Search results for: heat equation

Authors: Raisa Kh. Bolotnova, Marat N. Galimzianov, Andrey S. Topolnikov, Uliana O. Agisheva, Valeria A. Buzina

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The paper presents the results of theoretical and numerical modeling of propagation of shock waves in bubbly liquids related to nonlinear effects (realistic equation of state, chemical reactions, two-dimensional effects). On the basis on the Rankine- Hugoniot equations the problem of determination of parameters of passing and reflected shock waves in gas-liquid medium for isothermal, adiabatic and shock compression of the gas component is solved by using the wide-range equation of state of water in the analitic form. The phenomenon of shock wave intensification is investigated in the channel of variable cross section for the propagation of a shock wave in the liquid filled with bubbles containing chemically active gases. The results of modeling of the wave impulse impact on the solid wall covered with bubble layer are presented.

Keywords: bubbly liquid, cavitation, equation of state, shock wave

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Authors: Rabeb Triki, Hassene Djemel, Mounir Baccar

Abstract:

Surface scraping is a passive heat transfer enhancement technique that is directly used in scraped surface heat exchanger (SSHE). The scraping action prevents the accumulation of the product on the inner wall, which intensifies the heat transfer and avoids the formation of dead zones. SSHEs are widely used in industry for several applications such as crystallization, sterilization, freezing, gelatinization, and many other continuous processes. They are designed to deal with products that are viscous, sticky or that contain particulate matter. This research work presents a three-dimensional numerical simulation of the coupled thermal and hydrodynamic behavior within a SSHE which includes Archimedes’ screw instead of scraper blades. The finite volume Fluent 15.0 was used to solve continuity, momentum and energy equations using multiple reference frame formulation. The process fluid investigated under this study is the pure glycerin. Different geometrical parameters were studied in the case of steady, non-isothermal, laminar flow. In particular, attention is focused on the effect of the conicity of the rotor and the pitch of Archimedes’ screw on temperature and velocity distribution and heat transfer rate. Numerical investigations show that the increase of the number of turns in the screw from five to seven turns leads to amelioration of heat transfer coefficient, and the increase of the conicity of the rotor from 0.1 to 0.15 leads to an increase in the rate of heat transfer. Further studies should investigate the effect of different operating parameters (axial and rotational Reynolds number) on the hydrodynamic and thermal behavior of the SSHE.

Keywords: ANSYS-Fluent, hydrodynamic behavior, SSHE, thermal behavior.

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Authors: Nopparat Pochai, Rujira Deepana

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Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: P. Amatachaya, P. Khantikomol, R. Sangchot, B. Krittacom

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The steady-state temperature for one-dimensional transpiration cooling system has been conducted experimentally and numerically to investigate the heat transfer characteristics of combined convection and radiation. The Nickel –Chrome (Ni-Cr) open-cellular porous material having porosity of 0.93 and pores per inch (PPI) of 21.5 was examined. The upper surface of porous plate was heated by the heat flux of incoming radiation varying from 7.7 - 16.6 kW/m2 whereas air injection velocity fed into the lower surface was varied from 0.36 - 1.27 m/s, and was then rearranged as Reynolds number (Re). For the report of the results in the present study, two efficiencies including of temperature and conversion efficiency were presented. Temperature efficiency indicating how close the mean temperature of a porous heat plate to that of inlet air, and increased rapidly with the air injection velocity (Re). It was then saturated and had a constant value at Re higher than 10. The conversion efficiency, which was regarded as the ability of porous material in transferring energy by convection after absorbed from heat radiation, decreased with increasing of the heat flux and air injection velocity. In addition, it was then asymptotic to a constant value at the Re higher than 10. The numerical predictions also agreed with experimental data very well.

Keywords: Convection, open-cellular, radiation, transpiration cooling, Reynolds number.

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Authors: Ram N. Singh, Abraham K. George, Dawood N. Al-Namaani

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The Euler-s equation of motion is extended to include the viscosity stress tensor leading to the formulation of Navier– Stokes type equation. The latter is linearized and applied to investigate the rotational motion or vorticity in a viscous fluid. Relations for the velocity of viscous waves and attenuation parameter are obtained in terms of viscosity (μ) and the density (¤ü) of the fluid. μ and ¤ü are measured experimentally as a function of temperature for two different samples of light and heavy crude oil. These data facilitated to determine the activation energy, velocity of viscous wave and the attenuation parameter. Shear wave velocity in heavy oil is found to be much larger than the light oil, whereas the attenuation parameter in heavy oil is quite low in comparison to light one. The activation energy of heavy oil is three times larger than light oil.

