The comparison of a discrete-continuous approach and a method of finite differences in solving the problem of unsteady-state heat and moisture transfer in the building envelope

Abstract This article is devoted to the development of methods for calculating heat and humidity regime in the building envelope. The equation of steady-state thermal conductivity with boundary conditions of the third kind and the formula for calculating heat losses of a building based on the heat transfer equation have been considered. The equation of unsteady-state thermal conductivity as well as its solution using the discrete-continual approach has also been studied. The solution of the unsteady-state heat conductivity problem with invariable over time boundary conditions using the discrete-continuous approach was proposed by A.B. Zolotov and P.A. Akimov. The subsequent modernization of the solution was conducted by V.N. Sidorov and S.M. Matskevich. The unsteady-state equation of moisture transfer based on Fick’s second law using the theory of moisture potential is derived. The solution of the unsteady-state moisture transfer equation using the finite difference method according to an explicit difference scheme as well as the solution of the unsteady-state moisture transfer equation using the discrete-continuous approach is demonstrated. To prove the effectiveness of using the discrete-continuous approach in the area of the unsteady-state humidity conditions we compared the calculation results of the distribution of moisture in a single-layer enclosing structure made of aerated concrete using two methods of moisture potential theory. It was found that the difference in the results of calculation by the discrete-continual formula and by the method of finite differences does not exceed 3.2%.

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DERIVATION OF THE EQUATION OF UNSTEADY-STATE MOISTURE BEHAVIOUR IN THE ENCLOSING STRUCTURES OF BUILDINGS USING A DISCRETE-CONTINUOUS APPROACH

International Journal for Computational Civil and Structural Engineering ◽

10.22337/2587-9618-2021-17-4-83-90 ◽

2021 ◽

Vol 17 (4) ◽

pp. 83-90

Author(s):

Kirill Zubarev

Keyword(s):

Boundary Conditions ◽

Moisture Transfer ◽

High Accuracy ◽

Continuous Method ◽

Engineering Practice ◽

Unsteady State ◽

Liquid Phases ◽

Continuous Approach ◽

Moisture Potential ◽

Transfer Mechanisms

Two differential equations of moisture transfer based on the theory of moisture potential have been considered. The first equation includes the record of moisture transfer mechanisms of vapor and liquid phases and their relationship. The second equation is a simplified form of the first equation which makes it possible to apply a discrete-continuous approach. The peculiar properties of the boundary conditions setting of the outside air for temperature and humidity fields have been presented. It is proved that the use of the discrete-continuous method provides high accuracy of calculations and can be used in engineering practice to assess the unsteady humidity regime of enclosing structures.

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UNSTEADY-STATE HEAT TRANSFER INVESTIGATION BY METHODS OF SOLVING THERMAL CONDUCTIVITY REVERSE PROBLEMS

10.1615/ihtc5.1250 ◽

1974 ◽

Author(s):

E. Tourilina ◽

I. T. Aladyev ◽

K. Voskresensky

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Unsteady State ◽

State Heat

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The use of sorption and excess sorption isotherm in the mathematical modeling of the unsteady-state heat and humidity regime of the building envelope

Journal of Physics Conference Series ◽

10.1088/1742-6596/2131/5/052072 ◽

2021 ◽

Vol 2131 (5) ◽

pp. 052072

Author(s):

Z Zhou ◽

K P Zubarev

Keyword(s):

Water Vapor ◽

Sorption Isotherm ◽

Moisture Transfer ◽

Sorption Isotherms ◽

Building Envelope ◽

Vapor Transfer ◽

Potential Capacity ◽

Partial Transfer ◽

Relative Potential ◽

Moisture Potential

Abstract In the given article the development of the moisture transfer equation based on the theory of moisture potential is considered. The task of combined heat and moisture transfer is one of the most complicated tasks in the building thermal physics field. The classical equations of moisture transfer by K.F. Fokin representing the transfer of moisture under the action of partial transfer potentials - the gradient of the partial pressure of water vapor and the gradient of humidity F - are listed. The possibility of uniform accounting of the combined water vapor transfer on the basis of the moisture potential F is described. The sorption isotherm for aerated concrete is constructed in accordance with the experiment carried out in a desiccator with an aqueous solution of sulfuric acid. A new equation of moisture transfer which takes into account moistening with vaporous moisture in the sorption zone of moisture and liquid moisture in the excess sorption zone of moisture is derived. In order to simplify the work with the obtained equation a new value of the relative potential capacity is introduced. A graph construction of sorption and excess sorption isotherms which are obtained using an analytical expression for the relative potential capacity is proposed. In the sorption zone of humidification the sorption and excess sorption isotherms coincide with the classical sorption isotherm. Meanwhile, in the excess sorption zone of humidification the sorption and excess sorption isotherms depend on temperature.

