Mathematical Modelling of Conveyor-Belt Dryers with Tangential Flow for Food Drying up to Final Moisture Content below the Critical Value

This work presents the mathematical modeling of the conveyor-belt dryer with tangential flow operating in co-current, which has the advantage of improving the preservation of the organoleptic and nutritional qualities of the dried food. On the one hand, it is a more cumbersome dryer than the perforated cross flow belt dryer but, on the other hand, it has a low air temperature in the final section where the product has a low moisture content and, therefore, it is more heat sensitive. The results of the mathematical modeling allowed a series of guidelines to be developed for a rational design of the conveyor-belt dryer with tangential flow for the specific case of the moisture content of the final product XF lower than the critical one XC (XF < XC). In fact, this work follows a precedent in which a mathematical model was developed through the differentiation of the drying rate equation along the dryer belt with the hypothesis that the final moisture content XF of the product was higher than the critical one XC. The relationships between the extensive quantities (air flow rate and product flow rate), the intensive quantities (temperatures, moisture content and enthalpies) and the dimensional ones (length and width of the belt) were then obtained. Finally, based on these relationships, the rules for an optimized design for XF < XC were obtained.

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Conveyor-Belt Dryers with Tangential Flow for Food Drying: Mathematical Modeling and Design Guidelines for Final Moisture Content Higher Than the Critical Value

Inventions ◽

10.3390/inventions5020022 ◽

2020 ◽

Vol 5 (2) ◽

pp. 22

Author(s):

Dario Friso

Keyword(s):

Mathematical Modeling ◽

Moisture Content ◽

Rational Design ◽

Conveyor Belt ◽

Design Guidelines ◽

Final Moisture Content ◽

Temperature Sensitive ◽

Optimized Design ◽

Tangential Flow ◽

Product Flow

The mathematical modeling presented in this work concerns the conveyor-belt dryer with the tangential flow of air with respect to food. This dryer, if operating in co-current, has the advantage of well preserving the organoleptic and nutritional qualities of the dried product. In fact, it has a low air temperature in the final stretch where the product has low moisture content and is therefore more temperature sensitive. It is a bulkier dryer than the continuous through-circulation conveyor dryer with a perforated belt. The latter is therefore more frequently used and has received greater study attention from researchers and designers of the industry. With the aim to propose guidelines for a rational design of the conveyor-belt dryer with tangential flow, a mathematical model was developed here through the differentiation of the drying rate equation followed by its integration performed along the dryer belt. Consequently, and with the assumption that the final moisture content XF of the product is higher than the critical moisture content XC, the relationships between the intensive quantities (temperatures, humidity and enthalpies), the extensive quantities (air and product flow rates) and the dimensional ones (length and width of the belt), were obtained. Finally, on the basis of these relationships, the rules for an optimized design for XF > XC were obtained and experimentally evaluated.

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Conveyor-Belt Dryers with Tangential Flow for Food Drying: Development of Drying ODEs Useful to Design and Process Adjustment

Inventions ◽

10.3390/inventions6010006 ◽

2021 ◽

Vol 6 (1) ◽

pp. 6

Author(s):

Dario Friso

Keyword(s):

Moisture Content ◽

Conveyor Belt ◽

Design Guidelines ◽

Final Moisture Content ◽

Optimized Design ◽

Tangential Flow ◽

Process Adjustment ◽

Mathematical Investigation ◽

Adjustment System ◽

The Relationship

The mathematical investigation presented in this paper concerns the conveyor-belt dryer with tangential flow operating in co-current. This dryer is bigger than the continuous through-circulation conveyor dryer but has the advantage of better preserving the organoleptic and nutritional qualities of the dried product. In a previous work a mathematical modeling of the conveyor-belt dryer with tangential flow was carried out to offer guidelines for its optimized design. The last of those design guidelines indicated the need for an optimized adjustment of the dryer to ensure the constant maintenance of the final moisture content of the product. The fast and very precise measurement of the moisture content as the first step in the feedback chain was therefore necessary. Considering the difficulty of this type of measurement, two specific ordinary differential equations (ODEs) were obtained with the mathematical investigation of this work. Their solution became a relationship between the final moisture content of the product, the outlet air temperature, and other quantities that could be easily implemented in an automatic dryer control system. Therefore, the fast and accurate and much less expensive measurement of the temperature of the air leaving the dryer, owing to the relationship found, replaces the measurement of moisture content for the adjustment system. The experimental verification of the relationship highlighted the need to introduce a modification by which the relationship was finally validated.

