Analytical solution and numerical approaches of the generalized Levèque equation to predict the thermal boundary layer

In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail

Numerical Solution of Extended Graetz Problem by Orthogonal Collocation and Crank-Nicholson Method

Abstract The present set of themes related to the investigations of heat transfer by convection and the transport phenomenon in a cylindrical pipe in laminar flow, which is to explore the evolution of the temperature profile for a fluid flow in fully developed laminar flow. A numerical method was developed in this work, for visualization of the temperature profile, whose strategy of calculation is based on the orthogonal collocation method followed by the finite difference method (Crank-Nicholson method). The calculations were effected through a FORTRAN computer program and the results show that orthogonal collocation method giving better results than Crank-Nicholson method

CFD modeling and computation of convective heat coefficient transfer of automotive disc brake rotors

Braking system is one of the important control systems of an automotive. For many years, the disc brakes have been used in automobiles for safe retardation of the vehicles. During braking enormous amount of heat will be generated and for effective braking sufficient heat dissipation is essential. The thermal performance of disc brake depends upon the characteristics of the airflow around the brake rotor and hence the aerodynamics is an important in the region of brake components. A CFD analysis is carried out on the braking system as a case study to make out the behaviour of airflow distribution around the disc brake components using ANSYS CFX software. We are interested in the determination of the heat transfer coefficient (HTC) on each surface of a ventilated disc rotor varying with time in a transient state using CFD analysis, and then imported the surface film condition data into a corresponding FEM model for disc temperature analysis.Braking system is one of the basic organs to control a car. For many years, the disc brakes have been used in automobiles for safe retardation of the vehicles. During braking, enormous amount of heat will be generated, and for effective braking, sufficient heat dissipation is essential. The specific air flow surrounding the brake rotor depends on the thermal performance of the disc brake and hence, the aerodynamics is an important in the region of brake components. A CFD analysis is carried out on the braking system as the study of this case, to make out the behaviour of air flow distribution around the disc brake components using ANSYS CFX software. The main object of this work is to calculate the heat transfer coefficient (h) of the full and ventilated brake discs as a function of time using the CDF analysis which will be used later in the transient thermal analysis of the disc in ANSYS Workbench 11.0

Similarity solution and Runge Kutta method to a thermal boundary layer model at the entrance region of a circular tube: The Lévêque Approximation

In the thermal entrance region, a thermal boundary layer develops and also reaches the circular tube center. The fully developed region is the zone in which the flow is both hydrodynamically and thermally developed. The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the thickness of the thermal boundary layer is zero and decreases gradually to the fully developed value. In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented. By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by Fortran code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail

Exact solution of boundary value problem describing the convective heat transfer in fully-developed laminar flow through a circular conduit

This paper proposes anexact solution in terms of an infinite series to the classical Graetz problem represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages are elaborated to reach the solution of the Graetz problem. MATLAB was used to compute the eigenvalues of the differential equation as well as the coefficient series. However, both the Nusselt number as an infinite series solution and the Graetz number are based on the heat transfer coefficient and the heat flux from the wall to the fluid. In addition, the analytical solution was compared to the numerical values obtained by the same author using a FORTRAN program, showing that the orthogonal collocation method gave better results. It is important to note that the analytical solution is in good agreement with published numerical data

Stres s analysis of automotive ventilate d disc brake rotor and pads using finite element method

The complexity of the physical or technological systems to be developed or studied led to employing numerical methods based on the principle of an approach as possible nominal solution, but these require large computations requiring efficient computers. The computer code ANSYS also allows the determination and the visualization of the structural deformations due to the contact of slipping between the disc and the pads. The results of the calculations of contact described in this work relate to displacements, Von Mises stress on the disc, contact pressures of the inner and outer pad at various moments of simulation. One precedes then the influence of some parameters on the computation results such as rotation of the disc, the smoothness of the mesh, the material of the brake pads and the friction coefficient enter the disc and the pads, the number of revolutions and the material of the disc, the pads groov

Supply Chain Management Strategy for an Effective Collaboration: A Case Study in Malaysia

