МОДЕЛИРОВАНИЕ ПРОЦЕССА РАСПЫЛИТЕЛЬНОЙ СУШКИ СУСПЕНЗИИ ПРОТЕИНОВОГО ЗЕЛЕНОГО КОНЦЕНТРАТА (ПЗК)

A multiphase model was developed to simulate heat and mass transfer during the baking process of flat bread (Sangak bread) by considering volume changes. In the proposed model, the equations of heat and mass transfer for liquid (water) and gas (vapor andCO2) phases were developed based onFourier's,Fick's andDarcy's laws, respectively. In addition, the effect of evaporation–condensation phenomenon was considered using the nonequilibrium relation of evaporation rate in the mass and heat transfer equations. The quantity of specific heat and density of each mesh was predicted using series and parallel models, and values of unknown parameters were estimated using the standard least square method. The nonlinear partial differential equations of the model were solved by using the finite element method byCOMSOLMultiphysics software. The changes in bread thickness were determined by ImageJsoftware. The model validation was also accomplished by comparing the predicted temperature and moisture content with the experimental results. The highR2and the low root mean squared error between experimental and predicted data confirmed the validity of the developed mathematical model.Practical ApplicationsThe uniformity of the product quality and the energy loss during the baking process has always been considered as a great challenge in the baking industry. In recent years, there has been increasing demand for minimally processed and near‐fresh quality products. To produce the part‐baked Sangak bread, the dough fully processes and baking occurs to at level in which, the texture properly forms and low color changes occur. Nowadays, it is essential to find methods based on equations, mathematical modeling and engineering principles to improve process control. In order to develop these models, the profound understanding of the procedures during the baking, particularly, mass and energy transfer are essential. Since, there are few researches on evaporation‐condensation and volume change in contact baking; it is important to understand its mechanism for exploiting this phenomenon in the food industries.

A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss–Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.

A recursive operator method was used to obtain a general solution of the system of linearized differential equations of heat and mass transfer in hardening concrete in a heating chamber. The solution contains arbitrary analytic functions determined from the boundary and initial conditions.

The mass-conduction (diffusion) properties of sunflower seeds of the "MAS 95 OL" variety were experimentally investigated. From the experimental drying curves obtained in the intradiffusion kinetic mode at two temperatures of the drying agent (air), the coefficients of mass conductivity (moisture diffusion) were calculated by the zonal method, which are presented as dependences on the moisture content of the core and shell, respectively. It is shown that the coefficients of mass conductivity of nuclei and shells depend on the moisture content of the material and differ significantly both in magnitude and in the nature of the concentration dependences. The coefficient of mass conductivity of nuclei in different areas of moisture content is 15-25 times higher than that of shells, this is explained by differences in the structure of these materials. In the area of moisture content less than 0.5 kg / (kg of dry materiall), both dependences have the same character of concave functions increasing with moisture content, this is a consequence of the same mechanism of mass transfer dominating in this area of moisture content, which is osmotic mass transfer. In seed kernels, the area of moisture content of more than 0.5 kg / (kg of dry material) is absent, but in seed shells it is present and vapor diffusion dominates in it. The data on the coefficient of mass conductivity for seed shells were compared with the coefficient of mass conductivity of another capillary-porous colloidal material with a similar structure - wood. The nature of the concentration dependences for both materials is the same, which is explained by the similarity of the morphological structure of wood and seed shells, which have a tree-like structure. The coefficient of mass conductivity of the seed kernel was compared with the coefficients of mass conductivity of other capillary-porous colloidal materials of plant and animal origin. Comparison showed that they have the same order of mass conductivity coefficient: 10-9 m2/s. This is explained by the identical structure of these materials, which have a cellular structure, and, probably, by the same mechanisms of mass transfer at the corresponding moisture content. The obtained data on the coefficients of mass conductivity of the kernel and shell of sunflower seed can be used for the kinetic calculation of the process of convective drying of this material based on the solution of the differential equations of internal heat and mass transfer A.V. Lykov with the representation of the seed as a two-layer body.

Contrary to the [regular] thick bread, the thin flatbread is consumed in few countries, which explains the scarcity of published research on this type of bread. The present work aims to investigate experimentally and numerically the effect of different heat flux profiles on temperature field and moisture content in the thin flatbread during the baking process, as well as their effect on the quality of the final baked bread. In order to investigate the effect of different heat flux profiles during the baking process, a machine built on a laboratory scale is used to bake the bread pieces used as samples in this experiment. Heat and mass transfer equations are modeled numerically using the finite difference method. The equations are discretized using the finite difference method and solved using the unconditionally stable transient implicit method implemented in MATLAB. Also, the energy required for baking is measured and compared for different heat flux profiles. Reasonable agreement is observed between the experimental and numerical results. Three different heat flux profiles, namely constant, descending, and ascending profiles, are evaluated experimentally and numerically, and the baked pieces of bread are subjected to sensory evaluation as well as colorimetry. It is observed that the baked bread samples subjected to the ascending profile are of a better quality due to the uniform and proper heating during the baking process. It is also observed that the type of heat flux profile affects the final bread quality and determines the energy consumption of the process.