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Mathematical Modeling to Estimate the Critical Oil Flow Rate for Sand Production Onset in the Mansouri Oil Field with a Stabilized Finite Element Method

Journal of Porous Media ◽

10.1615/jpormedia.v12.i4.80 ◽

2009 ◽

Vol 12 (4) ◽

pp. 379-386 ◽

Cited By ~ 1

Author(s):

A. Kohandel Shirazi ◽

D. Mowla ◽

F. Esmaeilzadeh

Keyword(s):

Mathematical Modeling ◽

Finite Element Method ◽

Finite Element ◽

Flow Rate ◽

Oil Field ◽

Sand Production ◽

Stabilized Finite Element ◽

Stabilized Finite Element Method ◽

Oil Flow ◽

Element Method

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Mathematical modeling of unsteady response of plate and fin heat exchanger to sudden change in liquid flow rate

E3S Web of Conferences ◽

10.1051/e3sconf/20171401023 ◽

2017 ◽

Vol 14 ◽

pp. 01023

Author(s):

Anna Korzeń ◽

Dawid Taler

Keyword(s):

Mathematical Modeling ◽

Heat Exchanger ◽

Flow Rate ◽

Liquid Flow ◽

Liquid Flow Rate ◽

Sudden Change

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Use of a membrane module for semi-direct air evaporative cooling

Indoor and Built Environment ◽

10.1177/1420326x19877510 ◽

2019 ◽

Vol 29 (10) ◽

pp. 1346-1358 ◽

Cited By ~ 1

Author(s):

Sebastian Englart

Keyword(s):

Moisture Content ◽

Relative Error ◽

Air Temperature ◽

Evaporative Cooling ◽

Cross Flow ◽

Membrane Module ◽

Transfer Model ◽

Air Cooling ◽

Heating Efficiency ◽

Circulating Water

This study discusses the use of a membrane module for semi-direct evaporative air cooling. A cross-flow membrane module was used to carry out this air treatment process. For such a flow, it was proposed to describe and solve the heat and mass transfer model as a one-dimensional problem. The mathematical model was used to determine the moisture content and air temperature at the outlet from the module and the temperature of the circulating water. Results obtained using the proposed model are in good agreement with the experimental data. The relative error for the air temperature at the module outlet did not exceed 0.5%. For the moisture content, the relative error did not exceed 4%. For the circulating water temperature, the relative error did not exceed 0.6%. This paper also discusses the heating efficiency of the evaporative cooling process. Methods for determining the unit cooling indicator and the energy efficiency ratio are also proposed.

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Effects of Drying Conditions, Final Moisture Content, and Degree of Milling on Rice Flavor

Cereal Chemistry ◽

10.1094/cchem.1997.74.5.566 ◽

1997 ◽

Vol 74 (5) ◽

pp. 566-570 ◽

Cited By ~ 48

Author(s):

Elaine T. Champagne ◽

Karen L. Bett ◽

Bryan T. Vinyard ◽

Bill D. Webb ◽

Anna M. McClung ◽

...

Keyword(s):

Moisture Content ◽

Final Moisture Content ◽

Degree Of Milling ◽

Drying Conditions ◽

Rice Flavor

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Design of Hybrid Drying- Dedusting Unit Processor for Rough Rice Processing

International Journal of Food Engineering ◽

10.2202/1556-3758.1487 ◽

2008 ◽

Vol 4 (6) ◽

Author(s):

Law Chung Lim ◽

Wan Ramli Wan Daud

Keyword(s):

