Search results

A precise and rapid temperature cycling of a small volume of fluid is vital for an effective DNA replication process using the polymerase chain reaction (PCR). The purpose of this paper is to study the velocity and temperature fields inside a rotating PCR‐tube during cooling of the enclosed liquid.

The velocity and temperature fields inside a rotating PCR‐tube during cooling of the enclosed liquid are studied. By using computational fluid dynamics, the time development of the flow can be investigated in detail. Owing to the rotation, the flow exhibits features which could never arise in a non‐rotating system.

An intricate azimuthal boundary layer flow is presented and explained. The inherent problem of stratification of the temperature is discussed, and different methods towards a remedy are presented. By analyzing the governing equations, some properties of the flow observed in the simulations are explained. It is shown that increasing the rate of rotation does not improve temperature homogenization.

The simulations were performed for a limited number of temperature boundary conditions, as well as a specific simulation geometry.

The analytical and simulation results offer fundamental insight into the physics behind increased DNA duplication. Further simulations offer possible design improvements.

While many studies have probed the effects of buoyancy in rotating cylinders and the development of boundary layers in stratified flows in conical containers rotating around their axis of symmetry, little work has been specifically focused on the case where the axis of rotation is normal to the direction of the stratification, which is the case in the present study.

The authors examined the numerical natural frequency analysis of a 2D functionally graded (FG) truncated thick hollow cone using 3D elasticity theory.

The material properties of the 2D-FGM (two dimensional-functionally graded materials) cone are graded along the radial and axial axes of the cone using a power–law distribution. The eigenvalue problem was solved using finite element analysis (FEA) employing graded hexahedral elements, and the verification of the finite element approach was assessed by comparing the current solution to earlier experimental studies.

The effects of semivertex angle, material distribution and the cone configuration on the natural frequencies have been analyzed. For various semivertex angles, thickness, length and power law exponents, many results in the form of natural frequencies and mode shapes are presented for the 2D-FGM cone. As a result, the effects of the given parameters were addressed, and the results were compared, demonstrating the direct efficiency of raising the power–law exponents and cone thickness on the rise of natural frequencies.

For the first time, the numerical natural frequency analysis of a 2D-FG truncated thick hollow truncated cone based on 3D equations of elasticity has been investigated. The material properties of the truncated cone have been distributed along two directions, which has not been considered before in any research for the truncated thick cone. The reason for using these innovative volume fraction functions is the lack of accurate coverage by functions that are available in the literature (Asemi et al., 2011; Babaei et al. 2021).

The purpose of this paper is to investigate the steady mixed convection boundary layer flow from a vertical frustum of a cone in water-based nanofluids. The problem is formulated to incorporate three kinds of nanoparticles: copper, alumina and titanium oxide. The working fluid is chosen as water with the Prandtl number of 6.2. The mathematical model used for the nanofluid incorporates the particle volume fraction parameter, the effective viscosity and the effective thermal diffusivity. The entire regime of the mixed convection includes the mixed convection parameter, which is positive for the assisting flow (heated surface of the frustum cone) and negative for the opposing flow (cooled surface of the frustum cone), respectively.

The transformed non-linear partial differential equations are solved numerically for some values of the governing parameters. The derivatives with respect to? were discretized using the first order upwind finite differences and the resulting ordinary differential equations with respect to? were solved using bvp4c routine from Matlab. The absolute error tolerance in bvp4c was 1e-9.

The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. The effects of the particle volume fraction parameter \phi, the mixed convection parameter \lambda and the dimensionless coordinate? on the flow and heat transfer characteristics are determined only for the Cu nanoparticles. It is found that dual solutions exist for the case of opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of the nanofluids.

The paper models the mixed convection from a vertical truncated cone using the boundary layer approximation. Multiple (dual) solutions for the flow reversals are obtained and the range of existence of the solutions was found. Particular cases for ?=0 (full cone), ? >>1 and (free convection limit) \lambda>>1were studied. To the authors best knowledge this problem has not been studied before and the results are new and original.

The purpose of this paper is to propose a new approach to determine the aeroelastic instability of truncated conical shells. In the proposed approach the governing equation of flutter for a truncated conical shell is established using Love's thin shell theory and the quasi-steady first-order piston theory.

