scholarly journals Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
R. Jooma ◽  
C. Harley
Keyword(s):  
Heat Transfer ◽  
Systems Analysis ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Transformation Method ◽  
Dynamical Systems Analysis ◽  
Equation Modelling ◽  
The Stability ◽  
The Impact ◽  
State Case

A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions.

scholarly journals Effect of Rotational Speed Modulation on the Weakly Nonlinear Heat Transfer in Walter-B Viscoelastic Fluid in the Highly Permeable Porous Medium

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1448
Author(s):  
Anand Kumar ◽  
Vinod K. Gupta ◽  
Neetu Meena ◽  
Ishak Hashim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Rotational Speed ◽  
Weakly Nonlinear ◽  
Speed Modulation ◽  
The Stability ◽  
The Impact

In this article, a study on the stability of Walter-B viscoelastic fluid in the highly permeable porous medium under the rotational speed modulation is presented. The impact of rotational modulation on heat transport is performed through a weakly nonlinear analysis. A perturbation procedure based on the small amplitude of the perturbing parameter is used to study the combined effect of rotation and permeability on the stability through a porous medium. Rayleigh–Bénard convection with the Coriolis expression has been examined to explain the impact of rotation on the convective flow. The graphical result of different parameters like modified Prandtl number, Darcy number, Rayleigh number, and Taylor number on heat transfer have discussed. Furthermore, it is found that the modified Prandtl number decelerates the heat transport which may be due to the combined effect of elastic parameter and Taylor number.

Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics

2020 ◽  
Vol 34 (29) ◽  
pp. 2050282
Author(s):  
Asıf Yokuş ◽  
Doğan Kaya
Keyword(s):  
Traveling Wave ◽  
Numerical Solutions ◽  
Traveling Wave Solutions ◽  
Transformation Method ◽  
Mkdv Equation ◽  
Traveling Wave Solution ◽  
Von Neumann ◽  
Wave Solutions ◽  
De Vries ◽  
The Stability

The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

Modeling and Simulation on Heat Transfer in Blood Vessels Subject to a Transient Laser Irradiation

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Xuelan Zhang ◽  
Liancun Zheng ◽  
Lin Liu ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Blood Vessels ◽  
Laser Irradiation ◽  
Numerical Solutions ◽  
Thermal Relaxation ◽  
Initial Time ◽  
Laser Exposure ◽  
Conduction Model ◽  
Heaviside Step Function ◽  
The Impact

Abstract This paper investigates heat transfer of blood vessels subject to transient laser irradiation, where the irradiation is extremely short times and has high power. The modified Fourier heat conduction model (Cattaneo–Christov flux) and Heaviside step function are used in describing the thermal relaxation and temperature jump characteristics in initial time. A novel auxiliary function is introduced to avoid three-level discretization and temporal–spatial mixed derivative, and the numerical solutions are obtained by Crank–Nicolson alternating direction implicit (ADI) scheme. Results indicate that the temperature distributions in blood vessels strongly depend on the blood property, the laser exposure time, the blood flowrate (Reynolds number) and the thermal relaxation parameter. The isothermal curve exhibits asymmetric characteristics due to the impact of blood flow, and the higher blood velocity leads to more asymmetric isotherm and less uniform thermal distribution. Further, the heat-flux relaxation phenomenon is also captured, and its effect on blood temperature becomes more noticeable as blood flows downstream of blood vessels.

scholarly journals Insights into the Stability of Mixed Convective Darcy–Forchheimer Flows of Cross Liquids from a Vertical Plate with Consideration of the Significant Impact of Velocity and Thermal Slip Conditions

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 31 ◽  
Author(s):  
Umair Khan ◽  
Aurang Zaib ◽  
Ilyas Khan ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Vertical Plate ◽  
Thermal Slip ◽  
Slip Conditions ◽  
Drag Forces ◽  
Similarity Transformations ◽  
Mixed Convective Flow ◽  
The Stability ◽  
The Impact

