The high strength-to-weight ratio and flexibility of single walled carbon nanotubes (SWCNT) make them of potential use in the control of nanoscale structures for thermal, electrical, structural and mechanical applications. This indicates that they will have a vital contribution to nanotechnology engineering. This paper presents an exact solution to the dynamic response of such CNTs considering the shear force and bending moment under uniformly distributed external pressure. The dynamic behaviour of the SWCNT is modeled by employing the theories of Euler-Bernoulli beam and thermal elasticity mechanics. The developed model that governs the physics of the behaviour of the SWCNT when excited by the aforementioned external agents is solved using Integral transforms. The results of the close form solution in this work were compared with results of past works and excellent agreements were achieved. Furthermore, the dynamic study revealed that a point of maximum shear force on the CNT produced the minimum bending moment at any mode and for any parameter value considered. It is envisaged that this work will enhance the application of SWCNT for structural, electrical and mechanical uses.
By associating last progresses in photography, computer science and additive manufacturing, cost-effective planar stitching of non-structured photographs of microscope slides into high definition large pictures is achievable. The proposed method, inspired by previous works and state-of-the art equipment, uses non-professional camera, little pre-processing, no post processing, and little to no investment is needed. A total duration of 41 min was observed to create a high-quality, high-resolution full picture of a sagittal cross-section of a permanent maxillary central incisor, from 16 original photographs with a \(\times\)40 microscope optical magnification. Final pictures weights are in-between 60 Mo and 340 Mo, depending on the format and the number of initial photographs. Higher magnification does not seem to enhance pictures, but sensibly increases file weight. This method has numerous applications, such as research, sharing and teaching and will certainly be enhanced in the future thanks to the high speed development of smartphone abilities.
The performance of fins, commonly used as heat enhancement devices are greatly affected by both the geometry and material properties. These consideration in fin design has stimulated an extensive research interest in the recent time. In this study, investigation on the thermal responses of moving irregular porous fins with trapezoidal, concave and convex profiles of copper, aluminium, silicon nitrides and stainless steel materials is examined. The developed thermal model is solved using differential transform method (DTM). On the verification of result obtained with numerical method using Runge-Kutta, a good agreement with the solution of approximate method is achieved. In the parametric studies carried out, the effect of physical parameters such as convective-conductive, convective-radiative term, internal heat generation, porosity, surface emissivity, power index of heat transfer coefficient, Peclet number and Darcy number on the thermal behaviour of fins are examined and discussed. The comparative analysis carried out on the effect of materials on non-dimensional temperature distribution reveals that copper obtains the highest temperature while the stainless steel gets the lowest. More-so, the fins with concave geometry gives the highest volume adjusted efficiency with increase in Peclet number while that with convex profile has the least. These result output are essential and would be useful in the future design of fins with optimum size reduction and high efficiency.
Generating homotopy-based approaches (HBAs) in thermal-fluid sciences is an efficient manner for finding absolutely convergent series expansions. The main objective of this paper is to analyze the viscoelastic Walter’s B fluid past a stretching wall. To answer this, the governing differential equation is derived by substituting similarity variables into the partial differential equations (PDEs) and associated boundary conditions. The present HBA is also developed by minimizing the averaged square residual error included in the quadratic resistance law (QRL). By comparing the present findings with those available in the literature, it is seen that the 9th-order HBA can provide an incredible degree of accuracy and reliability. Furthermore, it is found that the central processing unit (CPU) time is greatly reduced when the auxiliary parameter is selected as \(\hbar\)=-0.122.
In this paper, we study the oscillatory theory for fractional differential equations (FDEs) via \(\psi\)-Hilfer fractional derivative. Sufficient conditions are established for the oscillation of solutions FDEs.
