In the present paper, a three dimensional annular developing incompressible laminar flow through 270- degree curved pipe is numerically simulated. The dimensionless governing equations of continuity, momentums and energy are driven in toroidal coordinates. The governing equations are discretized by projection algorithm using forward difference in time and central difference in space. A three-di...

Contents 1 Introduction 2 The geometry of operators of Laplace and Dirac type 3 Heat trace asymptotics for closed manifolds 4 Hearing the shape of a drum 5 Heat trace asymptotics of manifolds with boundary 6 Heat trace asymptotics and index theory 7 Heat content asymptotics 8 Heat content with source terms 9 Time dependent phenomena 10 Spectral boundary conditions 11 Operators which are not of ...

The paper shall demonstrate how concentrated source terms can be included by Delta functions in models with distributed parameters and, moreover, that the abstraction of sharply concentrated quantities leads to decisive numeric advantages. The system of differential equations loses its stiffness here at the method of lines. The eigenvalues of the Jacobian matrix (A-matrix) show that it becomes ...

In this work, analysis of transient three-dimensional heat transfer in a slab with internal heat generation and heated by a point moving heat source along its axis is carried out using integral transforms methods. The heat input into slab or workpiece by the moving heat source is considered in the model. From the results, it was established that the temperature of the material during the heat t...

Mixed convection fluid flow and heat transfer of water-Al2O3 nanofluid inside a lid-driven square cavity has been examined numerically in order to find the optimal distribution of discrete heat sources on the wall of a cavity. The effects of different heat source length, Richardson number and Grashof number on optimal heat source location has been investigated. Moreover, the average Nusselt num...

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

A multimedia feature for unsteady magnetic hydrodynamic (MHD) flow of two-dimensional mixed convection flow of an incompressible viscoelastic fluid over a vertical stretching sheet with viscous dissipation was studied. Similar transformation and an implicit finite-difference method were used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature ...

Heat sinks are used in industrial equipment to dissipate the excess heat from their heat-generating parts to the ambient. In the last few years, efforts on manufacturing electronic or mechanical devices with less weight, space, and lower cost were spent. Heat dissipation from the heat sink is stalling a big problem which many researchers are trying to solve. The aim of this study is to brief th...

The Sun encompasses planet Earth, supplies the heat that warms it, and even shakes it. The United Nation’s Intergovernmental Panel on Climate Change (IPCC) assumed that solar influence on Earth’s climate is limited to changes in solar irradiance and adopted the consensus opinion of a hydrogen-filled Sun—the Standard Solar Model (SSM). They did not consider the alternative solar model and instea...