Optimizing the exponent in the heat balance and refined integral methods

2009 ◽  
Vol 36 (2) ◽  
pp. 143-147 ◽  
Author(s):  
T.G. Myers
Keyword(s):  
Heat Balance ◽  
Integral Methods ◽  
The Heat Balance

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.

The Heat-Balance Integral—Further Considerations and Refinements

1961 ◽  
Vol 83 (1) ◽  
pp. 83-85 ◽  
Author(s):  
Theodore R. Goodman
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Surface Temperature ◽  
Heat Balance ◽  
Transient Heat Conduction ◽  
Temperature Dependent ◽  
Integral Methods ◽  
Infinite Slab ◽  
The Heat Balance ◽  
Excellent Accuracy

Integral methods have previously been applied to transient heat conduction in a slab with constant thermal properties. In this paper the method is extended so as to include temperature-dependent thermal properties in the analysis. In addition, it is shown how to improve the accuracy of a solution by increasing the order of the polynomial used to represent the temperature profile. For the case of a prescribed step surface temperature in a semi-infinite slab, a quartic profile is shown to give excellent accuracy.

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 Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
S. L. Mitchell ◽  
T. G. Myers
Keyword(s):  
Phase Change ◽  
Least Squares ◽  
Heat Balance ◽  
Integral Method ◽  
New Method ◽  
Error Measure ◽  
One Dimensional ◽  
Integral Methods ◽  
Heat Balance Integral Method ◽  
The Heat Balance

We employ the Heat Balance Integral Method (HBIM) to solve a number of thermal and phase change problems which occur in a multitude of industrial contexts. As part of our analysis, we propose a new error measure for the HBIM that combines the least-squares error with a boundary immobilisation method. We describe how to determine this error for three basic thermal problems and show how it can be used to determine an optimal heat balance formulation. We then show how the HBIM, with the new error measure, may be used to approximate the solution of an aircraft deicing problem. Finally we apply the new method to two industrially important phase change problems.

scholarly journals Approximate solutions to one-phase Stefan-like problems with space-dependent latent heat

2020 ◽  
pp. 1-33
Author(s):  
J. BOLLATI ◽  
D. A. TARZIA
Keyword(s):  
Latent Heat ◽  
Heat Balance ◽  
Integral Method ◽  
Approximate Solutions ◽  
Convective Condition ◽  
One Dimensional ◽  
Stefan Number ◽  
Integral Methods ◽  
Approximate Integral ◽  
The Heat Balance

The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), the modified HBIM and the refined integral method (RIM). Taking advantage of the exact analytical solutions, we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalised Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimising the least-squares error, obtaining also approximate solutions for the classical Stefan problem.

Analysis of electro- and thermophysical processes occurring during electrocontact baking of flour products.

2020 ◽  
Vol 29 (11) ◽  
pp. 50-55
Author(s):  
V.I. Maklyukov ◽  
◽  
E.O. Gerasimova ◽  
N. V. Labutina ◽  
E.N. Rogozkin ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Theoretical Calculation ◽  
Heat Balance ◽  
Electric Contact ◽  
Wheat Dough ◽  
Baking Process ◽  
Free Moisture ◽  
Contact Heating ◽  
The Heat Balance

The article considers the results of research conducted during electric contact heating of rye-wheat dough pieces. It is established that the electrical conductivity of the crumb dough does not depend on the total humidity of the material, but mainly on the amount of free moisture. Using the current and temperature graphs, you can imagine how free moisture changes during the baking process and the influence of the thermophysical and colloidal process on the change in the value of free moisture. Experimentally determined the amount of heat that is spent on baking 1 kg of bread. The accuracy of the theoretical calculation of this parameter in the heat balance of the baking chamber is confirmed.

Refined thermal calculation of the locomotive heat engine collector

2020 ◽  
pp. 56-58
Author(s):  
P.V. Gubarev ◽  
D.V. Glazunov ◽  
V.G. Ruban ◽  
A.S. Shapshal
Keyword(s):  
Experimental Data ◽  
Electric Motor ◽  
Heat Balance ◽  
Thermal Imaging ◽  
Heat Engine ◽  
Thermal Calculation ◽  
Calculation Results ◽  
Cooling Air ◽  
The Heat Balance ◽  
Traction Electric Motor

The thermal calculation of the locomotive traction engine collector is proposed. The equations of the heat balance of its elements are obtained taking into account the cooling air. The calculation results and experimental data of thermal imaging control are presented. Keywords: traction electric motor, collector, thermal calculation, thermal imaging control. [email protected]

Research on On-Line Anti-Icing Technology for Carenary along Electrified Railway

2013 ◽  
Vol 676 ◽  
pp. 321-324
Author(s):  
Lei Guo ◽  
Qun Zhan Li
Keyword(s):  
Simulation Model ◽  
Heat Balance ◽  
Normal Operation ◽  
Balance Equations ◽  
Model Based ◽  
Static Var Generator ◽  
On Line ◽  
Electrified Railway ◽  
The Heat Balance

Accidents of icing on catenary have great impacts on normal operation of trains. An on-line anti-icing technology used static var generator (SVG) for catenary was proposed, which can prevent icing formation without interrupting trains normal operation. The heat balance equations for catenary were solved, whose results were compared with data provided by TB/T 3111 and testing show the equation was correct. The simulation model based on Matlab was bulit , whose results and analysis show the correctness of the method.

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