Moisture Content ◽

Fluidized Bed ◽

Separation Efficiency ◽

Cross Flow ◽

Drying Kinetics ◽

Rice Husks ◽

Two Stage ◽

Fluidized Bed Dryer ◽

Rough Rice ◽

Superficial Gas Velocity

Advanced drying technology enables drying of rough rice and dedusting of rice husks to be carried out simultaneously in the same unit processor. This paper reports the efficiency of dedusting of rice husks in a two-stage inclined cross flow fluidized bed dryer and the drying kinetics of rough rice in a batch fluidized bed dryer as well as the conceptual design of a hybrid drying dedusting unit processor. Experimental works had been carried out using rough rice (a Group D particle according to Geldart classification of powders) in a 2.5 m height two-stage inclined fluidized bed column of cross sectional area of 0.61m x 0.15m and a 3 m high batch fluidized bed dryer. The objectives of the study was to investigate the separation efficiency of dedusting of rice husks in the two-stage cross flow fluidized bed dryer and to study the drying kinetics of rough rice drying in the batch fluidized bed dryer. The experimental results showed that the dedusting separation efficiency at low superficial gas velocity gave unsatisfactory separation of merely 40% of rice husks. At higher superficial gas velocity, separation efficiency of rice husks as high as 93% was achieved. In addition, higher distributor inclination angle gave slightly improved separation efficiency. The drying kinetics showed that the residence time that is required to reduce the moisture content of rough rice to 18% (intermediate storage moisture content for second stage drying) is 3 minutes whereas the residence time that is required to reduce the moisture content to 13% (desirable final moisture content) is approximately 10 minutes regardless of the effect of kernel cracking. It was also found that higher drying temperatures gave higher drying rate. A conceptual design has been developed based on the results obtained in the studies. In order to maximize the heat utilization and to carry out two processes viz. dedusting and drying in one unit processor, it is suggested that drying dedusting can be carried out in a multistage mode where drying is taken place at each stage while dedusting is taking place at the upper stage. This concept can be applied to a packed bed or a fluidized bed unit processor.

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Heat and Mass Transfer to Air in a Cross Flow Heat Exchanger with Surface Deluge Cooling

International Journal of Air-Conditioning and Refrigeration ◽

10.1142/s2010132516500024 ◽

2016 ◽

Vol 24 (01) ◽

pp. 1650002 ◽

Cited By ~ 1

Author(s):

Andrea Diani ◽

Luisa Rossetto ◽

Roberto Dall’Olio ◽

Daniele De Zen ◽

Filippo Masetto

Keyword(s):

Heat Exchanger ◽

Heat Flow ◽

Flow Rate ◽

Data Center ◽

Heat Dissipation ◽

Cross Flow ◽

Critical Conditions ◽

Heat Flow Rate ◽

External Temperature ◽

Flow Heat

Cross flow heat exchangers, when applied to cool data center rooms, use external air (process air) to cool the air stream coming from the data center room (primary air). However, an air–air heat exchanger is not enough to cope with extreme high heat loads in critical conditions (high external temperature). Therefore, water can be sprayed in the process air to increase the heat dissipation capability (wet mode). Water evaporates, and the heat flow rate is transferred to the process air as sensible and latent heat. This paper proposes an analytical approach to predict the behavior of a cross flow heat exchanger in wet mode. The theoretical results are then compared to experimental tests carried out on a real machine in wet mode conditions. Comparisons are given in terms of calculated versus experimental heat flow rate and evaporated water mass flow rate, showing a good match between theoretical and experimental values.

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Evaluation of Design Characteristics for Animal Mortality Composting Systems

Journal of the ASABE ◽

10.13031/ja.14628 ◽

2021 ◽

Vol 65 (1) ◽

pp. 23-30

Author(s):

Tiago Costa ◽

Neslihan Akdeniz

Keyword(s):

Moisture Content ◽

Linear Relationship ◽

Compressive Stress ◽

Flow Rate ◽

Volumetric Flow Rate ◽

Airflow Rate ◽

List Type ◽

Design Characteristics ◽

The Impact ◽

Composting Systems

HighlightsDesign characteristics for animal mortality compost cover materials were tested.Compressive stress was applied to simulate the effects of the mortalities on cover materials.The highest permeability was measured for sawdust at 25% moisture content.A linear relationship was found between the volumetric flow rate and the power required to aerate the piles.Abstract. Composting is an aerobic process that relies on natural aeration to maintain proper oxygen levels. Air-filled porosity, mechanical strength, and permeability are among the essential parameters used to optimize the process. This study’s objective was to measure the physical parameters and airflow characteristics of three commonly used cover materials at four moisture levels, which could be used in designing actively aerated swine mortality composting systems. A laboratory-scale experiment was conducted to measure pressure drops across the cover materials as a function of the airflow rate and the material’s moisture content. Compressive stress was applied for 48 h to simulate the impact of swine mortalities on the cover materials. The power required to aerate each material was determined as a function of volumetric flow rate and moisture content. As expected, air-filled porosity and permeability decreased with increasing bulk density and moisture content. The highest average permeability values were measured at 25% moisture content and ranged from 66 × 10-4 to 70 × 10-4 mm2, from 161 × 10-4 to 209 × 10-4 mm2, and from 481 × 10-4 to 586 × 10-4 mm2 for woodchips, ground cornstalks, and sawdust, respectively. For the range of airflow rates tested in this study (0.0025 to 0.0050 m3 s-1 m-2), a linear relationship (R2 = 0.975) was found between the volumetric flow rate (m3 s-1) and the power required to aerate the compost pile (W per 100 kg of swine mortality). Keywords: Airflow, Darcy’s law, Livestock, Modeling, Permeability, Pressure drop.

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