Mass Transfer Operations Research Articles

The effect of turbulence on the minimum thickness of a liquid film flowing down a vertical tube

When a liquid flows down a vertical tube at a low flowrate, it may not be able to completely cover the surface as a film, and the flow will comprise a number of rivulets separated by unwetted areas. Predictions of the minimum film thickness and corresponding minimum flowrate below which films cannot be sustained are needed in many industrial heat and mass transfer operations. In this paper a model is developed using the minimum energy method to calculate the minimum film thicknesses that can be maintained for flows down a vertical tube. It is concluded that inclusion of the effect of turbulence in the model can significantly increase the values of the calculated minimum film thicknesses. In these calculations (for 100⁰C water flowing down a 6 mm inside diameter tube) the effect of turbulence increased as the tube to liquid contact angle increased. For a flow at the highest contact angle of 90⁰, the minimum film thickness increased by 22% above the laminar value and the corresponding minimum flowrate increased by 75%. The model presented in this paper can be used to calculate the thermal performance of falling film evaporators over the whole range of flowrate.

Strengthening the Attainment of Major Competencies of Program Outcomes through Open-ended Experiment using Statistical Designs

Abstract—Unit operations are very essential part of the chemical engineering and allied disciplines; and hence, basic knowledge about the principles and equipment used for various unit operations is mandatory for process engineer. Unit operations course introduces the foundation of process engineering concepts at the second year of undergraduate program of Bachelor of Engineering in Biotechnology. This course mainly focuses on the most essential unit operations utilized in Chemical and allied process industries such as mass transfer, heat transfer, momentum transfer and mechanical operations. The conventional teaching approach practiced so far in Unit Operations Laboratory course was not so effective in the attainment of certain specific core competencies of Program Outcomes (POs). To tackle this challenge, we introduced a system of classifying laboratory experiments into four distinct categories: Demonstration, Exercise, Structural Inquiry, and Open-ended experiments. These categorized experiments were thoughtfully crafted to target various significant technical and professional outcomes such as Investigations of Complex Engineering Problems, Communication, Life-long learning, Follow of Standard Operating Procedure (SOP) and Good Laboratory Practices (GLP). The evaluation criteria for each type of experiment were aligned with program outcomes, competencies, and performance indicators. This alignment proved highly beneficial in achieving a more precise assessment of program outcomes. This study focuses on implementing an interactive and collaborative learning approach in the Unit Operations laboratory course. of Experiments. More precisely, the study employs Central Composite Design (CCD) and Response Surface Methodology (RSM) concepts to examine how various factors influence the Leaching (Solid-Liquid Extraction) process. The leaching process is most important unit operations used in the extraction of substances from solids. The study helped in addressing several important competencies pertaining to the Program Outcomes- PO-4: Demonstrating the capacity to design, execute experiments, and analyze data; PO-10: Exhibiting effective communication skills; PO-12: Embracing lifelong learning; PSO-13: Adhering to Standard Operating Procedures (SOP) and Good Laboratory Practices (GLP). The assessment of student performance employed a rubric-based approach, and the attainment of program outcomes was documented. It was observed that, open-ended experimental approach, led to the improvements in the attainment of PO’s in terms of competencies and performance indicators. To enhance the teaching-learning process, formal and anonymous feedback was gathered from students to identify areas of improvement and deficiencies. Keywords—Central Composite Design; Collaborative learning; Design of experiments; Open-ended experiment; Program outcome; Response Surface Methodology;

Facile synthesis of ZIF-8 modified PES beads with improved sorption characteristics for elimination of Congo red from aquatic stream

The adsorption is a well know mass transfer operation that was employed for more than decades in water industry. Predominately carbon based, inorganic materials and MOF etc. have been widely employed as an adsorbent. In contrast in the present study polymeric nano beads incorporated with MOF were synthesized for efficient adsorption performances. The polymeric beads were obtained from Polyethersulfone (PES) and was incorporated with ZIF-8. In the inception phase, ZIF-8 incorporated PES polymeric beads were prepared through non-solvent induced phase separation (NIPS) process to discern the factors governing the adsorption mechanism. The zeta potential analysis showed that adding ZIF-8 into the PES matrix changed the charge from negative to positive. The ZIF-8@PES showed a maximum adsorption efficiency of 99.7% for CR dye removal compared to 14% of unmodified PES. The enhanced CR removal due to ZIF-8 addition was specifically due to π-π interactions between the linker and CR molecules, open Zn metal sites and electrostatic attraction. The sorption followed the Langmuir isotherm and Elovich kinetic model. The performance and regeneration studies showed that the modified beads were 91.1% efficient up to 4 cycles.