The relationship between the refinery and other oil palm industries represent there is an industry that affects other supply chain actors through power collaboration for influencing the supply chain strategy. The purpose of this study is to analyze supply chain relationships in an oil palm refinery. The study employed case study research which the data collection adopted through semi-structured interviews and observation. Oil palm refinery in Malaysia was selected in the case study and analyzed using supply chain operations reference (SCOR) model. Finding showed that the oil palm refinery adopted push strategy. Then, the refinery and vessels emerged to be dominant actors in this supply chain relationship. The result provided implications for analyzing the supply chain relationships between supply chain actors which can be applied to any industry that decide to establish an effective collaboration

Development of low liquid fuel Burnera

Recently, most of the gas turbine combustion research and development involves in lowering the emissions emitted from the combustor. Emission causes adverse affect to the world and mankind especially. Main concern of the present work is to reduce the NOx emission since the CO emission could be reduced through homogeneous mixing of fuel and air. Homogeneous mixing of fuel and air is also needed in order to reduce NOx emission. A liquid fuel burner system with radial air swirler vane angle of 30o, 40o, 50o and 60o has been investigated using 163mm inside diameter combustor. Orifice plates with three different sizes of 20mm, 25mm and 30mm were inserted at the back plate of swirler outlet. All tests were conducted using diesel as fuel. Fuel was injected at two different positions, i.e. at upstream and downstream of the swirler outlet using central fuel injector with single fuel nozzle pointing axially outwards. Experiment has been carried out to compare the three emissions NOx, CO and SO2. NOx reduction of about 53 percent was achieved for orifice plate of 20mm with downstream injection compared to orifice plate of 20mm with upstream injection. CO2 and SO2 was reduced about 26 percent and 56 percent respectively for the same configuration. This comparison was taken using swirler vane angle of 60o. The overall study shows that larger swirler vane angle produces lower emission results compared to the smaller ones. Smaller orifice plates produce better emission reduction. Meanwhile, downstream injection position significantly decreases the emission levels compared to upstream injection position. Combination of smallest orifice plate and largest swirler vane angle with downstream injection produce widest and shortest flame length

A discourse on structure of acknowledgments in doctoral dissertation in a multiracial setting

The existence of acknowledgment in academic paper has become an academic practice. This paper explores the generic structure of doctoral dissertation acknowledgments of three major races in Malaysia through discourse analysis. It also aims to find differences of the moves and steps used by the three races. Fifty samples from each race were selected based on their availability from local and foreign universities. The fundamental moves and steps were scrutinised and documented in the categories of the collected acknowledgements. The findings of the study disclosed that the structural arrangement of doctoral dissertation acknowledgements has the same structure with the arrangement of Arab dissertation acknowledgements. However, there is no vast difference of acknowledgement writing between the three races. From the findings, this study comes out with a modified model of generic structure of doctoral dissertation acknowledgements. The findings of this paper might be of interest to genre analysts as well as to second language theorists and practitioners even though it was done on small corpora. Based on the outcome of this paper, it is suggested that future study is carried out to determine the effects of academic disciplines differences in writing acknowledgements of doctoral dissertation

Experimental analysis on the formation of CO-NO-HC in swirling flow combustion chamber

The main purpose of this paper is to evaluate the production of CO-NO-HC emissions while varying the swirl angle of curve vane radial swirler. Swirling flow generates central recirculation region (CRZ) which is necessary for flame stability and enhances fuel air mixing. Therefore designing an appropriate air swirler is a challenge to produce stable, efficient and low emission combustion inside burner system. Four radial curved vane swirlers with 30o, 40o, 50o and 60o vane angles corresponding to swirl numbers of 0.366, 0.630, 0.978 and 1.427 respectively were used in this experiment to measure the vane angles effect on emission production in the combustion chamber. Emission measurements were conducted at 5 axial distances from the burner throat, and at 5 locations along the radius starting the central axis at each section. It was found that at the core near the throat, CO and HC concentrations are low due to high available O2 and high fuel mixing rate producing efficient combustion. This is due to the high shear region created the high swirl flow