scholarly journals Identification of heat and mass transfer processes in bread during baking

2005 ◽  
Vol 9 (2) ◽  
pp. 73-86 ◽  
Author(s):  
Ivanka Zheleva ◽  
Vesselka Kambourova
Keyword(s):  
Partial Differential Equations ◽  
Moisture Content ◽  
Differential Equations ◽  
Moisture Transfer ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Mass Transfer Processes ◽  
Model Equations ◽  
Heat And Moisture ◽  
Simultaneous Heat

A mathematical model representing temperature and moisture content in bread during baking is developed. The model employs the coupled partial differential equations proposed by Luikov. Dependences of mass and thermal properties of dough on temperature and moisture content are included in the model. Resulting system of non-linear partial differential equations in time and one space dimension is reduced to algebraic system by applying a finite difference numerical method. A numerical solution of the model equations is obtained and simultaneous heat and moisture transfer in dough during baking is predicted. The changes of temperature and moisture content during the time of the process are graphically presented and commented.

scholarly journals On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer

2005 ◽  
Vol 2005 (3) ◽  
pp. 275-291 ◽  
Author(s):  
Don Kulasiri ◽  
Ian Woodhead
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Porous Materials ◽  
Moisture Transfer ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Potential Gradients ◽  
Heat And Moisture ◽  
Moisture Profiles ◽  
Moisture Potential

Luikov's theory of heat and mass transfer provides a framework to model drying porous materials. Coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically in a setting suitable for industrial drying situations. We discuss the nature of the solutions using the physical properties ofPinus radiata. It is shown that the temperature gradients play a significant role in deciding the moisture profiles within the material when thickness is large and that models based only on moisture potential gradients may not be sufficient to explain the drying phenomena in moist porous materials.

Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Dirichlet Boundary Conditions ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Lyapunov Inequalities ◽  
Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

Beam Vibrations With Time-Dependent Boundary Conditions

1950 ◽  
Vol 17 (4) ◽  
pp. 377-380
Author(s):  
R. D. Mindlin ◽  
L. E. Goodman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Time Dependent ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Vibration Problems

Abstract A procedure is described for extending the method of separation of variables to the solution of beam-vibration problems with time-dependent boundary conditions. The procedure is applicable to a wide variety of time-dependent boundary-value problems in systems governed by linear partial differential equations.

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