Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier's law

A Description of the Isothermal Ageing Creep Process in Polymethyl Methacrylate Using Fractional Differential Models

Fractional differential viscoelastic models can describe complex material behaviours and fit experimental data well; however, the physical significance of model parameters is difficult to express. In this study, the fractional differential Maxwell, Kelvin, and Zener models were used to fit the short-term creep compliance curves of polymethyl methacrylate at different ageing times. The model fits were in good agreement with the experimental data. As the ageing time increased, the fractional differential Zener model showed a relative increase in the modulus parameter of the spring and a relative decrease in the modulus parameter reflecting the viscosity of the spring-pot, which indicated that physical ageing made the material more elastic. The relaxation time of the material increased, which indicated that the physical ageing reduced the free volume of the material, hindered the movement of molecules/segments, and increased the time required for the material to reach equilibrium. The fractional order of the model decreased, which reflected the phenomenon that physical ageing reduced the creep compliance of the material. Using the relaxation time as the time scale, the creep curves at different ageing times under the same stress level could be superimposed, naturally presenting the time-ageing time equivalence principle.

Fractal fractional analysis of non linear electro osmotic flow with cadmium telluride nanoparticles

Numerical simulations of non-linear Casson nanofluid flow were carried out in a microchannel using the fractal-fractional flow model. The nano-liquid is prepared by dispersing Cadmium Telluride nanoparticles in common engine oil. Using relative constitutive equations, the system of mathematical governing equations has been formulated along with initial and boundary conditions. Dimensionless variables have been used to obtain the non-dimensional form of the governing equations. The fractal-fractional model has been obtained by employing the fractal-fractional operator of the exponential kernel. As the exact solution of the non-linear fractal-fractional model is very tough to find, therefore the formulated model has been solved numerically via the Crank-Nicolson scheme. Various plots are generated for the inserted parameters. From the analysis, it has been observed that a greater magnitude of the electro-kinetic parameter slows down the fluid's velocity. It is also worth noting that the fractional and classical models can also be derived from the fractal-fractional model by taking the parameters tend to zero. From the analysis, it is also observed that in response to 0.04 volume fraction of cadmium telluride nanoparticles, the rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) increased by 15.27% and 2.07% respectively.

ABC Fractional Order Vaccination Model for Covid-19 with Self-Protective Measures

A mathematical model delineating the control strategies in transference of Covid-19 pandemic is examined through Atangana-Baleanu Caputo type fractional derivatives. The total count of people under observation is classified into Susceptible, Vaccinated, Infected and Protected groups (SVIP). The designed model studies the efficiency of vaccination and personal precautions incorporated qualitatively by every individual via fixed point theorem. Stability of the system has been investigated with spectral characterisation of Ulam Hyer's kind. Numerical interpolation has been derived by Adam's semi-analytical technique and we have approximated the solution. We have proved the theoretical analysis through graphical simulations that vaccination and self protective interventions are the significant role to decrease the contagious expansion of the virus among the people in process.

Space-fractional heat transfer analysis of hybrid nanofluid along a permeable plate considering inclined magnetic field

In this study, the Caputo space-fractional derivatives of energy equation are used to model the heat transfer of hybrid nanofluid flow along a plate. The plate is considered permeable and affected by an inclined magnetic field. We use the space-fractional derivative of Fourier's law to communicate between the nonlocal temperature gradient and heat flux. The hybrid nanofluid is formed by dispersing graphene oxide and silver nanoparticles in water. The new fractional integro-differential boundary layer equations are reduced to ordinary nonlinear equations utilizing suitable normalizations and solved via a novel semi-analytical approach, namely the optimized collocation method. The results reveal that the increment of the order of space-fractional derivatives and the magnetic inclination angle increase the Nusselt number. Also, an increase in the order of space-fractional derivatives leads to a thicker thermal boundary layer thickness resulting in a higher temperature. It is also found that the temperature of the fluid rises by changing the working fluid from pure water to single nanofluid and hybrid nanofluid, respectively. What is more, the proposed semi-analytical method will be beneficial to future research in fractional boundary layer problems.