Performance of slurry contact adsorber operating under high gravity for removal of fluoride

Fine adsorbent particles though associated with large surface area and high adsorption rate are not employed in fixed bed adsorber for wastewater treatment due to high-pressure drop. In this investigation, slurry contact adsorption wherein fine adsorbent particles can be utilized was studied for the removal of fluoride using commercial activated charcoal as adsorbent (size<100 µm). The mass transfer operation was performed in two rotating contactors (rotating packed bed and rotating spiral) operating under centrifugal acceleration up to fifty times the terrestrial gravity, and conventional contactors (continuous stirred tank and fixed bed). The results indicated that the removal efficiency with slurry contact adsorption is higher in rotating spiral contactors compared to rotating packed bed or traditional contactors. Maximum utilization (equilibrium loading) of adsorbent particles at contactor exit is approached at high rotational speed and adsorbent dosage, and low feed flow rate and feed concentration. The magnitude of the volumetric mass transfer coefficient in a rotating spiral contactor obtained from mathematical modeling varied between 1.5 × 10−2 1/s to 8.0 × 10−2 1/s.

Gas/Liquid Operations in the Taylor-Couette Disc Contactor: Continuous Chemisorption of CO2

Gas/liquid contactors are widely used in chemical and biotechnological applications. The selection and design of bubble-column-type gas/liquid contactors requires knowledge about the gas distributor design to provide appropriate gas flow patterns. This study presents the continuous chemisorption of CO2 in 0.1 molar sodium hydroxide solution in a counter currently operated gas/liquid Taylor-Couette disc contactor (TCDC). This vertical-column-type contactor is a multi-stage agitated gas/liquid contactor. The performance of a lab-size TCDC contactor in gas/liquid mass transfer operations was investigated. The apparatus design was adjusted for gas/liquid operations by installing perforated rotor discs to provide a rotational-speed-dependent dispersed gas phase holdup in the column. The parameters of dispersed gas phase holdup, volumetric mass transfer coefficient and residence time distribution were measured. In the first step, hydraulic characterization was performed. Then, the efficiency in gas/liquid operations was investigated by continuous neutralization of 0.1 molar sodium hydroxide with a gas mixture of 30 vol% CO2 and 70 vol% N2. Temperature, rotational speed and gas flow rate were varied. The desired pH value of pH 9 at the column outlet was kept constant by adjusting the sodium hydroxide feed. From the experimental results, the volume-based liquid-side mass transfer coefficient kLa was deduced in order to model the reaction according to the two-film theory over the column height. The CSTR cascade model fitted the experimental data best. The experimental results confirm stable and efficient reactive gas/liquid contact in the Taylor-Couette disc contactor.

Heat and mass transfer analysis of MHD stagnation point flow of carbon nanotubes with convective stretching disk and viscous dissipation

The research of single and multi-wall carbon nanotubes (SWCNTs/MWCNTs) mixed in sodium alginate-based nanofluid with MHD stagnation-point flow on a convective heated stretching disk with viscous dissipation and suction effects is being done with the intention of decoding the heat and mass transmission mechanism. It is possible to transform PDEs that govern the boundary layer into ODEs. MATLAB’s Bvp5c is used to numerically solve the revised equations. The Yamada-Ota model and the Buongiorno model are used in this work to scrutinize the flow, heat, and mass transfer parameters. The following parameters were brought up for discussion: volume fraction nanoparticle, magnetic parameter, suction, Brownian motion, thermophoresis, Lewis number, Eckert number, Biot number, stretching, and thermophoresis. This study found that nanofluid (SWCNT/sodium alginate) has a superior flow, heat, and mass transfer rate than nanofluid (MWCNT/sodium alginate). Graphical representations of the effects of various factors are shown, and a comparison of current and prior findings is given in a table. A comparison of current and previous findings reveals a 0% relative inaccuracy. The velocity ratio parameter has solutions that look close to the separation value. The performance of heat and mass transfer operations may be improved by increasing suction parameters. Increases in Brownian motion [Formula: see text] and suction decrease the temperature profile, whereas increases in velocity ratio and magnetic parameters increase velocity. This research is critical for estimating flow, temperature, and concentration behavior for CNTs with incorporated physical properties.