Keywords: Activation Energy, Attenuation, Crude Oil, Navier- Stokes Equation, Viscosity.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Gyu-Jin Shim, Seung-Moon Baek, Choon-Geun Moon, Ho-Saeng Lee, Jung-In Yoon

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The experimental thermal performance of two heat exchangers in closed-wet cooling tower (CWCT) was investigated in this study. The test sections are heat exchangers which have multi path that is used as the entrance of cooling water and are consisting of bare-type copper tubes between 15.88mm and 19.05mm. The process fluids are the cooling water that flows from top part of heat exchanger to bottom side in the inner side of tube, and spray water that flows gravitational direction in the outer side of it. Air contacts its outer side of that as it counterflows. Heat and mass transfer coefficients and cooling capacity were calculated with variations of process fluids, multi path and different diameter tubes to figure out the performance of characteristics of CWCT. The main results were summarized as follows: The results show this experiment is reliable with values of heat and mass transfer coefficients comparing to values of correlations. Heat and mass transfer coefficients and cooling capacity of two paths are higher than these with one path using 15.88 and 19.05mm tubes. Cooling capacity per unit volume with 15.88mm tube using one and two paths are higher than 19.05mm tube due to increase of surface area per unit volume.

Keywords: Closed–Wet Cooling Tower, Cooling Capacity, Heatand Mass Transfer Coefficients.

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Authors: Minghui Wang, Juntao Zhang

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An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: K. Fraňa, M. Müller

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A presentation of the design of the Organic Rankine cycle (ORC) with heat regeneration and superheating processes is a subject of this paper. The maximum temperature level in the ORC is considered to be 110°C and the maximum pressure varies up to 2.5MPa. The selection process of the appropriate working fluids, thermal design and calculation of the cycle and its components are described. With respect to the safety, toxicity, flammability, price and thermal cycle efficiency, the working fluid selected is R134a. As a particular example, the thermal design of the condenser used for the ORC engine with a theoretical thermal power of 179 kW was introduced. The minimal heat transfer area for a completed condensation was determined to be approximately 520m². 

Keywords: Organic Rankine Cycle, thermal efficiency, working fluids.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

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Authors: Li Xiguang

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In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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Authors: Samad Jafarmadar, Amin Habibzadeh

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A power and cooling cycle, which combines the organic Rankine cycle and the ejector refrigeration cycle supplied by waste heat energy sources, is discussed in this paper. 13 working fluids including wet, dry, and isentropic fluids are studied in order to find their performances on the combined cycle. Various operating conditions’ effects on the proposed cycle are examined by fixing power/refrigeration ratio. According to the results, dry and isentropic fluids have better performance compared with wet fluids.

Keywords: Combined power and refrigeration cycle, low temperature heat sources, organic rankine cycle, working fluids.

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Authors: Huei-Fu Lu

Abstract:

This study links up the theories of social psychology, economics and sport management to assess the impact of sport participation on subjective well-being (SWB) and use a simple statistic method to estimate the relative monetary value that sport participation derives SWB for Taiwan-s college students. By constructing proper measurements on sport participation and SWB respectively, a structural equation model (SEM) is developed to perform a confirmatory factory analysis, and the causal relationship between sport participation and SWB as well as the effect of the demographic variables on these two concepts are also discussed.

Keywords: Demographics, Economic value, Sport participation, Structural equation modeling (SEM), Subjective well-being.

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Authors: Ameni Mokni , Hatem Mhiri , Georges Le Palec , Philippe Bournot

Abstract:

In mechanical and environmental engineering, mixed convection is a frequently encountered thermal fluid phenomenon which exists in atmospheric environment, urban canopy flows, ocean currents, gas turbines, heat exchangers, and computer chip cooling systems etc... . This paper deals with a numerical investigation of mixed convection in a vertical heated channel. This flow results from the mixing of the up-going fluid along walls of the channel with the one issued from a flat nozzle located in its entry section. The fluiddynamic and heat-transfer characteristics of vented vertical channels are investigated for constant heat-flux boundary conditions, a Rayleigh number equal to 2.57 1010, for two jet Reynolds number Re=3 103 and 2104 and the aspect ratio in the 8-20 range. The system of governing equations is solved with a finite volumes method and an implicit scheme. The obtained results show that the turbulence and the jet-wall interaction activate the heat transfer, as does the drive of ambient air by the jet. For low Reynolds number Re=3 103, the increase of the aspect Ratio enhances the heat transfer of about 3%, however; for Re=2 104, the heat transfer enhancement is of about 12%. The numerical velocity, pressure and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, and average Nusselt number, in terms of Rayleigh, Reynolds numbers and dimensionless geometric parameters are presented.