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Moisture potental theory application for modelling of enclosing structure unsteady-state moisture regime

Vestnik MGSU ◽

10.22227/1997-0935.2019.4.484-495 ◽

2019 ◽

pp. 484-495 ◽

Cited By ~ 2

Author(s):

About the authors: Vladimir G. Gagarin ◽

Kirill P. Zubarev

Keyword(s):

Moisture Transfer ◽

Single Layer ◽

Mineral Wool ◽

Expanded Polystyrene ◽

Moisture Regime ◽

Unsteady State ◽

Concrete Masonry ◽

Aerated Concrete ◽

Moisture Potential ◽

Maximum Moisture Content

Introduction. Known calculation methods for enclosing structure unsteady-state moisture regime proposed by K.F. Fokin, are examined. The first one describes moisture transfer in a sorption zone, and another allows calculation in oversorption zone also. “Thermodynamic moisture potential” of enclosing structure materials introduced by V.N. Bogoslovsky is described. Moisture potential F developed by V.G. Gagarin and V.V. Kozlov is shown. The moisture potential F allows describing water vapor and liquid moisture movement in material in a consistent way. The scientific novelty of the study is the development of calculation method based on moisture potential F. Practical relevance of the study is the possibility to obtain performance humidity values of enclosing structure materials by means of calculations for engineering practice. Materials and methods. A moisture transfer equation is derived on the basis of process physical interpretation, A mathematical model, consisting of heat conductivity equation, derived moisture transfer equation, spatial-time domain, boundary and initial conditions, is formulated. Moisture potential in single-layer and multilayer enclosing structures is determined using finite difference method. Results. Calculations for four types of enclosing structures are made on the basis of the proposed mathematical model: single-layer aerated concrete wall; a wall made of aerated concrete masonry base and clay brick cladding; a wall made of aerated concrete masonry base and mineral wool insulation with thin plaster layer; a wall made of aerated concrete masonry base and expanded polystyrene insulation with thin plaster layer. Conclusions. Calculated performance humidity values of enclosing structure materials were lower than values stated in regulatory documents. The presented results allow to define building heat loss definition and heating system design more accurately. Specification data on maximum wetting plane position obtained earlier were proved within the framework of the developed theory: in enclosing structures with aerated concrete base and mineral wool insulation maximum moisture content is located at the joint of plaster and insulation layers; in enclosing structures with aerated concrete base and expanded polystyrene insulation maximum moisture content is located in the insulation layer. Acknowledgements. Authors are deeply indebted to V.V. Kozlov, PhD in Technical Sciences, and V.K. Akhmetov, Doctor of Engineering Science, Professor, for discussion and useful comment in the course of study.

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Unsteady-State Heat Conduction in Semi-Infinite Regions With Mixed-Type Boundary Conditions

Journal of Heat Transfer ◽

10.1115/1.3247446 ◽

1985 ◽

Vol 107 (2) ◽

pp. 489-491 ◽

Cited By ~ 12

Author(s):

S. C. Huang

Keyword(s):

Heat Conduction ◽

Boundary Conditions ◽

Mixed Type ◽

Unsteady State ◽

State Heat ◽

Type Boundary

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Meshless analysis of unsteady-state heat transfer in semi-infinite solid with temperature-dependent thermal conductivity

International Communications in Heat and Mass Transfer ◽

10.1016/j.icheatmasstransfer.2005.10.008 ◽

2006 ◽

Vol 33 (2) ◽

pp. 231-239 ◽

Cited By ~ 19

Author(s):

Akhilendra Singh ◽

Indra Vir Singh ◽

Ravi Prakash

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Unsteady State ◽

Temperature Dependent ◽

State Heat ◽

Temperature Dependent Thermal Conductivity

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USING DISCRETE-CONTINUOUS APPROACH FOR THE SOLUTION OF UNSTEADY-STATE MOISTURE TRANSFER EQUATION FOR MULTILAYER BUILDING WALLS

International Journal for Computational Civil and Structural Engineering ◽

10.22337/2587-9618-2021-17-2-50-57 ◽

2021 ◽

Vol 17 (2) ◽

pp. 50-57

Author(s):

Kirill Zubarev

Keyword(s):

