Abstract:-Enhanced heat transfer in tubes under laminar flow conditions can be found in coils or corrugated tubes or in the presence of high wall relative roughness, curves, pipe fittings or mechanical vibration. Modeling these cases can be complex because of the induced secondary flow. A modification of the Graetz problem for non-Newtonian power-law flow is proposed to take into account the augmented heat transfer by the introduction of an effective radial thermal diffusivity. The induced mixing was modeled as an incr… Show more
“…Based on the case study with: D efA = 10 −5 m 2 .s −1 and F heat1 = 15, Figure allows observing the influence of the diffusion parameters change. Methods for estimating the effective radial conductivity of heat are described by Morais and Gut () while method for determine effective radial diffusivities under laminar flow are presented by Dantas et al ().…”
Section: Resultsmentioning
confidence: 99%
“…Enhanced diffusion can occur due to corrugated tube wall, high relative wall roughness, mechanical vibration or presence of curves or coils (Bergles & Joshi, ). In the case of heat transfer, Morais and Gut () defined an enhancement factor for the radial diffusivity ( F h eat ) that multiplies the thermal conductivity of the fluid, and consequently the thermal diffusivity ( α = k / ρ. C p ).…”
Section: Mathematical Modelingmentioning
confidence: 99%
“…Since the inner tube of the ViscoLine™ Monotube is corrugated, effective diffusion parameters were used for product flow: D efA = 10 −5 m 2 .s −1 (Dantas et al, ) F heat1 = 15 (Morais & Gut, ). The reference mass diffusion value for liquid–liquid systems is 10 −9 m 2 s −1 (Bird et al, ; Foster & Cussler, ).…”
Section: Case Studymentioning
confidence: 99%
“…Heat and mass diffusions can be enhanced in laminar flow with the use of coiled tubes or corrugated tubes. Moreover, mechanical vibration or high relative wall roughness can also induce mixing under laminar flow (Bergles & Joshi, ; Dantas, Pegoraro, & Gut, ; Morais & Gut, ).…”
Thermal processing of a liquid food under diffusive laminar flow was modeled coupling fluid flow, heat transfer, diffusion, and inactivation/degradation kinetics. Model considers associated countercurrent tubular exchangers for heating and cooling and the holding tube. Axial and radial distributions of temperature and concentration in the food product (non‐Newtonian power‐law flow) were accounted and parameters for effective diffusion of heat and mass were used to model enhanced transfer from corrugate tubes or coils. Heat exchanged with environment was included. A case study of 40.2 °Brix blackberry juice pasteurization is presented, and results discussed. Influence of effective diffusivities, inlet heating media temperature and product flow rate were analyzed, and it was possible to minimize anthocyanin degradation while meeting food safety requirements (5‐log reduction on yeasts) considering the contributions from the whole process.
Practical applications
Mathematical modeling of a chemical process based on first principles, also called physical or phenomenological models, is a powerful tool to couple fluid flow, heat transfer, mass diffusion, and reaction kinetics, thus creating a virtual prototype of the process that is useful for design, analysis, control, and optimization. The model presented considers important features that are often neglected in process design, but without unnecessarily increasing complexity and computational requirements, such as in a CFD model (computational fluid dynamics) that requires a detailed representation of the geometry and specialized software and hardware for simulation. Lower computational times allow the use of this model to solve optimization or predictive control problems with a reliable representation of transport phenomena and reaction kinetics.
