Mathematical model of an integrated circuit cooling through cylindrical rods

One of the main challenges in integrated circuits development is to propose alternatives to handle the extreme heat generated by high frequency of electrons moving in a reduced space that cause overheating and reduce the lifespan of the device. The use of cooling fins offers an alternative to enhance the heat transfer using combined a conduction-convection systems. Mathematical model of such process is important for parametric design and also to gain information about temperature distribution along the surface of the transistor. In this paper, we aim to obtain the equations for heat transfer along the chip and the fin by performing energy balance and heat transfer by conduction from the chip to the rod, followed by dissipation to the surrounding by convection. Newton's law of cooling and Fourier law were used to obtain the equations that describe the profile temperature in the rod and the surface of the chip. Ordinary differential equations were obtained and the respective analytical solutions were derived after consideration of boundary conditions. The temperature along the rod decreased considerably from the initial temperature (in contatct with the chip surface). This indicates the benefit of using a cilindrical rod to distribute the heat generated in the chip.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)]; European Regional Development Fund under the project CEBIA [CZ.1.05/2.1.00/03.0089]; Grant Agency of the Czech Republic [GACR 588 P103/15/06700S]; Internal Grant Agency of Tomas Bata University in Zlin [IGA/CebiaTech/2016/007]; National Council for Science and Technology (CONACYT) in Mexico; Council for Science and Technology of the State of Guanajuato (CONCYTEG) in Mexic

Parameters determination for column design in gas absorption systems

Separation processes by means of mass transfer play a key role in chemical industry. Very often, a number of different components are present in streams from chemical reactors and some of them may be separated from the main stream for environmental reasons, for purification purposes, for commercialization, to be used in other chemical manufacturing process or even reused in the same process, to improve industrial performance, or for sale as a final product. Gas adsorption is one example of this separation process, where it is normally desired to separate a dilute component from a gas stream. In the present paper we studied packed columns by graphical and algebraic methods and determine the tower height using volumetric mass transfer coefficients, we analyze a gas stream that contains a defined amount of a gas, which concentration decreases after being in contact to a packed absorption tower, and model this process by mass balance taking into consideration volumetric mass transfer coefficients, operating line and equilibrium line of the process. The model allows us finally to understand the variation of height column with column diameter, which is particularly useful for the design of absorption columns as it requires the determination of these parameters. © 2019, World Scientific and Engineering Academy and Society. All rights reserved

Application of finite difference method in the study of diffusion with chemical kinetics of first order

The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)

Development of a catalytic model system using nitrous oxide

Currently, special attention is paid to partial oxidation of several sugar alcohols because it generates oxidation intermediate products with high utility value. In the present paper, we study the modelling of oxidation reaction of 1,2,3 propanotriol using an oxidizing agent in low concentrations. A major problem of such oxidation system is its low reactivity and high oxidation reactivity of products, As a result, the yield to a specific compound (i.e. dihydroxypropanal) depends on the ratio of rate constants of the consecutive reactions and also on the initial concentration of oxidizing agent. In this case, as the input value for the model calculations we chose a ratio of values of the specified rate constants and initial concentrations of nitrous oxide and 1,2,3-propanotriol. Accordingly, an experimental setup was proposed to follow the variation of temperature of the reaction blend after gradual addition of ammonium nitrate to a solution of 1,2,3 propanotriol, which can provide insights for the control of the chemical reactor. © 2018, World Scientific and Engineering Academy and Society. All Rights Reserved.LO1303, MŠMT, Ministerstvo Školství, Mládeže a Tělovýchov

Study of dissolution process and its modelling

The use of mathematical concepts and language aiming to describe and represent the interactions and dynamics of a system is known as a mathematical model. Mathematical modelling finds a huge number of successful applications in a vast amount of science, social and engineering fields, including biology, chemistry, physics, computer sciences, artificial intelligence, bioengineering, finance, economy and others. In this research, we aim to propose a mathematical model that predicts the dissolution of a solid material immersed in a fluid. The developed model can be used to evaluate the rate of mass transfer and the mass transfer coefficient. Further research is expected to be carried out to use the model as a base to develop useful models for the pharmaceutical industry to gain information about the dissolution of medicaments in the body stream and this could play a key role in formulation of medicaments. © The Authors, published by EDP Sciences, 2017

Modeling of the partial oxidation of glycerol by estimation of its transfer function

The reaction pathway for the conversion of glycerol into different products, namely glyceraldehyde, glyceric acid, glycolic acid, mesoxalic acid and tartronic acid was studied by means of electrochemistry. Multiple Pulse Amperometry technique was used to control the potential during the electrooxidation reaction. The estimation of the transfer function was realized on the basis of dynamic models for the oxidation reaction. The equations obtained in the s-domain were expressed in the time domain using Inverse Laplace transformation to describe the variation of glycerol and products concentration.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)]; European Regional Development Fund under the project CEBIA-Tech [CZ.1.05/2.1.00/03.0089