The derivatives in both the governing equations and the boundary conditions are discretized with the differential quadrature method, and the critical flutter chamber pressure is obtained by eigenvalue analysis.

The influence of the shell geometry parameters, such as semi-cone angle, radius-thickness ratio and length-radius ratio, on the critical flutter chamber pressure is studied. Results are also presented to indicate the stabilizing effects of aerodynamic damping and the destabilizing effects of the curvature correction term of piston theory on flutter of truncated conical shell.

The present approach is an efficient method for the free vibration and flutter analysis of truncated conical shells due to its high order of accuracy and less requirement of virtual storage and computational effort.

First, a synopsis of the major changes of natural science, mathematics and philosophy within the 17th century shall highlight the birth of the new age of science and technology. Based on Fermat's principle of the shortest light‐way and Galilei's first attempt of an approximative solution of the so‐called Brachistochrone problem using a quarter of the circle, Johann Bernoulli published a competition for this problem in 1696, and six solutions were submitted by the most famous scientists of the time and published in 1697, even though the variational calculus was only published in 1744 by Euler for the first time. Especially the analytical solution of Jakob Bernoulli contains already the main idea of Euler's variational calculus, i.e. to vary only one function value at a time using a finite difference method and proceeding to the infinitesimal limit. Also Leibniz' geometric solution is very remarkable, realizing a direct discrete variational method geometrically which was invented numerically much later in the 19th century by Ritz and Galerkin and generalized to the finite element method by introducing test and trial functions in finite subspaces. A new finite element solution of the non‐linear Brachistochrone problem concludes the paper. It is important to recognize that besides the roots of variational calculus also the first formulations of conservation laws in mechanics and their applications originated in the 17th century.

A steady, two‐dimensional natural convection flow of a viscous, incompressible fluid having temperature‐dependent viscosity and thermal conductivity about a truncated cone is considered. We use suitable transformations to obtain the equations governing the flow in convenient form and integrate them by using an implicit finite difference method. Perturbation solutions are employed to obtain the solution in the regimes near and far away from the point of truncation. The results are obtained in terms of the local skin friction and the local Nusselt number. Perturbation solutions are compared with the finite difference solutions and found to be in excellent agreement. The dimensionless velocity, viscosity and thermal conductivity distributions are also displayed graphically, showing the effects of various values of the pertinent parameter for smaller values of Prandtl number.

THIS paper is intended as a sequel to a paper by Dr. J. F. C. Conn entitled “Vibration of a Truncated Wedge” (AIRCRAFT ENGINEERING, Vol. XVI, April 1944, pp. 103–105). The three modes of vibration—longitudinal, flexural and torsional—of a truncated cone encastré at one end and free at the other are considered separately. Special attention is given to the vibration frequencies of the cone and uniform cylinder.

The purpose of this paper is to solve the problem of steady, laminar, coupled heat and mass transfer by MHD natural convective boundary‐layer flow over a permeable truncated cone with variable surface temperature and concentration in the presence of thermal radiation and chemical reaction effects.

The governing equations are derived and transformed into a set of non‐similar equations which are then solved by an adequate implicit finite difference method.

It is found that the presence of thermal radiation, magnetic field and chemical reaction have significant effects on the rates of heat and mass transfer. The variation of the wall temperature and concentration exponent contribute to significant changes in the Nusselt and Sherwood numbers as well.

The titled problem with the various considered effects has not been solved before and it is of special importance in various industries. The problem is original.

IN a previous paper by the author (‘The Calculation of Frequencies of Vibration of a Truncated Cone’, AIRCRAFT ENGINEERING, Vol. XVIII, July 1946, pp. 235–236) expressions for the fundamental frequencies of longitudinal, flexual and torsional vibrations were obtained. The methods used have now been extended to include the vibrations of truncated pyramids encastré at one end and free at the other, and the results obtained are given in this paper. Special attention is given to the pyramids having equilateral triangle and square cross‐sections.

In an aircraft, a gas turbine having a truncated tail cone over which turbine effluent flows, the small end of said truncated tail cone being open and directed rearwardly, and a rocket motor within said truncated tail cone and issuing its effluent through the rearward open small end thereof, said rocket motor having selectively operable liquid fuel and liquid oxidizer feed mechanisms driven by said gas turbine and disposed within said tail cone and forward of said rocket motor.