This paper reflects the effects of velocity and thermal slip conditions on the stagnation-point mixed convective flow of Cross liquid moving over a vertical plate entrenched in a Darcy–Forchheimer porous medium. A Cross liquid is a type of non-Newtonian liquid whose viscosity depends on the shear rate. The leading partial differential equations (PDEs) are altered to nonlinear ordinary differential equations (ODEs) via feasible similarity transformations. These transmuted equations are computed numerically through the bvp4c solver. The authority of sundry parameters on the temperature and velocity distributions is examined graphically. In addition, the characteristics of heat transfer are analyzed in the presence of the impact of drag forces. The outcomes reveal that the permeability parameter decelerates the drag forces and declines the rate of heat transfer in both forms of solutions. Moreover, it is found that the drag forces decline with the growing value of the Weissenberg parameter in the upper branch solutions, while a reverse trend is revealed in the lower branch solutions. However, the rate of heat transfer shows a diminishing behavior with an increasing value of the Weissenberg parameter.

Implications of agricultural policy for species invasion in shifting cultivation systems

2006 ◽  
Vol 11 (4) ◽  
pp. 429-452 ◽  
Author(s):  
HEIDI J. ALBERS ◽  
MICHAEL J. GOLDBACH ◽  
DANIEL T. KAFFINE
Keyword(s):  
Invasive Species ◽  
Shifting Cultivation ◽  
Native Species ◽  
Numerical Solutions ◽  
Economic Systems ◽  
Species Invasions ◽  
Invasive Grasses ◽  
Land Use Decisions ◽  
The Stability ◽  
The Impact

Policies to influence land use decisions in agriculture or grazing can increase the ability of invasive species to out-compete native species and thereby disrupt seemingly stable ecological-economic systems. Building off of models of interdependent resources, invasive species and soil fertility, this paper develops a model of shifting cultivation decisions for two types of farmers, one who sees the threat of invasive grasses and one who does not. The paper uses numerical solutions to this dynamic decision problem to examine the impact of various policies on farmer welfare and on the stability of the economic-ecological system. Some policies undermine the resilience of the system, while other policies augment the system's ability to withstand species invasions.

Heat Transfer and Pressure Drop Correlation for Helicoidal Pipes of Rectangular Cross Section

2009 ◽  
Author(s):  
Christopher Katinas ◽  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Friction Factor ◽  
Cross Section ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Dean Number ◽  
Curvature Effects ◽  
The Impact

In this study, flow and heat transfer for laminar flow in curved channels of rectangular cross section is examined. The focus of the numerical solutions is on rectangular cross sections with an aspect ratio less than one, since little information is available for heat transfer in curved rectangular pipes whose width is greater than height. The study examines the impact of the aspect ratio and Dean number on both friction factor and Nusselt number. The results show that although both friction factor and Nusselt number increase as a result of curvature effects, the heat transfer enhancements significantly outweigh the friction factor penalty. Numerical solutions in this study consider the more realistic case of hydrodynamically developed and thermally developing flow.

scholarly journals DAMPAK SUBSIDI SOLAR TERHADAP KELESTARIAN SUMBER DAYA IKAN DI BITUNG, SULAWESI UTARA

2017 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Yesi Dewita Sari ◽  
Estu Sri Luhur ◽  
Armen Zulham
Keyword(s):  
Systems Analysis ◽  
Fishing Effort ◽  
Operating Costs ◽  
Subsidy Policy ◽  
Fish Stocks ◽  
Fish Resources ◽  
Fishery Resources ◽  
Dynamical Systems Analysis ◽  
Operational Costs ◽  
The Impact

