The effect of temperature and slice thickness on drying kinetics tomato in the infrared dryer

In this study thin layer drying of tomato slices were investigated in the infrared dryer. Drying rate increased with increasing temperature and reduction thickness and thus reduced the drying time. The effective diffusivity increased with increasing temperature and with increasing thickness of the samples. The effective diffusivity values changed from 1.094 × 10^?9 to 4.468 × 10^?9 m²/s and for activation energy varied from 110 to 120 kJ/mol. The best model for drying process of tomato slices was Midilli model.     

Investigation on rough rice drying kinetics at various thin layers of a deep bed

Moisture content gradients along the bed column are commonly neglected during simulation of deep-bed grain drying. In this study, rough rice drying kinetics at various thin layers of a deep bed was investigated. The experiments were conducted under different drying conditions and the data were compared with the values predicted by a previously developed non-equilibrium model for numerical simulation of grain drying. The moisture content gradients related to the rough rice column indicated that the higher the drying layer, the more was the moisture content at each drying time. The constant drying rate period was observed neither for any thin layers nor for the entire drying column. The drying rate of the lower layers continuously decreased with drying time, whereas that of the upper layers firstly increased and then decreased. The implemented model predicted drying process with a high accuracy at various layers. However, the values of maximum relative error (RE _max ) and mean relative error (MRE) increased as the air temperature increased, and reversely decreased with the air velocity. The higher values of MRE and RE _max were related to the layer 1 (0–5 cm bed height) at temperature of 60 °C and air velocity of 0.4 m s^?1, and the lower values belonged to the layer 4 (15–20 cm bed height) at temperature of 40 °C and air velocity of 0.9 m s^?1.     

Problems and trends in mathematical modeling

Main problems and trends in mathematical modeling — a new line of research into various processes and phenomena — are formulated. The status and future prospects are analyzed using as an example the mechanics of continuous media. Emphasis is on two stages of modeling — the selection of physicomathematical models of the mechanics of continuous media and numerical algorithms of solution.     

Thin-layer drying characteristics of sweet potato slices and mathematical modelling

The effect of blanching and drying temperature (50, 60 and 70°C) on drying kinetics and rehydration ratio of sweet potatoes was investigated. It was observed that both the drying temperature and blanching affected the drying time and rehydration ratio. The logarithmic model showed the best fit to experimental drying data. The values of effective moisture diffusivity and activation energy ranged from 9.32 × 10⁻¹¹ to 1.75 × 10⁻¹⁰ m²/s, and 22.7–23.2 kJ/mol, respectively.     

Realistic mathematical modeling of the rattleback

The rattleback (also called a Celt or wobblestone) is an object which, when placed on a horizontal surface and caused to rotate about a vertical axis, sometimes begins to oscillate, stops turning, and then starts rotating in the direction opposite to that associated with the original motion. Earlier analyses dealing with this phenomenon have been based on a variety of assumptions. In the present work, it is shown by means of numerical solutions of full, non-linear equations of motion that one can construct a realistic mathematical model by assuming rolling without slipping and employing a torque proportional to angular velocity to provide for energy dissipation.     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

Dehydration characteristics and mathematical modelling of lemon slices drying undergoing oven treatment

In this study, the effect of drying temperature on drying behaviour and mass transfer parameters of lemon slices was investigated. The drying experiments were conducted in a laboratory air ventilated oven dryer at temperatures of 50, 60 and 75 °C. It was observed that the drying temperature affected the drying time and drying rate significantly. Drying rate curves revealed that the process at the temperature levels taken place in the falling rate period entirely. The usefulness of eight thin layer models to simulate the drying kinetics was evaluated and the Midilli and Kucuk model showed the best fit to experimental drying curves. The effective moisture diffusivity was determined on the basis of Fick’s second law and obtained to be 1.62 × 10^?11, 3.25 × 10^?11 and 8.11 × 10^?11 m² s^?1 for the temperatures of 50, 60 and 75 °C, respectively. The activation energy and Arrhenius constant were calculated to be 60.08 kJ mol^?1 and 0.08511 m² s^?1, respectively. The average value of convective mass transfer coefficient for the drying temperatures of 50, 60 and 75 °C was calculated to be 5.71 × 10^?7, 1.62 × 10^?6 and 2.53 × 10^?6 m s^?1, respectively.     

Flow of a thin plastic layer

Moscow University. Translated from Prikladnaya Mekhanika, Vol. 24, No. 10, pp. 88–94, October, 1988.     

Thermal analysis of thin layer boilover

A mathematical model is developed to simulate the thin layer boilover phenomenon. This model takes into account convective currents as well as conduction and radiation absorption through the fuel layer and is resolved numerically employing a scheme of Runge–Kutta, combined with the numerical method of lines. Solutions of the model showed a good agreement with the experimental data, both from this work and by other authors, demonstrating the importance of the convective currents. The model provided velocities of these currents, of the same order of magnitude as the values reported in the technical literature. Thickness of the remaining fuel and the interface temperature are correctly calculated by the model, allowing the prediction of the time required for the boilover to start.     

Mathematical modeling of piezomagnetoelectric thin plates

We present the outline of the rigorous mathematical derivation of linearized piezomagnetoelectric thin plate models and focus on the results it leads to. It is in particular shown how four different models emerge from theoretical tools. New mixed ‘senso-actuator’ and ‘actuato-sensor’ behaviors appear. Moreover, the influence of all the 45 crystal symmetry classes on our models is described. We point out the extremely important structural switch-off phenomenon for which the electromagnetoelastic coupling disappear for some specific crystal classes.     

Numerical modeling of turbulent boundary layer suction

For the problem of gas suction from the turbulent flow over a plate, the results of numerically solving the Navier-Stokes equations complemented by a differential model of turbulence are presented. On the range of Mach numbers from 0.8 to 1, the effect of suction of various intensities on the flow parameters in the neighborhood of the suction region and downstream is considered.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 45–49, November–December, 1996.     

A mathematical modeling of rotating waves in axial and radial compressors

Summary A comparison between meteorological systems and fluid motions through compressors is proposed. A mathematical analysis analogous to the geophysical one emphasizes characteristic dimensions. A dimensionless kinematic parameter, akin to the Rossby number, emerges, and thus leads to the study of different cases. Two kinds of solutions of rotating waves are presented here. The first describes a Rossby wave propagation in compressors, and the second depicts a limit form of part-span stall.     

Determination of properties for the calculation of aqueous thin film drying

 This paper deals with the determination of various properties required for the numerical calculation of the thin film drying of a water based varnish applied on paper. Experimental and analytical methods which provide the activity of water in paper and in a water based varnish, and the diffusion coefficient of water in this varnish are presented. Received on 23 March 2001