Building Materials ◽

Moisture Transfer ◽

State Equation ◽

Climate Impact ◽

Mineral Wool ◽

Moisture Regime ◽

Unsteady State ◽

Continuous Approach ◽

Aerated Concrete ◽

Building Walls

Moisture regime of enclosing structures is one of the most complicated and controversial directions in construction industry. Temporary climate impact on enclosing structures and low moisture inertia of building materials lead to the situation in which it is impossible to calculate the steady-state moisture regime. Numerical methods are usually used to assess the moisture behaviour of the enclosing structures. In the current paper, a differential equation of moisture transfer is formulated. The solution of the unsteady-state equation of moisture transfer was obtained using the discrete-continuous approach. Thus, a formula which allows scientists to calculate unsteady-state moisture transfer in multilayer walls of buildings was obtained. A two-layer building enclosing structure with aerated concrete base and mineral wool insulation was calculated.

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Mathematical modeling of the unsteady moisture condition of enclosures with application of the discrete-continuous approach

Vestnik MGSU ◽

10.22227/1997-0935.2020.2.244-256 ◽

2020 ◽

pp. 244-256

Author(s):

Vladimir G. Gagarin ◽

Kirill P. Zubarev

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Moisture Transfer ◽

Heat Insulation ◽

Moisture Distribution ◽

Analytical Expression ◽

Continuous Approach ◽

The Finite Difference Method ◽

Moisture Potential

Introduction. The paper considers mathematical models developed by K.F. Fokin, A.V. Lykov, V.I. Lukyanov, V.N. Bogoslovskiy, and H.M. Künzel and shows the advantages of using the moisture potential as compared with separate consideration of the transfer potentials. An analytical expression for the moisture potential F developed by V.G. Gagarin and V.V. Kozlov is given. Materials and methods. The article formulated a differential moisture transfer equation with time-constant coefficients and and described boundary conditions. An analytical expression determining the moisture potential using the discrete-continuous approach was obtained. Results. The article compares some calculation methods on the theory of moisture potential F for the single-layer aerated concrete enclosure, the two-layer brick wall, as well as two composite facade heat-insulation systems with external plaster layers with heat-insulation of mineral wool and foamed polystyrene. The solution of the unsteady equation of moisture transfer by the finite difference method using an explicit difference scheme and by the discrete-continuous method, the solution of the stationary equation of moisture transfer are considered. Conclusions. The moisture distribution obtained using the discrete-continuous approach, both quantitatively and qualitatively, coincides with the moisture distribution by the finite difference method. However, this distribution is obtained by the final formula without using the numerical method, which simplifies the calculation. The scientific novelty of the research consists in the development of a mathematical model based on the moisture potential F as well as in solving the equation of the unsteady moisture transfer through the discrete-continuous approach. The possibility of obtaining moisture distribution over the thickness of the enclosure according to the obtained formula is the practical relevance of the research.

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Heat and Mass Transfer Modeling to Predict Temperature Distribution during Potato Frying after Pre-Treatment with Pulsed Electric Field

Foods ◽

10.3390/foods10081679 ◽

2021 ◽

Vol 10 (8) ◽

pp. 1679

Author(s):

Gohar Gholamibozanjani ◽

Sze Ying Leong ◽

Indrawati Oey ◽

Phil Bremer ◽

Patrick Silcock ◽

...

Keyword(s):

Heat Conduction ◽

Electric Field ◽

Moisture Transfer ◽

Pulsed Electric Field ◽

Boiling Temperature ◽

Unsteady State ◽

Heat And Moisture Transfer ◽

State Heat ◽

Heat And Moisture ◽

Potato Disc

Based on unsteady state heat conduction, a mathematical model has been developed to describe the simultaneous heat and moisture transfer during potato frying. For the first time, the equation was solved using both enthalpy and Variable Space Network (VSN) methods, based on a moving interface defined by the boiling temperature of water in a potato disc during frying. Two separate regions of the potato disc namely fried (crust) and unfried (core), were considered as heat transfer domains. A variable boiling temperature of the water in potato discs was required as an input parameter for the model as the water is evaporated during frying, resulting in an increase in the soluble solid concentration of the potato sample. Pulsed electric field (PEF) pretreatment prior to frying had no significant effect on the measured moisture content, thermal conductivity or frying time compared to potatoes that did not receive a PEF pretreatment. However, a PEF pretreatment at 1.1 kV/cm and 56 kJ/kg reduced the temperature variation in the experimentally measured potato center by up to 30%. The proposed heat and moisture transfer model based on unsteady state heat conduction successfully predicted the experimental measurements, especially when the equation was solved using the enthalpy method.

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