fluid to simulate the physical situations under consideration. The Darcy Forchhemier hybrid nanofluid flow has been studied under the influence of heat source and magnetic field over a two-dimensionally stretchable moving permeable surface. The phenomena are characterized as a nonlinear system of PDEs. Using resemblance replacement, the modeled equations are simplified to a nondimensional set of ODEs. The Parametric Continuation Method has been used to simulate the resulting sets of nonlinear differential equations. Figures and tables depict the effects of physical constraints on energy, velocity and concentration profiles. It has been noted that the dispersion of copper and graphene nanoparticulate to the base fluid ethylene glycol significantly improves velocity and heat conduction rate over a stretching surface.

The energy and mass dissemination rate have been studied through Williamson hybrid nanofluid (NF) flow comprised of silver (Ag) and magnesium oxide (MgO) nanoparticles (NPs) past over an extending porous surface.The hybrid nanofluid has synthesized by dispersion of Ag and MgO nanoparticles in the base fluid (engine oil). The effects of the constant magnetic field, thermal dissipation, and heat source are also studied in the present analysis. The above scenario has been designed in the form of a nonlinear system of partial differential equations, which are processed through a similarity framework to the system of dimensionless ordinary differential equations.The results are obtained by the numerical computational approach parametric continuation method. It has been perceived that the velocity contour decreases with rising upshots of porosity parameter K p and magnetic force M, while enhances with the variation of volume friction coefficient. The increment of Biot number Bi, heat source Q, and Eckert number Ec enhances the energy profile, respectively. Furthermore, the mass conversion rate decreases with the variation of thermophoretic parameters and Schmidt number.

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A magneto couple stress nanofluid flow along with double diffusive convection is presented for peristaltic induce flow through symmetric nonuniform channel. A comprehensive mathematical model is scrutinized for couple stress nanofluid magneto nanofluids and corresponding equations of motions are tackled by applying small Reynolds and long wavelength approximation in viewing the scenario of the biological flow. Computational solution is exhibited with the help of graphical illustration for nanoparticle volume fraction, solutal concentration and temperature profiles in MATHEMTICA software. Stream function is also computed numerically by utilizing the analytical expression for nanoparticle volume fraction, solutal concentration and temperature profiles. Whereas pressure gradient profiles are investigated analytically. Impact of various crucial flow parameter on the pressure gradient, pressure rise per wavelength, nanoparticle volume fraction, solutal concentration, temperature and the velocity distribution are exhibited graphically. It has been deduced that temperature profile is significantly rise with Brownian motion, thermophoresis, Dufour effect, also it is revealed that velocity distribution really effected with strong magnetic field and with increasing non-uniformity of the micro channel. The information of current investigation will be instrumental in the development of smart magneto-peristaltic pumps in certain thermal and drug delivery phenomenon.