The role of coupled water and solute diffusion and product shrinkage during osmotic dehydration

Osmotic dehydration (OD) is a coupled mass transfer operation where foods are partially dewatered while simultaneously impregnated with solute from the solution. Nonetheless, water loss ( W L ) and solute gain ( S G ) are treated as independent processes for modeling purposes and the effect of their coupling on the estimation of water/solute diffusivities ( D w , D s ) and equilibrium dehydration/impregnation levels ( W L e , S G e ) has not been elucidated yet. The objective of this study was to develop a new model considering the coupled mass transport of water and solute occurring during OD of foods and to evaluate the contribution of this coupling on the estimation of D w , D s , W L e , and S G e in comparison with the rigid/shrinking solid assumption. Experimental W L , S G , and volume kinetics were obtained during OD of papaya cubes in sucrose solutions (50°Bx; 45, 55 and 65 °C) and further analyzed with the proposed model solved under different assumptions: coupled and partially coupled mass transfer equations (MTEs) in a shrinking solid and uncoupled MTEs in a rigid solid (no shrinkage) with uncorrected and corrected lengths for diffusion. Properties D w , D s , W L e , and S G e with coupled MTEs and shrinkage were estimated in the ranges of (2.52–5.48) × 10 −10 m 2 /s, (3.91–5.43) × 10 −10 m 2 /s, 0.47–0.53 g/g and 0.18–0.30 g/g, respectively, with partially coupled and uncoupled MTEs leading to a significant overestimation of diffusivities under the tested experimental conditions (up to 281% for water and 75% for solute), even when shrinkage was considered in the 3D model solution. Current findings demonstrate that, like shrinkage, coupling of W L and S G is of upmost importance for a reliable estimation of mass transfer properties during OD. • A mass transfer model is proposed to analyze the OD of shrinking foods. • Mass transfer of water and solute are fully coupled by a density-related term. • OD experiments with papaya cubes were conducted to validate the model. • The effect of different modeling assumptions on mass transfer properties is analyzed. • Non-fully coupled models overestimate diffusivities even considering food shrinkage.

HEAT AND MASS TRANSFER CONSIDERATIONS IN THE DESIGN OF A COILED ABSORBER FOR AMMONIA-WATER REFRIGERATION SYSTEM

The performance of the absorber significantly affect the overall efficiency of any absorption refrigeration system. One of the major reasons for the poor design of the absorber for ammonia-water refrigeration systems is the neglect of mass transfer resistances in the vapour or liquid phase in favour of only heat transfer considerations. Heat removal is critical to the absorption process, however, the ammonia gas is constantly absorbed by the liquid ammonia-water solution. This means that two-phase mass and heat transfer operations take place during the absorption process. Therefore, this implies that, for any proper absorber design, both heat and mass transfer considerations are paramount. Accurate absorber design is further predicated on accurate properties correlations. The correlations required for the absorber design include liquid and vapour enthalpies, saturated vapour pressure, specific heat capacity of water and ammonia vapour, liquid solution dynamic viscosity, liquid solution density, surface tension, liquid solution thermal conductivity, liquid-liquid diffusivity and vapour-liquid diffusivity. Procedures for calculating these parameters have been presented in this paper and their accuracy with previous studies compared. Results showed relatively low percentage deviations and so can be applied for the design and simulation of the absorber. Designs of the absorber for various cooling capacities have been carried in this paper. The variation of ammonia vapour temperatures, liquid ammonia-water solution temperatures, cooling water temperatures, and flow rates of ammonia-water solution and ammonia vapour across the absorber is investigated for the four cooling capacities. For refrigeration systems with cooling capacities of 1 kW, 2 kW, 3 kW and 4 kW, the calculated lengths for a water-cooled coiled absorber are 4.484 m, 8.1467 m, 12.50459 m and 14.78329 m respectively. The calculated overall heat transfer coefficients for the absorption process for the four cooling capacities (1 kW, 2 kW, 3 kW and 4 kW) were 0.4427, 0.4376, 0.4208 and 0.4309 kWm-2K-1 while the mass transfer coefficients were 3.721 x10-9, 4.206 x10-9, 4.556 x10-9and 4.856 x10-9 m2s-1 respectively. Concurrent flow is considered in this study, but the procedure can also be applied to countercurrent flow. KEYWORDS: Absorption Refrigeration, Ammonia Water Heat and Mass Transfer, Design

