scholarly journals Logistic Heat Integral Methods for the One-Phase Stefan Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
O. P. Layeni ◽  
A. M. Adegoke
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Stefan Problem ◽  
Heat Balance ◽  
Time Dependent ◽  
Integral Methods ◽  
The One ◽  
The Heat Balance ◽  
Moving Front

Logistic versions of the heat balance integral and refined integral methods are introduced. A benchmark with a one-phase Stefan problem under constant and time-dependent boundary conditions shows remarkable accuracy at estimating temperature distribution and position of the moving front.

scholarly journals Numerical solution of Stefan problem with time-dependent boundary conditions by variable space grid method

2009 ◽  
Vol 13 (4) ◽  
pp. 165-174 ◽  
Author(s):  
Svetislav Savovic ◽  
James Caldwell
Keyword(s):  
Temperature Distribution ◽  
Boundary Conditions ◽  
Stefan Problem ◽  
Finite Differences ◽  
Moving Boundary ◽  
Grid Method ◽  
Time Dependent ◽  
Time Step ◽  
Space Grid ◽  
Variable Space

The variable space grid method based on finite differences is applied to the one-dimensional Stefan problem with time-dependent boundary conditions describing the solidification/melting process. The temperature distribution, the position of the moving boundary and its velocity are evaluated in terms of finite differences. It is found that the computational results obtained by the variable space grid method exhibit good agreement with the exact solution. Also the present results for temperature distribution are found to be more accurate compared to those obtained previously by the variable time step method.

scholarly journals Numerical and experimental study of pyrophoric activated metal Mg surface combustion characteristics

2018 ◽  
Vol 5 (5) ◽  
pp. 172064
Author(s):  
Hesong Huang ◽  
Zhongxiang Tong ◽  
Chaozhe Wang ◽  
Biao Wang
Keyword(s):  
Temperature Distribution ◽  
Heat Balance ◽  
High Speed ◽  
Difficult Problem ◽  
Combustion Mechanism ◽  
Thermal Imager ◽  
Balance Equations ◽  
Adiabatic Wall ◽  
The Heat Balance ◽  
Infrared Thermal Imager

The combustion of multi-hole pyrophoric activated metal is solid combustion and the combustion mechanism is quite complex, which is a difficult problem to be solved. Once the pyrophoric activated metal is exposed to air, the oxygen diffuses to the interior of the activated metal within plenty of holes and reacts with it, which enlarges the contact area with oxygen. Consequently, the whole combustion is vigorous and the temperature rises rapidly. To study the combustion mechanism of the chaff, the surface heat balance equation is established in this work by taking Mg as the activated metal. To solve this equation, the chaff adiabatic wall temperature distribution is computed by computational fluid dynamics in the presence of high-speed airflow. Then, the chaff surface temperature distribution is obtained by solving the heat balance equations. Finally, numerical and experimental results obtained via an infrared thermal imager are compared to demonstrate the effectiveness of the established equation.

scholarly journals Integral Balance Methods for Stokes’ First Equation Described by the Left Generalized Fractional Derivative

Physics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 154-166 ◽  
Author(s):  
Ndolane Sene
Keyword(s):  
Approximate Solution ◽  
Fractional Derivative ◽  
Heat Balance ◽  
Time Derivative ◽  
Double Integral ◽  
Derivative Operator ◽  
Integral Methods ◽  
Fractional Time Derivative ◽  
The Heat Balance ◽  
Generalized Fractional Derivative

In this paper, the integral balance methods of the Stokes’ first equation have been presented. The approximate solution of the fractional Stokes’ first equation using the heat balance integral method has been proposed. The approximate solution of the fractional Stokes’ first equation using the double integral methods has been proposed. The generalized fractional time derivative operator has been used. The graphical representations of the cubic profile and the quadratic profile for the Stokes’ first problem have been provided. The impacts of the orders of the generalized fractional derivative in the Stokes’ first problem have been investigated. The exponent of the assumed profile for the Stokes’ first equation has been discussed.

Sign in / Sign up

Export Citation Format

Share Document