Influence of PST and PHF heating conditions on the swirl flow of Al+Mg+TiO2 ternary hybrid water-ethylene glycol based nanofluid with a rotating cone

Swirl flow heat exchangers are commonly used in industrial processes such as power generation, chemical processing, and refrigeration. They can be used for both heating and cooling applications and can be designed to handle a wide range of fluid flow rates and temperatures. This study investigated the influence of PST (prescribed surface temperature) and PHF (prescribed heat flux) heating conditions on the swirl flow of Al+Mg+TiO2 ternary hybrid water-ethylene glycol (50/50) based nanofluid with a heated rotating cone. The governing ordinary differential equations were derived from the partial differential equations using the proper similarity transformations. The problem was solved using the Shifted Legendre Collocation Method (SLCM), which is a powerful numerical method. The results showed that the PST heating conditions had a significant impact on the flow and heat transfer characteristics of the ternary hybrid nanofluid. Under PHF heating conditions, the swirl velocity distribution was leading to a noteworthy influence. The use of the Al+Mg+TiO2 ternary hybrid water-ethylene glycol based nanofluid resulted in a significant enhancement in the convective heat transfer coefficient. The SLCM method provided accurate and efficient numerical solutions for the problem, demonstrating its suitability for simulating complex fluid flow and heat transfer problems

Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio

Analysis and computation of the cross-flow past an oscillatiang cylinder with two degrees of freedom

The present thesis deals with analysis and numerical simulation of a new class of wake flows created by combined recti-linear (translational) and rotational oscillation of a cylinder placed in a steady uniform flow. The flow is incompressible and two-dimensional, and recti-linear and rotational oscillations are harmonic. The instantaneous translation and rotation start at the same moment and the development of the flow is studied in a coordinate frame which moves with the cylinder but does not rotate. The analysis is carried out for combined phase-locked translation and rotation with a single frequency. The results are presented for five set of the four dimensionless groups which characterize this flow. The resulting vortex formation modes and synchronization (lock-on) phenomena behind the cylinder (in the near-wake region) as well as the fluid forces acting on the cylinder are analyzed. In addition, a series of one-degree-of-freedom (1-DoF) forced vibration calculations are carried out to better understand what differences result from the addition of rotational oscillations to streamwise (in-line) or cross-stream (transverse) motion and to see which effects a transverse-only or in-line-only simulations miss. The numerical scheme is verified by applying it to the special cases of uniform flow past a stationary cylinder; a steadily rotating cylinder; a cylinder undergoing (1-DoF) forced (recti-linear or rotational) oscillations. Exceptionally good comparisons with previous experimental and numerical results are obtained. Furthermore, the simulations of the start-up flow for the case of combined (2-DoF) forced recti-linear and rotational cylinder oscillations at a moderate Reynolds number are consistent with the results of the analytical solution

Convergent Power Series of sech⁡(x) and Solutions to Nonlinear Differential Equations

It is known that power series expansion of certain functions such as sech⁡(x) diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of sech⁡(x) that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x) and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2). A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed

Modified Sinc-Galerkin Method for Nonlinear Boundary Value Problems

This paper presents a modified Galerkin method based on sinc basis functions to numerically solve nonlinear boundary value problems. The modifications allow for the accurate approximation of the solution with accurate derivatives at the endpoints. The algorithm is applied to well-known problems: Bratu and Thomas-Fermi problems. Numerical results demonstrate the clear advantage of the suggested modifications in obtaining accurate numerical solutions as well as accurate derivatives at the endpoints

Heat Transfer Enhancement in Free Convection Flow of CNTs Maxwell Nanofluids with Four Different Types of Molecular Liquids

This article investigates heat transfer enhancement in free convection flow of Maxwell nanofluids with carbon nanotubes (CNTs) over a vertically static plate with constant wall temperature. Two kinds of CNTs i.e. single walls carbon nanotubes (SWCNTs) and multiple walls carbon nanotubes (MWCNTs) are suspended in four different types of base liquids (Kerosene oil, Engine oil, water and ethylene glycol). Kerosene oil-based nanofluids are given a special consideration due to their higher thermal conductivities, unique properties and applications. The problem is modelled in terms of PDE’s with initial and boundary conditions. Some relevant non-dimensional variables are inserted in order to transmute the governing problem into dimensionless form. The resulting problem is solved via Laplace transform technique and exact solutions for velocity, shear stress and temperature are acquired. These solutions are significantly controlled by the variations of parameters including the relaxation time, Prandtl number, Grashof number and nanoparticles volume fraction. Velocity and temperature increases with elevation in Grashof number while Shear stress minimizes with increasing Maxwell parameter. A comparison between SWCNTs and MWCNTs in each case is made. Moreover, a graph showing the comparison amongst four different types of nanofluids for both CNTs is also plotted