Penelitian bertujuan mengetahui dampak penetapan subsidi harga solar terhadap kelestarian sumber daya ikan telah dilakukan di Pelabuhan Perikanan Samudera Bitung Kota Bitung pada Bulan April, Agustus dan Oktober 2010. Analisis pendugaan parameter biologi dilakukan dengan menggunakan model surplus produksi berdasarkan metode Clark, Yoshimoto and Pooley (CYP). Adapun analisis dinamika dan hubungan sebab akibat antara eksploitasi sumber daya perikanan dengan usaha penangkapan ikan dilakukan dengan metode analisis sistem dinamik. Hasil penelitian menunjukkan bahwa pada kondisi baseline (harga solar Rp 4.500 per liter), rata-rata harga ikan Rp 6.200 per kg dan biaya operasional Rp 14.924.373 per trip maka jumlah effort yang diperbolehkan adalah sebanyak 1.601 trip per bulan dan jumlah produksi 982 ton per bulan serta ketersediaan stok ikan 1.306 ton. Tanpa subsidi solar (Rp 7.500 per liter) maka terjadi peningkatan biaya operasional per trip sebesar 36,76% (Rp 20.410.696 per trip), sedangkan jumlah effort yang diperbolehkan relatif tetap (1.600 trip per bulan). Hasil ini menunjukkan bahwa kebijakan subsidi solar tidak memberikan dampak signifikan terhadap kelestarian sumber daya ikan di Bitung. Oleh karena itu, subsidi solar harus tetap diberikan kepada nelayan di Bitung agar mereka dapat melakukan pemanfaatan sumber daya ikan secara berkelanjutan disamping mengurangi potensi pemanfaatannya oleh nelayan negara tetangga secara ilegal.Title: Impact of Fuel Subsidy on Sustainablity to Fishery Resources in Bitung, North SulawesiThe study aims to determine the impact of diesel price fixing subsidy to sustainability of fish resources has been carried out in the port of Ocean Fishery Bitung, Bitung City in April, August and October 2010. Analysis of biological parameter estimation is done using a production surplus model based on the method of Clark, Yoshimoto and Pooley (CYP). The analysis of the dynamics and the causal relationship between the exploitation of fishery resources to fishing effort carried out by the method of dynamical systems analysis. The results showed that in the baseline condition (diesel price of Rp 4,500 per liter), the average price of Rp 6,200 per kg of fish and operational costs Rp 14,924,373 per trip allowed the amount of effort that is as much a 1601 trips per month and the amount of production of 982 tons per month, and 1306 tons of fish stocks. Without the solar subsidy (Rp 7,500 per liter), then an increase in operating costs per trip by 36.76% (Rp 20,410,696 per trip), while the amount of effort that allowed relatively fixed (1,600 trips per month). These results indicate that the diesel subsidy policy does not provide a significant impact on the sustainability of fish resources in Bitung. Therefore, solar subsidies should be given to fishermen in Bitung so that they can perform the utilization of fish resources in a sustainable manner as well as reducing the potential for use by fishermen neighboring countries illegally.

On the exact and numerical solutions to the FitzHugh–Nagumo equation

2020 ◽  
Vol 34 (17) ◽  
pp. 2050149 ◽  
Author(s):  
Asıf Yokus
Keyword(s):  
Difference Method ◽  
Numerical Solutions ◽  
Transformation Method ◽  
Von Neumann ◽  
Wave Solutions ◽  
Forward Difference ◽  
Package Program ◽  
Von Neumann Stability ◽  
The Stability ◽  
Von Neumann Stability Analysis

In this paper, with the help of a computer package program, the auto-Bäcklund transformation method (aBTM) and the finite forward difference method are used for obtaining the wave solutions and the numeric and exact approximations to the FitzHugh–Nagumo (F-N) equation, respectively. We successfully obtain some wave solutions to this equation by using aBTM. We then employ the finite difference method (FDM) in approximating the exact and numerical solutions to this equation by taking one of the obtained wave solutions into consideration. We also present the comparison between exact and numeric approximations and support the comparison with a graphic plot. Moreover, the Fourier von-Neumann stability analysis is used in checking the stability of the numeric scheme. We also present the [Formula: see text] and [Formula: see text] error norms of the solutions to this equation.