Numerical study of regenerative evaporative coolers for sub-wet bulb cooling with cross- and counter-flow configuration

A two-stage third-order numerical scheme is proposed for solving ordinary differential equations. The scheme is explicit and implicit type in two stages. First, the stability region of the scheme is found when it is applied to the linear equation. Further, the stability conditions of the scheme are found using a linearized homogenous set of differential equations. This set of equations is obtained by applying transformations on the governing equations of heat and mass transfer of incompressible, laminar, steady, two-dimensional, and non-Newtonian power-law fluid flows over a stretching sheet with effects of thermal radiations and chemical reaction. The proposed scheme with an iterative method is employed in two different forms called linearized and non-linearized. But it is found that the non-linearized approach performs better than the linearized one when residuals are compared through plots. Additionally, the proposed scheme is compared to the second-order central finite difference method for second-order non-linear differential equations and the Keller-Box/trapezoidal method for a linear differential equation. It is determined that the proposed scheme is more effective and computationally less expensive than the standard/classical finite difference methods. Moreover, the impact of magnetic parameter, radiation parameter, modified Prandtl and Schmidt numbers for power-law fluid, and chemical reaction rate parameter on velocity, temperature, and concentration profiles are displayed through graphs and discussed. The power-law fluid’s heat and mass transfer simulations are also carried out with varying flow behavior index, sheet velocity, and mass diffusivity. We hoped that this effort would serve as a guide for investigators tasked with resolving unresolved issues in the field of enclosures used in industry and engineering.

Heat and mass transfer in individual coffee beans during roasting were simulated using computational fluid dynamics (CFD). Numerical equations for heat and mass transfer inside the coffee bean were solved using the finite volume technique in the commercial CFD code Fluent; the software was complemented with specific user-defined functions (UDFs). To experimentally validate the numerical model, a single coffee bean was placed in a cylindrical glass tube and roasted by a hot air flow, using the identical geometrical 3D configuration and hot air flow conditions as the ones used for numerical simulations. Temperature and humidity calculations obtained with the model were compared with experimental data. The model predicts the actual process quite accurately and represents a useful approach to monitor the coffee roasting process in real time. It provides valuable information on time-resolved process variables that are otherwise difficult to obtain experimentally, but critical to a better understanding of the coffee roasting process at the individual bean level. This includes variables such as time-resolved 3D profiles of bean temperature and moisture content, and temperature profiles of the roasting air in the vicinity of the coffee bean.

Natural convection, diffusion and chemical reaction in a catalytic reactor: Numerical results

Drip irrigation strategy for tomatoes grown in greenhouse on the basis of fuzzy Borda and K-means analysis method

The effect of axialacoustic Ž elds on the evaporationof individualdroplets is investigatedboth experimentallyand theoretically. A setup was developed in which images of droplets moving through an acoustic Ž eld were acquired using a state-of-the-art, high-speed, intensiŽ ed video system. The evaporation rates of droplets were determined from the droplet diameters measured from these images. Experimental investigations using methanol droplets showed that the presence of an acoustic Ž eld signiŽ cantly enhances the evaporation of droplets. The evaporation rate is a strong function of the acoustic amplitude, but increases only slightlywith frequency. The effect of acoustic oscillations on water and methanol droplet evaporation was theoretically modeled by numerically integrating the differential equations for droplet mass, momentum,and heat transfer. The model uses quasisteady correlations for momentumheat and mass transfer. The model predicted the measured trends correctly. However, the quantitative agreement of these predictions with the experimental data depends strongly on the correlations for Nussult and Sherwood numbers used to model the energy and mass transfer, respectively.

Solutions of Luikov equations of heat and mass transfer in capillary porous bodies through matrix calculus: a new approach

Two-dimensional laminar boundary-layer equations of momentum, heat and mass transfer have been numerically solved tinder forced convection. A finite difference approximation of the governing equations in a Goertler-type variable domain has been implemented on computer. To provide rigorous initial conditions at x 0 in the boundary-layer code, differential equations governing heat and mass transfer in the stagnation region have been set up and solved numerically. The effect of outer flow condition on skin friction as well as heat and mass transfer has been demonstrated. Results obtained made an improvement over past theoretical predictions based on analytical approximation, and agreed favorably with experimental data available.

Green's function method (GFM) and mathematical solution for coupled equations of transport problem during convective drying

A mathematical model was developed for the absorption of gas in liquid considering diffusion and a reaction of a gas through a non-isothermal, exothermic, irreversible first order reaction. The model consists of a set of coupled partial differential equations for heat and mass transfer, which were solved using a finite-difference backward implicit scheme. Parameters like the Thiele modulus, the Arrhenius factor and the Biot number for mass transfer of different kinetic mechanisms were optimized using a genetic algorithm. The utility of this model is illustrated by applying it to the absorption of chlorine gas into n-decane solution. A comparison of this model with literature has also been done.