Preliminary mathematical and numerical transient models of convective heating and drying of a brick

Abstract

The paper presents the initial approach to mathematical and numerical modelling and optimization of heat and mass transfer in elements of the masonry wall. The considered single moist brick is placed in the channel through which the dry air is flowing. Only one wall of the brick is in contact with the flowing air and through this boundary heat and moisture are exchanged. The non-equilibrium mathematical model is formulated for general case with three phases of moisture present in the porous building material, i.e., water vapour in the moist air filling the pores, liquid water (bound water) adsorbed at the surface of the solid component of the material and free liquid water either in a discontinuous form (funicular) or continuous one (pendular). However, at this stage of development of the numerical model the moisture in the form of motionless liquid water and water vapour which reside in the ceramic material are considered. Moreover, the moisture and heat diffusion in the porous hydroscopic material of the brick as well as moisture and heat convection in the flowing air are assumed. The numerical model is developed with the aid of the commercial software ANSYS Fluent and its advanced customisation functionalities like the User-Defined Function, User-Defined Scalar and User-Defined Memory. Subsequently, investigation of the influence of the mass transfer coefficient between the free liquid water and moist air in the porous building material are carried out.

Analysis of Non-Equilibrium and Equilibrium Models of Heat and Moisture Transfer in a Wet Porous Building Material

“…In the non-equilibrium model liquid and heat transfer are related to moisture movement, but in the pendular state of water they are neglected. The total pressure, p, in the porous medium is assumed constant and equal to 101,325 Pa, which allows for simplification of both mathematical models and elimination of the equation for balance of air [11,12]. In the two subsequent sections both models of concurrent moisture and heat transfer, namely the non-equilibrium and equilibrium ones, are presented.…”

“…A model of the moisture transfer in the clay brick was developed Allam et al [10]. This model was based on the same driving potentials used in [9].The extended model of moisture and heat transfer in homogeneous porous building materials was presented in [11,12]. It consisted of four transport equations, describing vapor, dry air, liquid moisture, and energy transport.…”

“…The extended model of moisture and heat transfer in homogeneous porous building materials was presented in [11,12]. It consisted of four transport equations, describing vapor, dry air, liquid moisture, and energy transport.…”

Investigation of the equilibrium and non–equilibrium models of heat and moisture transport in a wet porous building material

“…Allam et al [7] developed the model of the hygrothermal transfer in the clay brick which utilized the temperature and vapor partial pressure as driving potentials. Recently, the model of heat and moisture transfer in porous building materials which consisted of four equations, i.e., energy, liquid moisture, vapor and dry air balance equation, was presented in [8,9]. In this model temperature, liquid moisture volume fraction as well as vapor and dry air densities were used as independent variables.…”

“…In this model temperature, liquid moisture volume fraction as well as vapor and dry air densities were used as independent variables. In the case of hygroscopic porous textile or fibrous materials heat and moisture transfer models are formulated applying, e.g., the temperature, water vapor concentration in pores, moisture concentration in fibers and water content in the fibrous batting as independent variables [8]. These models account for moisture movement induced by the partial water vapor pressure, a supersaturation state in condensing region as well as the dynamic moisture absorption of fibrous materials and the movement of liquid condensate.…”