Keywords: Aspect Ratio, Channel, Jet, Mixed convection

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Authors: Aouattou Nabila, Saighi Mohamed, Fekih Malika

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The modeling of water transfer in the unsaturated zone uses techniques and methods of the soil physics to solve the Richards-s equation. However, there is a disaccord between the size of the measurements provided by the soil physics and the size of the fields of hydrological modeling problem, to which is added the strong spatial variability of soil hydraulic properties. The objective of this work was to develop a methodology to estimate the hydrodynamic parameters for modeling water transfers at different hydrological scales in the soil-plant atmosphere systems.

Keywords: Hydraulic properties, Modeling, Unsaturated zone, Transfer, Water

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Authors: Fatma Ghangir, Andrzej F. Nowakowski, Franck C. G. A. Nicolleau, Thomas M. Michelitsch

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The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

Keywords: Multiphase flow, gas-liquid flow, Godunov schems, Riemann solvers, HLL scheme, HLLC scheme.

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Authors: Rebhi A. Damseh, H. M. Duwairi, Benbella A. Shannak

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This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate with variable surface heat flux embedded in a fluid saturated porous medium in the presence of thermophoresis particle deposition effect. The governing partial differential equations are transformed into no-similar form by using special transformation and solved numerically by using an implicit finite difference method. Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increase wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pronounced near pure natural convection heat transfer limit; because this phenomenon is directly a temperature gradient or buoyancy forces dependent. Comparisons with previously published work in the limits are performed and the results are found to be in excellent agreement.

Keywords: Thermophoresis, porous medium, variable surface heat flux.

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Authors: A. A. Samat, N. A. Abdullah, M. A. M. Ishak, N. Osman

Abstract:

Powder of La0.6Sr0.4CoO3-α (LSCO) was synthesized by a combined citrate-EDTA method. The as-synthesized LSCO powder was calcined, respectively at temperatures of 800, 900 and 1000 °C with different heating/cooling rates which are 2, 5, 10 and 15 °C min-1. The effects of heat treatments on the phase formation of perovskite phase of LSCO were investigated by powder X-ray diffraction (XRD). The XRD patterns revealed that the rate of 5 °C min-1 is the optimum heating/cooling rate to obtain a single perovskite phase of LSCO with calcination temperature of 800 °C. This result was confirmed by a thermogravimetric analysis (TGA) as it showed a complete decomposition of intermediate compounds to form oxide material was also observed at 800 °C.

Keywords: La0.6Sr0.4CoO3-α, heat treatment, perovskite-type oxide, XRD.

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Authors: Nabnit Panigrahi, M. K. Mohanty, S. K. Acharya, S. R Mishra, R. C. Mohanty

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This paper presents experimental investigation carried out on an unmodified four stroke diesel engine running with preheated straight vegetable oil (SVO) of Karanja. The viscosity of straight karanja oil was reduced by preheating the oil up to 1600C under different load condition. The preheating was done with the help of a Shell and Tube heat exchanger equipment without using any external power source. The heat exchanger was designed in the lab and the heating source was by waste exhaust gas from engine. The experimental results data were analyzed by using 20% blends of svo of Karanja with 80% diesel by volume and 100% preheated svo of karanja for various parameters like specific fuel consumption, brake thermal efficiency and emission of exhaust gas like CO, CO₂, HC and NOx. The results indicated that by using straight karanja oil, the emission parameter increases as compared to diesel but regarding engine performance it was found to be very close to that of diesel. All total it can be a replacement of diesel with a small efficiency drop.

Keywords: Karanja oil, Performance analysis, Shell &Tube heat exchanger, SVO.

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Authors: Dong-Eun Lee

Abstract:

To calculate the temperature distribution of the slab in a hot rolled reheating furnace a mathematical model has been developed by considering the thermal radiation in the furnace and transient conduction in the slab. The furnace is modeled as radiating medium with spatially varying temperature. Radiative heat flux within the furnace including the effect of furnace walls, combustion gases, skid beams and buttons is calculated using the FVM and is applied as the boundary condition of the transient conduction equation of the slab. After determining the slab emissivity by comparison between simulation and experimental work, variation of heating characteristics in the slab is investigated in the case of changing furnace temperature with various time and the slab residence time is optimized with this evaluation.

Keywords: Reheating Furnace, Thermal Radiation, ResidenceTime, FVM for Radiation

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Authors: Neetu Rani, Hema Setia, Marut Dutt. R.K. Wanchoo

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An empirical correlation for predicting the heat transfer coefficient for a cylinder under free convection, inclined at any arbitrary angle with the horizontal has been developed in terms of Nusselt number, Prandtl number and Grashof number. Available experimental data was used to determine the parameters for the proposed correlation. The proposed correlation predicts the available data well within ±10%, for Prandtl number in the range 0.68-0.72 and Grashof number in the range 1.4×10⁴–1.2×10¹⁰.