“…Based on the case study with: D efA = 10 −5 m 2 .s −1 and F heat1 = 15, Figure allows observing the influence of the diffusion parameters change. Methods for estimating the effective radial conductivity of heat are described by Morais and Gut () while method for determine effective radial diffusivities under laminar flow are presented by Dantas et al ().…”
Section: Resultsmentioning
confidence: 99%
“…Enhanced diffusion can occur due to corrugated tube wall, high relative wall roughness, mechanical vibration or presence of curves or coils (Bergles & Joshi, ). In the case of heat transfer, Morais and Gut () defined an enhancement factor for the radial diffusivity ( F h eat ) that multiplies the thermal conductivity of the fluid, and consequently the thermal diffusivity ( α = k / ρ. C p ).…”
Section: Mathematical Modelingmentioning
confidence: 99%
“…Since the inner tube of the ViscoLine™ Monotube is corrugated, effective diffusion parameters were used for product flow: D efA = 10 −5 m 2 .s −1 (Dantas et al, ) F heat1 = 15 (Morais & Gut, ). The reference mass diffusion value for liquid–liquid systems is 10 −9 m 2 s −1 (Bird et al, ; Foster & Cussler, ).…”
Section: Case Studymentioning
confidence: 99%
“…Heat and mass diffusions can be enhanced in laminar flow with the use of coiled tubes or corrugated tubes. Moreover, mechanical vibration or high relative wall roughness can also induce mixing under laminar flow (Bergles & Joshi, ; Dantas, Pegoraro, & Gut, ; Morais & Gut, ).…”
Thermal processing of a liquid food under diffusive laminar flow was modeled coupling fluid flow, heat transfer, diffusion, and inactivation/degradation kinetics. Model considers associated countercurrent tubular exchangers for heating and cooling and the holding tube. Axial and radial distributions of temperature and concentration in the food product (non‐Newtonian power‐law flow) were accounted and parameters for effective diffusion of heat and mass were used to model enhanced transfer from corrugate tubes or coils. Heat exchanged with environment was included. A case study of 40.2 °Brix blackberry juice pasteurization is presented, and results discussed. Influence of effective diffusivities, inlet heating media temperature and product flow rate were analyzed, and it was possible to minimize anthocyanin degradation while meeting food safety requirements (5‐log reduction on yeasts) considering the contributions from the whole process.
Practical applications
Mathematical modeling of a chemical process based on first principles, also called physical or phenomenological models, is a powerful tool to couple fluid flow, heat transfer, mass diffusion, and reaction kinetics, thus creating a virtual prototype of the process that is useful for design, analysis, control, and optimization. The model presented considers important features that are often neglected in process design, but without unnecessarily increasing complexity and computational requirements, such as in a CFD model (computational fluid dynamics) that requires a detailed representation of the geometry and specialized software and hardware for simulation. Lower computational times allow the use of this model to solve optimization or predictive control problems with a reliable representation of transport phenomena and reaction kinetics.
“…Optimal control of the drying process is fundamental and requires complete information on the drying behavior of the materials, requiring an accurate model capable of predicting water removal rates and describing the drying performance of each product under certain conditions (Khatchatourian et al, 2013). Mathematical models are an effective tool in the development, design, and improvement of drying systems and analysis of mass transfer phenomena during the drying process (Silva et al, 2014;Morais & Gut, 2015;Zarein et al, 2015;Qiu et al, 2018). Dincer & Dost (1995) developed analytical models to characterize the mass transfer during drying of objects presenting regular geometry (plate, cylinder, and sphere) and based on the assumption that the effective moisture diffusivity during drying process remains constant.…”
Dioscorea trifida tuber contains starch, vitamins, minerals and bioactive compounds. It is perishable, requiring dehydration treatment to increase shelf life. This study aimed to investigate the mass transfer parameters and thermodynamic properties of Dioscorea trifida using Refractance Window (RW) drying (70, 80, and 90 °C). It was observed that the dehydration process occurred in a short time (40 min). The moisture diffusivity and the mass transfer coefficient were determined using the Dincer and Dost model. The diffusivity coefficients ranged from 2.62 × 10 -6 at 6.13 × 10 -6 m 2 s -1 , the mass transfer coefficient ranged from 3.46 × 10 -4 at 4.04 × 10 -4 m s -1 and the estimated of activation energy was 44.091 kJ mol -1 . In the Dioscorea trifida Refractance Window drying, the enthalpy and entropy are positive and negative, respectively, decreasing with increasing temperature and thus indicating that the process is endothermic. Gibbs free energy increases with increasing temperature, indicating that the process does not occur spontaneously.
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