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This paper presents thorough computational and theoretical analyses of steady forced convective flow over a rotating disc submerged in a water-based nanofluid containing microorganisms. It delves into the examination of boundary layer flow characteristics of a viscous nanofluid, considering Stefan blowing effects and multiple slip conditions influenced by a magnetic field. Notably, the study accounts for novel aspects such as thermal radiation and both constructive and destructive chemical reactions. The movement of nanoparticles is elucidated based on thermophoresis and microscopic behaviors, while changes in volume fraction do not affect the thermo-physical properties of the nanofluid. To address the altered nonlinear set of differential equations, an effective numerical approach, the Keller-Box method, is implemented for critical and efficient solutions. These appropriate transformations are defined and applied. When compared to blowing suction, it shows a better enhancement in the rate of heat transfer, mass, and microorganisms. Some of the main observations are there is a decrease in wall skin friction in the directions of radial and tangential as magnetic field strength is increased. The evaluation of thermal boundary layer thickness and temperature is noted for the radiation parameter (Rd) improvement. The present analysis has applications in electromagnetic micro-pumps and nanomechanics. As to the applications in the science and engineering fields, technologies such as micro-electromechanical systems-based microfluidic devices and microfluidic-related technologies will be accepted.

The similarity solution for the steady stagnation flow toward an off-centered rotating disc gives a system of nonlinear partial differential equations. These nonlinear differential equations are analytically solved by applying a newly developed method called DTM–Padé technique (the combination of the differential transform method (DTM) and the Padé approximation). This technique is extended to give solutions for nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the rotation ratio α on the radial velocity, azimuthal velocity, and the induced velocity. In order to show the effectiveness of the DTM–Padé technique, the results obtained from the DTM–Padé technique are compared with available solutions obtained using shooting method to generate the numerical solution. The obtained results demonstrate the reliability of the algorithm and the DTM–Padé technique is an attractive method in solving the systems of nonlinear partial differential equations.

An attempt has been made to investigate steady state creep behavior of thermally graded isotropic discs rotating at elevated temperatures. For this purpose, composite discs of aluminum matrix reinforced with silicon carbide particulate have been taken. Modeling of stress and strain rate distributions for discs operating under linear thermal gradient has been done using von Mises’ yield criterion and threshold stress-based creep law. Similarly modeling has been done for discs operating under non-linear thermal gradient. The results are compared with the disc having a uniform temperature profile from inner to outer radius and are displayed graphically in designer friendly format for the said temperature profiles. A small variation is observed for radial and tangential stresses for the said thermal gradations. However, the strain rates vary significantly in the presence of thermal gradations as compared to a disc having uniform temperature throughout the radial distance. Thus, it is observed that there is a need to extend the domain of thermal gradation for designing rotating discs.

The stresses and deformations of a functionally graded piezoelectric material (FGPM) non-uniform thickness rotating disc under magneto-thermo-mechanical loads including convection and radiation heat transfer were examined in this paper. The material constants were considered to be a power-law function of radius. Also, the heat convection coefficient and heat conduction coefficient are functions of radius and temperature. The equation of heat transfer was derived considering thermal gradient, convection thermal boundary, and solar radiation. The nonlinear final differential equation was solved using the Differential Transformation Method (DTM). Then, the equilibrium equation together with the electrostatic equation of the disc was derived and solved analytically. So, the radial and circumferential stress, radial deformation, and electric potential were obtained. Finally, the effects of solar radiation, convection heat transfer, temperature dependency, inhomogeneity index, angular velocity, and magnetic field on the stress, deformation, and electric potential of the disc were investigated in numerical examples. The results show that solar radiation, convection boundary, thickness function, and inhomogeneity index have a considerable effect on the responses of the rotating FGPM disc.

The influence of the thermal residual stress and reinforcement geometry on the creep behavior of a composite disc has been analyzed in this paper. The creep analysis in a rotating disc made of Al-SiC (particle/whisker) composite having hyperbolically varying thickness has been carried out using anisotropic Hoffman yield criterion and results obtained are compared with those using Hill's criterion ignoring difference in yield stresses. The steady state creep behavior has been described by Sherby's creep law. The creep parameters characterizing difference in yield stresses have been used from the available experimental results in literature. It is observed that the stresses are not much affected by the presence of thermal residual stress, while thermal residual stress introduces significant change in the strain rates in an anisotropic rotating disc. Secondly, it is noticed that the steady state creep rates in whisker reinforced disc with/without residual stress are observed to be significantly lower than those observed in particle reinforced disc with/without residual stress. It is concluded that the presence of residual stress in an anisotropic disc with varying thickness needs attention for designing a disc.

The creep behavior of an anisotropic rotating disc of functionally gradient material (FGM) has been investigated in the present study using Hill's yield criteria and the creep behavior in this case is assumed to follow Sherby's constitutive model. The stress and strain rate distributions are calculated for disc having different types of anisotropy and the results obtained are compared graphically. It is concluded that the anisotropy of the material has a significant effect on the creep behavior of the FGM disc. It is also observed that the FGM disc shows better creep behavior than the non-FGM disc.

In this paper, an effort has been made to study the effect of anisotropy on the steady state creep behavior in the functionally graded material disc with hyperbolic thickness made of Al-SiC (particle). The content of silicon carbide particles in the disc is assumed to decrease linearly from the inner to the outer radius of the disc. The creep behavior of the disc under stresses developing due to rotation at 15,000 rpm has been determined by Sherby's law. The creep parameters of the FGM disc vary along the radial distance due to varying composition and this variation has been estimated by regression fit of the available experimental data. The creep response of rotating disc is expressed by a threshold stress with value of stress exponent as 8. The study reveals that the anisotropy has a significant effect on the steady state creep response of rotating FGM disc. Thus, the care to introduce anisotropy should be taken for the safe design of the rotating FGM disc with hyperbolic thickness.

Based on the basic equations of a transversely isotropic magnetoelectroelastic axisymmetric problem, a three-dimensional (3D) analytical solution for a functionally graded, magnetoelectroelastic disc rotating with a constant angular velocity is obtained. The displacement components, electric potential and magnetic potential are assumed in forms of polynomials of the radial coordinate (r), with coefficients being unknown functions of the axial (thickness) coordinate (Z), which can be determined by solve a group of simply governing equations. Since the material parameters can be arbitrary functions of the Z-coordinate, the present solution can be degenerated into that for corresponding homogeneous materials cases and various uncoupled cases. The numerical results of a particular functionally graded magnetoelectroelastic rotating disc clearly show the effect of material inhomogeneity (i.e. gradient index) on the elastic, electric and magnetic fields, which can be used to guide the optimization design of rotating discs.