Keywords: Heat transfer, inclined cylinders, natural convection, Nusselt number, Prandtl number, Grashof number.

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Authors: Andrew R.H. Rigit, Patrick T.K. Low

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Majority of pepper farmers in Malaysia are using the open-sun method for drying the pepper berries. This method is time consuming and exposed the berries to rain and contamination. A maintenance-friendly and properly enclosed dryer is therefore desired. A dryer design with a solar collector and a chimney was studied and adapted to suit the needs of small-scale pepper farmers in Malaysia. The dryer will provide an environment with an optimum operating temperature meant for drying pepper berries. The dryer model was evaluated by using commercially available computational fluid dynamic (CFD) software in order to understand the heat and mass transfer inside the dryer. Natural convection was the only mode of heat transportation considered in this study as in accordance to the idea of having a simple and maintenance-friendly design. To accommodate the effect of low buoyancy found in natural convection driers, a biomass burner was integrated into the solar dryer design.

Keywords: Computational fluid dynamics, heat and masstransfer, solar dryer.

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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Authors: Hirbod Varasteh, Hamidreza Gohari Darabkhani

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The global warming and its impact on climate change is one of main challenges for current century. Global warming is mainly due to the emission of greenhouse gases (GHG) and carbon dioxide (CO₂) is known to be the major contributor to the GHG emission profile. Whilst the energy sector is the primary source for CO₂ emission, Carbon Capture and Storage (CCS) are believed to be the solution for controlling this emission. Oxyfuel combustion (Oxy-combustion) is one of the major technologies for capturing CO₂ from power plants. For gas turbines, several Oxy-combustion power cycles (Oxyturbine cycles) have been investigated by means of thermodynamic analysis. NetPower cycle is one of the leading oxyturbine power cycles with almost full carbon capture capability from a natural gas fired power plant. In this manuscript, sensitivity analysis of the heat exchanger design in NetPower cycle is completed by means of process modelling. The heat capacity variation and supercritical CO₂ with gaseous admixtures are considered for multi-zone analysis with Aspen Plus software. It is found that the heat exchanger design has a major role to increase the efficiency of NetPower cycle. The pinch-point analysis is done to extract the composite and grand composite curve for the heat exchanger. In this paper, relationship between the cycle efficiency and the minimum approach temperature (∆Tmin) of the heat exchanger has also been evaluated.  Increase in ∆Tmin causes a decrease in the temperature of the recycle flue gases (RFG) and an overall decrease in the required power for the recycled gas compressor. The main challenge in the design of heat exchangers in power plants is a tradeoff between the capital and operational costs. To achieve lower ∆Tmin, larger size of heat exchanger is required. This means a higher capital cost but leading to a better heat recovery and lower operational cost. To achieve this, ∆Tmin is selected from the minimum point in the diagrams of capital and operational costs. This study provides an insight into the NetPower Oxy-combustion cycle’s performance analysis and operational condition based on its heat exchanger design.

Keywords: Carbon capture and storage, oxy-combustion, netpower cycle, oxyturbine power cycles, heat exchanger design, supercritical carbon dioxide, pinch point analysis.

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Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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Authors: Y. T. Yang, H. S. Peng, H. T. Hsu

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This study presents the numerical simulation of optimum pin-fin heat sink with air impinging cooling by using Taguchi method. 9 L ( 4 3 ) orthogonal array is selected as a plan for the four design-parameters with three levels. The governing equations are discretized by using the control-volume-based-finite-difference method with a power-law scheme on the non-uniform staggered grid. We solved the coupling of the velocity and the pressure terms of momentum equations using SIMPLEC algorithm. We employ the k −ε two-equations turbulence model to describe the turbulent behavior. The parameters studied include fin height H (35mm-45mm), inter-fin spacing a , b , and c (2 mm-6.4 mm), and Reynolds number ( Re = 10000- 25000). The objective of this study is to examine the effects of the fin spacings and fin height on the thermal resistance and to find the optimum group by using the Taguchi method. We found that the fin spacings from the center to the edge of the heat sink gradually extended, and the longer the fin’s height the better the results. The optimum group is 3 1 2 3 H a b c . In addition, the effects of parameters are ranked by importance as a , H , c , and b .

Keywords: Heat sink, Optimum, Electronics cooling, CFD.

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Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

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One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

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Authors: F. Soleymani, M. Sharifi

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Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: A.Tajaddini

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In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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