MATLAB Model for designing mass exchange networks: A case study on pyrolysis plant for effective waste minimization

Enormous amounts of raw materials are consumed through various industrial processes worldwide. Vast amounts of raw materials utilized by the chemical industry typically go to waste. Mass integration is a distinctive method of streamlining the consumption of raw materials in chemical industries. Mass integration was developed by employing principles of pinch analysis in order to optimize mass exchange networks. To apply the concepts of mass integration, this work introduces a Matrix Laboratory (MATLAB) code designed on the bases of the composition driving force graphical design approach. This MATLAB code was devised to analyze details of mass transfer operations with the lowest number of calculations possible. The algorithm’s detailed coding allows for designing mass exchange networks above and below the pinch. For maximum mass recovery, pinch principles were employed, and were delivered in an educational manner to students and young researchers in the field. The MATLAB code was designed to develop a useful toolbox for process integration as well as determine the number of plates required for each mass exchanger. The model was tested at pyrolysis plant with the aim of achieving mass targets and optimum matches for maximum recovery at the lowest costs possible.

Optimization of semi‐pulsatile liquid‐liquid extraction operations in milli‐channels

AbstractThe work in this manuscript presents liquid‐liquid extraction augmentation and optimization due to flow pulsations on a continuous flow. The mass transfer is achieved via a transfer species (acetic acid) that diffuses in the aqueous phase (water), which is in a continuous flow, from the organic phase (toluene), exhibiting pulsed flow pattern. It is observed through experiments that the incorporation of pulsation leads to enhanced extraction/mass transfer compared to continuous flows. Also, an increase of the pulsation parameters, such as amplitude and frequency, increases the mass transfer, but when the process is evaluated in terms of economy, it is found that the rate of extraction per unit power is maximum for moderate frequencies and amplitudes. Based on the experiments, a Linton and Sherwood‐like correlation for determining extracted concentration at the exit of the test section in semi‐pulsatile flow conditions is proposed. During the course of experiments, it is found that the flow pattern changes from dispersed‐type flow pattern of the organic phase to slug and then slug dispersed with an increase of superficial velocity of toluene, at a particular superficial velocity of the water. Also, the total power consumed during the extraction process increases with an increase in the product of amplitude and frequency. With the experimental approach presented in this paper, one will be able to optimize semi‐pulsatile liquid‐liquid mass transfer operations.

Numerical investigation of performance trade-off characteristics of a packed bed dehumidifier using aqueous blends of lithium chloride and calcium chloride

Current research in dehumidification systems is mainly focused on thermally driven liquid desiccant systems. However, the selection of proper desiccant solution has a greater significance on the performance of a dehumidifier. In this perspective, current work is presented with governing equations of energy, mass and species balance to study the performance of a dehumidifier. The governing equations are solved using finite difference method coupled with Jacobi’s model for an air–desiccant contact system of a cross-flow packed bed adiabatic dehumidifier operating with different desiccant blends of lithium chloride (LiCl) and calcium chloride (CaCl2) solution. The effect of variation in blend proportion on outlet parameters of a packed bed dehumidifier is patterned under various desiccant to air (L/G) mass flow rate ratios. It is observed that the addition of CaCl2 desiccant solution into LiCl changes the nature of thermo-physical properties of blends‚ which are predicted using non-random two liquid (NRTL) equation. Further, a trade-off analysis among the performance parameters is presented. It demonstrates that dehumidifier performance paradox such as enthalpy effectiveness (ɛh), moisture removal rate (MRR) and moisture effectiveness (ɛm) have a tendency to be optimal for 35% LiCl with 5% CaCl2 blend (BL1) among all blends at L/G ratio of 2. The variation of thermodynamic properties (air temperature, humidity, desiccant temperature and desiccant concentration) inside the dehumidifier module is visualized in terms of contour plots. Furthermore, the irreversibility in heat and mass transfer operation for the optimal blend is investigated in terms of physical and chemical exergy destruction paradigm. The result of such investigation elucidated that the maximum chemical exergy destruction is 0.88 kW, whereas the physical exergy destruction is 0.06 kW.

