Fractal aggregation kinetics contributions to thermal conductivity of nano-suspensions in unsteady thermal convection

Nano-suspensions (NS) exhibit unusual thermophysical behaviors once interparticle aggregations and the shear flows are imposed, which occur ubiquitously in applications but remain poorly understood, because existing theories have not paid these attentions but focused mainly on stationary NS. Here we report the critical role of time-dependent fractal aggregation in the unsteady thermal convection of NS systematically. Interestingly, a time ratio λ = t(p)/t(m) (t(p) is the aggregate characteristic time, t(m) the mean convection time) is introduced to characterize the slow and fast aggregations, which affect distinctly the thermal convection process over time. The increase of fractal dimension reduces both momentum and thermal boundary layers, meanwhile extends the time duration for the full development of thermal convection. We find a nonlinear growth relation of the momentum layer, but a linear one of the thermal layer, with the increase of primary volume fraction of nanoparticles for different fractal dimensions. We present two global fractal scaling formulas to describe these two distinct relations properly, respectively. Our theories and methods in this study provide new evidence for understanding shear-flow and anomalous heat transfer of NS associated non-equilibrium aggregation processes by fractal laws, moreover, applications in modern micro-flow technology in nanodevices

Unified inequalities of the q-Trapezium-Jensen-Mercer type that incorporate majorization theory with applications

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of ${\mathfrak{q}}$-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the $_{{\varsigma_{1}}}{\mathfrak{q}}$ and $^{{{\varsigma_{2}}}}{\mathfrak{q}}$ differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint ${\mathfrak{q}}$-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations

The method of fundamental solutions for Helmholtz-type problems

The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated with two- or three-dimensional Helmholtz-type equations. Inverse problems have become more and more important in various fields of sicence and technology, and have certainly been one of the fastest growing areas in applied mathematics over the last three decades. However, as inverse geometric problems typically lead to mathematical models which are ill-posed, their solutions are unstable under data perturbations and classical numerical techniques fail to provide accurate and stable solutions

Global Bounds for the Generalized Jensen Functional with Applications

In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means

Simpson’s Rule and Hermite–Hadamard Inequality for Non-Convex Functions

In this article we give a variant of the Hermite–Hadamard integral inequality for twice differentiable functions. It represents an improvement of this inequality in the case of convex/concave functions. Sharp two-sided inequalities for Simpson’s rule are also proven along with several extensions

Some Improvements of the Hermite–Hadamard Integral Inequality

We propose several improvements of the Hermite–Hadamard inequality in the form of linear combination of its end-points and establish best possible constants. Improvements of a second order for the class Φ ( I ) with applications in Analysis and Theory of Means are also given

Global Bounds for the Generalized Jensen Functional with Applications

In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means

Hydromagnetic flow and heat transfer with various nanoparticles additives past a wedge with high order velocity slip and temperature jump

Nanofluids slip flow with distinct solid paticles past a wedge with convective surface and high order slip is discussed in this paper. The wedge model is modified by considering the effects of Brownian motion and thermophphoresis together with the high order velocity slip and temperature jump. In this study, the governing fundamental equations are first transformed into third order ordinary differential equations and solved by using the homotopy analysis method(HAM). Through error analysis and comparison with previous research, the effectiveness of HAM is attained, and the crucial influence of nanoparticles and high-order slip on the fluid skin-friction coefficient and heat transfer coefficient is analyed. Thermophphoresis parameter and suction/injection parameter are found to cause an increase in velocity and temperature. The rate of heat transfer in the Cu-Water nanofluid is found to be higher than the others.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

A regularization method for time-fractional linear inverse diffusion problems

In this article, we consider an inverse problem for a time-fractional diffusion equation with a linear source in a one-dimensional semi-infinite domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. We show that the problem is ill-posed, then apply a regularization method to solve it based on the solution in the frequency domain. Convergence estimates are presented under the a priori bound assumptions for the exact solution. We also provide a numerical example to illustrate our results

Numerical Solution of the Multiterm Time-Fractional Model for Heat Conductivity by Local Meshless Technique

Fractional partial differential equation models are frequently used to several physical phenomena. Despite the ability to express many complex phenomena in different disciplines, researchers have found that multiterm time-fractional PDEs improve the modeling accuracy for describing diffusion processes in contrast to the results of a single term. Nowadays, it attracts the attention of the active researchers. The aim of this work is concerned with the approximate numerical solutions of the three-term time-fractional Sobolev model equation using computationally attractive and reliable technique, known as a local meshless method. Because of the meshless character and the simple application in higher dimensions, there is a growing interest in meshless techniques. To assess the reliability and accuracy of the proposed method, three test problems and two types of irregular domains are taken into account