Numerical analysis of initial amount of substrate and biomass in substrate inhibition process

-The process of inhibition of enzymes is important because it serves as a fundamental control mechanism in many biological systems and allows the regulation of metabolic pathways. In fact, many medications act by inhibiting specific enzymes in the brain or in body tissues. Therefore, the understanding of enzymatic inhibition mechanism is, essential. Inhibitors are frequently used as tools for the study of the mechanism of the enzymes themselves. In the present paper we have studied the process of substrate inhibition by developing a mathematical model that allow us to understand the influence of initial amount of substrate and initial biomass concentration on maximum growth rate value. Numerical analysis using Matlab software was performed to model this inhibition process. © 2018, World Scientific and Engineering Academy and Society. All rights reserved

Mathematical modeling of urea reaction with sulfuric acid and phosphoric acid to produce ammonium sulfate and ammonium dihydrogen phosphate respectively

Urea is the final product of protein metabolism in mammals and can be found in different biological fluids. Use of mammalian urine in agricultural production as organic fertilizer requires safe handling to avoid the formation of ammonia that will decrease the fertilizer value due to the loss of nitrogen. Safe handling is also required to minimize the decomposition of urea into con-densed products such as biuret and cyanuric acid, which will also have a negative impact on the potential sustainable production of crops and sanitation technologies. The study of thermodynamics and reaction kinetics of urea stabilization plays a key role in understanding the conditions under which undesirable compounds and impurities in urea‐based fertilizers and urea‐based selective catalytic reduction systems are formed. For this reason, we studied the reaction of urea in acid media to achieve urea stabilization by modeling the reaction of urea with sulfuric acid and phosphoric acid, and estimating the reaction enthalpy and adiabatic heat difference for control of the heat re-leased from the neutralization step using Ca(OH)2 or MgO for the safety of the process. Numerical and simulation analyses were performed by studying the effect of the surrounding temperature, the ratio of acid reagent to urea concentration, the rate of addition, and the reaction rate to estimate the required time to achieve an optimum value of urea conversion into ammonium dihydrogen phosphate or ammonium sulfate as potential technological opportunities for by‐product valorization. Full conversion of urea was achieved in about 10 h for reaction rates in the order of 1 × 10−5 s−1when the ratio of H2SO4 to CH4N2O was 1.5. When increasing the ratio to 10, the time required for full conversion was considerably reduced to 3 h. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Ministerstvo Průmyslu a Obchodu, MPO: CZ.01.1.02/0.0/0.0/18_215/0020606ZDV Frystak (Zemedelske druzstvo vlastniku Frystak); Ministry of Industry and Trade of the Czech Republic [CZ.01.1.02/0.0/0.0/18_215/0020606

Catalytic oxidation using nitrous oxide

Nitrous oxide is a very inert gas used generally as oxidant as it offers some advantage compared with other oxidants such as O2 but a considerably higher temperature (> 526 °C) is often required. For particular cases such as the oxidation of sugar alcohols, especially for the oxidation of primary alcohols to aldehydes, N2O has the advantage over O2 of a higher reaction selectivity. In the present paper we present the modelling of oxidation reaction of sugar alcohols using an oxidizing agent in low concentrations, which is important to suppress subsequent oxidation reactions due to the very low residual concentrations of the oxidizing agent. For orientation experiments we chose nitrous oxide generated by thermal decomposition of ammonium nitrate. Kinetic modeling of the reaction was performed after determination of the differential equations that describe the system under study. © The Authors, published by EDP Sciences, 2017

Mathematical modeling of thermal management at different atmospheric pressure conditions

Cooling process is an important element in the correct functioning of all electronic devices. While some components can resist high temperatures, others are damaged during overheating conditions. We performed numerical simulation to study the temperature variation during cooling process of electronic devices that are subject to the effect of different pressures. Commonly the correct functioning of instruments is tested under specific conditions given by the location of the manufacturer but generally the consumer uses the device in a different region. Cooling process performed by convection uses the air provided by a fan. Fluid properties such as kinematic viscosity are influenced by pressure and the effect in cooling is demonstrated by analyzing the variation of surface temperature at different pressures. This study allows us to understand the importance of fluid flow speed in controlling the heating rate. We performed numerical simulation at different air speed (10 - 20 m/s) and pressure (77 - 100 kPa) which corresponds to the elevation of cities that are located between 31mand 2240 m., additionally we studied the maximum amount of power dissipation as a function of air velocity with radiation contribution and without radiation effect