On the integration of Mathcad capabilities into a mass transfer operations course in Chemical Engineering studies

AbstractMass transfer unit operations are of extreme importance to chemical engineers. However, they involve complex and tedious calculations which provoke real fear among the students who end up failing and, sometimes, quitting. The exclusive use of hand calculations in engineering studies is discouraging, old‐fashioned, and a primary source of mistakes. The integration of software packages very much facilitates the calculations and engages the students. Computing skills using the latest technologies are prized by employers and can be critical in a recruitment process. This paper reports an example of the unique capabilities of the Mathcad software for the implementation of more appealing teaching strategies. Unknowns and equations are easily associated with specific process variables and engineering phenomena. Thus, if used conveniently, Mathcad Prime can improve the students’ predisposition to learn.

Determination and use of feasible operation region in flash distillation control

Flash distillation is essentially a single stage mass transfer operation. The flash distillation operation is used in this work to highlight the importance of identifying the zone where a system has an appropriate behavior. In this sense, this paper presents a discussion about the use of the feasible operation region (FOR) in the design of process control structures. For this reason, three control structures are presented. The first one is the traditional one, a PID multiloop control structure. The second structure uses the FOR graphically in order to determine a better operation point and improve the control response. Finally, the third structure uses the FOR numerically for guiding the controller using a modified control structure. The improvement of the closed loop operation of the flash using the last control structure is notorious when compared with the traditional control structure.

Modeling mass transfer for adsorptive removal of Pb(II) onto phosphate modified ordered mesoporous carbon (OMC)

Phosphate modified ordered mesoporous carbon (MOMC-NP) has been synthesized and proven to be an effective adsorbent for Pb(II) removal from aqueous solutions. However, the key application components of the mass transfer operations and diffusion coefficient have not been determined. In this study, a modified Finite Bath Diffusion Control Model was mathematically developed containing a constant related to the radius of the adsorbent particle and the fractional attainment of adsorption. The adsorption experiments were conducted under various initial Pb(II) concentrations ranging from 60 mg L−1 to 100 mg L−1. The results suggested that the modified Finite Bath Diffusion Control Model was more applicable to the experimental data than the original Finite Bath Diffusion Control Model. The average value of the diffusion coefficient (λD¯) obtained from the modified finite bath diffusion control model was 1.63 × 10−2 cm2 s−1 indicating the effective diffusivity in the adsorption of Pb(II) on MOMC-NP. Overall, the modified Finite Bath Diffusion Control Model exhibited the precise description and simulation of the mass transfer kinetics for Pb(II) adsorption onto MOMC-NP. Therefore, the modified Finite Bath Diffusion Control Model could be effectively used to investigate the mass transfer kinetics of the adsorption process.

Effect of surfactants on mass transfer coefficients in bubble column contactors: an interpretative critical review study

Abstract Since surfactants have been recognized as the most frequently faced contaminants of bubble column-related processes over time, their impact on the mass transfer operation of these columns has become a demanding research interest for two recent decades. Despite the similarities expressing the overall negative and positive influence of these chemicals on mass transfer coefficients and specific interfacial area, respectively, the discrepancies and, sometimes, paradoxical results are still under debate in the literature. To make a more comprehensive recognition of the mentioned subject, the current paper has tried to pave the path by reviewing all the major methods utilized in related research works. Thereafter, an interpretative argumentative comparison of the main findings of relevant studies has also been proposed, enlightening some of the research gaps which can be the potential candidates for future studies.