Melting and dynamic pressure: coupling of reactions, heat transfer and deformation

2021 ◽  
Author(s):  
Stefan Markus Schmalholz ◽  
Evangelos Moulas ◽  
Yuri Podladchikov
Keyword(s):  
Heat Transfer ◽  
Latent Heat ◽  
Numerical Solutions ◽  
Dynamic Pressure ◽  
Rock Deformation ◽  
Plate Boundaries ◽  
Melting Heat ◽  
Melt Migration ◽  
Melting Heat Transfer ◽  
The Impact

<p>Melting is a major process of plate tectonics, affecting divergent and convergent plate boundaries. Melting of rock is also a typical example of a coupled geological process, in which the associated transformation affects the heat transfer via the latent heat of fusion and the rock deformation via the volume change. However, petrological studies on melting usually focus on chemical aspects, such as differentiation of involved components, thermal studies usually focus only on the impact of latent heat on heat transfer, such as done in the classical Stefan problem of solidification. Similarly, studies focusing on lithosphere and mantle deformation usually only consider the impact on the effective viscosity, such as weakening due to partial melting, or the impact on buoyancy due to density changes. Many studies do, therefore, not consider coupling of melting, heat transfer and rock deformation. Indeed, a common assumption is that rock pressure, or mean stress, remains lithostatic during melting. While this assumption is attractive due to its simplicity, it is against the common knowledge derived from physical experiments and the well-established mechanical theories. Furthermore, theoretical models of melt migration would not work if pressure is everywhere lithostatic, or hydrostatic, because melt migration is driven by local deviations from the static stress state.</p><p>Here, we present simple mathematical models based on the fundamental laws of physics and thermodynamics (e.g. conservation of mass, momentum and energy) to study the fundamental coupling of melting, heat transfer and rock deformation, and to quantify dynamic pressure variations due to melting. We show both analytical and numerical solutions for these models. We discuss applications of these solutions to experiments and geological observations and estimate magnitudes of dynamic pressure resulting from melting under natural conditions.</p>

Impact of Rotor–Stator Interaction on Turbine Blade Film Cooling

1996 ◽  
Vol 118 (1) ◽  
pp. 123-133 ◽  
Author(s):  
R. S. Abhari
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Film Cooling ◽  
Numerical Code ◽  
Test Facility ◽  
Time Resolved ◽  
Injection Model ◽  
Rotor Stator Interaction ◽  
The Impact ◽  
State Case

The goal of this study is to quantify the impact of rotor–stator interaction on surface heat transfer of film cooled turbine blades. In Section I, a steady-state injection model of the film cooling is incorporated into a two-dimensional, thin shear layer, multiblade row CFD code. This injection model accounts for the penetration and spreading of the coolant jet, as well as the entrainment of the boundary layer fluid by the coolant. The code is validated, in the steady state, by comparing its predictions to data from a blade tested in linear cascade. In Section II, time-resolved film cooled turbine rotor heat transfer measurements are compared with numerical predictions. Data were taken on a fully film cooled blade in a transonic, high pressure ratio, single-stage turbine in a short duration turbine test facility, which simulates full-engine nondimensional conditions. Film cooled heat flux on the pressure surface is predicted to be as much as a factor of two higher in the time average of the unsteady calculations compared to the steady-state case. Time-resolved film cooled heat transfer comparison of data to prediction at two spanwise positions is used to validate the numerical code. The unsteady stator–rotor interaction results in the pulsation of the coolant injection flow out of the film holes with large-scale fluctuations. The combination of pulsating coolant flow and the interaction of the coolant with this unsteady external flow is shown to lower the local pressure side adiabatic film effectiveness by as much as 64 percent when compared to the steady-state case.

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