An inclination in Thermal Energy Using Nanoparticles with Casson Liquid Past an Expanding Porous Surface

About Inverse Laplace Transform of a Dynamic Viscosity Function

A dynamic viscosity function plays an important role in water hammer modeling. It is responsible for dispersion and decay of pressure and velocity histories. In this paper, a novel method for inverse Laplace transform of this complicated function being the square root of the ratio of Bessel functions of zero and second order is presented. The obtained time domain solutions are dependent on infinite exponential series and Calogero–Ahmed summation formulas. Both of these functions are based on zeros of Bessel functions. An analytical inverse will help in the near future to derive a complete analytical solution of this unsolved mathematical problem concerning the water hammer phenomenon. One can next present a simplified approximate form of this solution. It will allow us to correctly simulate water hammer events in large ranges of water hammer number, e.g., in oil–hydraulic systems. A complete analytical solution is essential to prevent pipeline failures while still designing the pipe network, as well as to monitor sensitive sections of hydraulic systems on a continuous basis (e.g., against possible overpressures, cavitation, and leaks that may occur). The presented solution has a high mathematical value because the inverse Laplace transforms of square roots from the ratios of other Bessel functions can be found in a similar way.

A dynamic assessment of various non-Newtonian models for ternary hybrid nanomaterial involving partially ionized mechanism

The dynamic of fluids and coolants in automobiles are achieved by enhancement in heat energy using ternary hybrid nanostructures. Ternary hybrid nanomaterial is obtained by suspension of three types of nanofluid (aluminum oxide, silicon dioxide and titanium dioxide) in base fluid (EG). Prime investigation is to address comparison study in thermal energy involving various flow models termed as Maxwell fluid and Williamson fluid. This exploration is carried out by partially ionized fluidic particles in the presence of ternary hybrid nanomaterial over cone. Heat transfer is carried out by heat source and thermal radiation. Equations regarding Ordinary differential are achieved from PDEs using variable transformations. The numerical consequences are obtained implementing finite element method. Flow into fluid particles is enhanced versus higher values of Hall and ion slip parameters. Thermal performance as well as flow performance for the case Williamson fluid is better than for case of Maxwell fluid. Production via energy is boosted versus heat source parameter.

An Effect of Radiation and MHD Newtonian Fluid over a Stretching/Shrinking Sheet with CNTs and Mass Transpiration

The invention of carbon nanotubes (CNT) has a wide range of industrial and medical applications. The notion of boundary layer flow is used in medicine, particularly in nanomedicine, and the use of magnetic fields is used to treat cancer tumour growth. The governing PDEs are altered into ODEs with the help of suitable transformations. The mass transfer of a chemically reactive species and the flow of MHD over a stretching plate subjected to an inclined magnetic field are investigated, and analytical solutions for velocity in terms of exponential function and temperature field in terms of incomplete Gamma function are obtained using the Laplace transformation. We investigate the variation of physically important parameters with varying suction, magnetic field, and slip using the analytical results. The differences in velocity and temperature profiles are explored in relation to a number of physical parameters. MWCNT nanofluids have higher effective velocities than the SWCNT deferred nanofluids, and this might assist in industrial applications and medical benefits. Earlier research tells us that carbon nanotubes are likely quicker than nanoparticles at achieving the same tumour instance. As a result, in the presence of CNTs or nanoparticles, the magnetic field can also act as a source. We found that SWCNTs nanofluids are better nanofluids than MWCNTs nanofluids.