Volumetric Reconstruction of Taylor Slug Gas Flow Using IR Transceiver in Minichannels

Taylor slug flow commonly occurs in crude oil pipelines, mini-/microreactors, space propulsion thrusters, heat exchangers, and nuclear reactors. The flow is an intermittent gas regime which occurs in flowing liquid inside pipelines and capillary tubes. Measurement of liquid-film thickness and cross-sectional and volumetric void fraction is necessary for an effective operation and safety of many industrial processes involving heat and mass transfer operations. In industrial applications such as miniheat exchangers, lab-on-chip devices, and pulsating heat pipes, gas–liquid Taylor flow enhances heat and mass transfer. The dominance of surface tension force is responsible for the occurrence of Taylor flow. Online measurement of void fraction is essential to determine heat and mass transfer characteristics of systems involving the two-phase flow. This article focuses on developing an instrumentation technique for the measurement of volumetric voids in minichannels. The effect of thickness of liquid films and nose/tail shape on infrared (IR) transceiver irradiation is studied. The experiments are done in two borosilicate glass tubes (3.40 and 1.50 mm inner diameter and 0.6 and 2.5 mm thickness, respectively) to measure liquid-film thickness and volumetric void fraction using a pair of IR transceiver. A numerical model is developed using COMSOL Multiphysics for the same experimental conditions. The effect of nose/tail curvature shape and liquid-film thickness on volumetric void fraction is predicted using a novel simple algorithm. A 3-D reconstruction technique is developed by measuring the undulations at the sides and top/bottom of the Taylor slug using a pair of IR transceiver output current (mA).

Gas transfer management by membrane contactors in an oenological context: Influence of operating parameters and membrane materials

Oxygen management in wine is one of most challenging issue for winemakers. Indeed, an excess of dissolved oxygen (O2) can prematurely age wine and leads to organoleptic deviation.Membrane contactors composed of hydrophobic hollow fiber are becoming a relevant technology especially for gas-liquid mass transfer operations. Nevertheless, their utilization in an oenological context to manage oxygen in wine has not been comprehensively studied. Fouling phenomena could be problematic and may limit their utilization during winemaking.The aim of this study is to develop (i) a simple and rapid method to characterize membrane contactors and (ii) to investigate the effects of two types of membrane contactor composed either of polypropylene (PP) or of PP with a dense coat layer (Teflon). The specific methodology proposed using volumetric transfer coefficient (KL·a) is used to investigate the performance of the membranes on gas transfer in terms of wetting and fouling, as well as the effect of the membrane material. After liquid flow rate optimization, which was necessary to determine a suitable value (300 mL·min−1), the membrane contactors’ performances were characterized with water, a wine model solution and two red wines with different fouling index. After several hydrodynamic optimization operations, we consider that the membrane contactors studied could remove oxygen while carbon dioxide is dissolved with KL·aCO2 close to 20 × 10−5 s−1 for both prototypes. The addition of a dense coat layer in an oenological context may be necessary for a non-prepared wine with a high fouling index.

Numerical equivalence between SPH and probabilistic mass transfer methods for Lagrangian simulation of dispersion

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length ℓ=2DΔt, at least given a “dense enough” distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute’s displacement by dispersion in a time step.

High power short time microwave finish drying of paprika (Capsicum annuum L.): Development of models for moisture diffusion and color degradation

The commercially available paprika at 16.25% (db) moisture was quickly finish-dried using microwaves at higher power density (5–25 W g−1). The moisture diffusivity was estimated using Fick’s second law of diffusion and the generalized kinetic model was used to estimate the color degradation rates. The moisture diffusivity and color degradation showed a close correlation with the difference between the average product temperature (T) achieved due to microwave heating, and average glass transition temperature (Tg) of paprika. Acceleration in moisture diffusion and color degradation was observed with the rise in the difference between the T and Tg. Further, the color degradation rate showed correlation with monolayer moisture content, average moisture content, T, and Tg of paprika during finish drying. The constants of the Gordon and Taylor model showed the less plasticization effect of water. Also, Tg showed a good correlation between water activity and moisture content. The activation energies for moisture diffusion and color degradation were found to be 92.53 and 11.03 kJ mol−1, respectively. The microstructural analysis of finish-dried paprika showed the expanded and newly formed intercellular spaces. The developed correlations can be used to simulate heat and mass transfer operations such as drying and sterilization.

Modeling of Effective Moisture Diffusivity in Corn Tortilla Baking.

The analytical solutions of the Fick's law of diffusion for the moisture content in products that can be represented as an infinite plate, considering variable diffusivity, can be useful in studies when accurate estimations of effective diffusivity and concentration are needed.