Modeling of the Convective Thermal Ignition Process of Solid Fuel Particles

1990 ◽  
Vol 112 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
Jing-Tang Yang ◽  
Gwo-Guang Wang ◽  
Hung-Yi Li
Keyword(s):  
Boundary Layer ◽  
Gas Phase ◽  
Azimuthal Angle ◽  
Ignition Process ◽  
Thermal Ignition ◽  
Boundary Layer Equations ◽  
Runge Kutta Method ◽  
Convective Thermal ◽  
Dimensional Boundary ◽  
Fuel Particles

This work uses the boundary layer theory to study the thermal ignition process of the solid particle. The theoretical model explores the two-dimensional boundary layer equations in the gaseous phase. The governing equations of mass, momentum, energy, and species in gas phase are first transformed to ordinary differential equations through series expansion with respect to the azimuthal angle. The equations are then quasi-linearized to be the initial value problem and solved using Runge-Kutta method. The minimum heat flux from the gas phase to the fuel is evaluated as the most suitable criterion for the convective thermal ignition. The influences of the heat transfer rate, fluid dynamics, and the gas phase chemical reaction rate on the ignition delay and ignition position are discussed in detail.

scholarly journals Numerical Method in Two Dimensional Boundary Layer Theory for Incompressible Viscous Fluid

2013 ◽  
Vol 38 ◽  
pp. 61-73
Author(s):  
MA Haque
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Initial Value Problem ◽  
Shooting Method ◽  
Boundary Layer Equation ◽  
Incompressible Viscous Fluid ◽  
Initial Value ◽  
Box Scheme ◽  
Runge Kutta Method ◽  
Dimensional Boundary

In this paper laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) Shooting Method. In Shooting Method, the boundary value problem has been converted into an equivalent initial value problem. Finally the Runge-Kutta method is used to solve the initial value problem. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16549 Rajshahi University J. of Sci. 38, 61-73 (2010)

scholarly journals Simultaneous Free Convection and Heat Generation on a Horizontal Isothermal Circular Cylinder

2015 ◽  
Vol 9 (12) ◽  
pp. 21 ◽  
Author(s):  
Sajjad Sedighi ◽  
Mohammad Saeed Aghighi
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Generation ◽  
Heat Rate ◽  
Horizontal Cylinder ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Boundary Layer Equations ◽  
Linear Partial Differential Equations ◽  
Dimensional Boundary

<p class="zhengwen"><span lang="EN-GB">The linear boundary layer of the free flow around a circular horizontal cylinder with uniform surface temperature in the presence of heat generation was studied. Upon obtaining the non-dimensional boundary layer equations, the Runge-Kutta series method was used to solve the non-linear partial differential equations numerically. The surface shear stress results and surface heat rate were subsequently obtained in terms of the internal shell friction and the local Nusselt number respectively. The following heat generation parameters (C) were selected:  0.0, 0.2, 0.5, 0.8, and 1.0. The following results were obtained: 1) increasing C led to a corresponding increase u, v , VM , and θ , 2) Increasing i led to a corresponding increase in u, v , and VM, and 3) increasing C increased velocity variations and, naturally, the value of Cf, and 4) increasing i from i=0 to i=100 led to a decrease in the Nusselt number (Nu). </span></p>

Application of a General Finite-Difference Method to Boundary Layer Flows

1972 ◽  
Vol 1 (3) ◽  
pp. 146-152
Author(s):  
S. D. Katotakis ◽  
J. Vlachopoulos
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Boundary Layer Flows ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Temperature Boundary ◽  
Dimensional Boundary ◽  
Finite Difference Solution ◽  
Suction Or Injection ◽  
Layer Problem

A straight-forward and general finite-difference solution of the boundary layer equations is presented. Several problems are examined for laminar flow conditions. These include velocity and temperature boundary layers over a flat plate, linearly retarded flows and several cases of suction or injection. The results obtained are in excellent agreement with existing accurate solutions. It appears that any kind of steady, two-dimensional boundary layer problem can be solved thus with accuracy and speed.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

On three-dimensional boundary layer flow over surface irregularities

1980 ◽  
Vol 373 (1754) ◽  
pp. 311-329 ◽  
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Solution Technique ◽  
Parabolic Boundary ◽  
Boundary Layer Equations ◽  
Surface Irregularities ◽  
Dimensional Boundary ◽  
Layer Flow

The three-dimensional pipeflow boundary layer equations of Smith (1976) are shown to apply to certain external flow problems, and a numerical method for their solution is developed. The method is used to study flow over surface irregularities, and some three-dimensional separated flows are calculated. Upstream influence in the form of so-called ‘free interactions’ requires an iterative solution technique, in which the initial conditions for the parabolic boundary layer equations must be determined to satisfy a downstream condition

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

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