Entropy Generation Analysis in Nonlinear Convection Flow of Thermally Stratified Fluid in Saturated Porous Medium With Convective Boundary Condition

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
B. Vasu ◽  
Ch. RamReddy ◽  
P. V. S. N. Murthy ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Local Similarity ◽  
Surface Boundary ◽  
Thermal Dispersion ◽  
Partial Differential

This article emphasizes the significance of entropy generation analysis and nonlinear temperature density relation on thermally stratified viscous fluid flow over a vertical plate embedded in a porous medium with a thermal dispersion effect. In addition, the convective surface boundary condition is taken into an account. By using the suitable transformations, the governing flow equations in dimensional form are converted into set of nondimensional partial differential equations. Then the local similarity and nonsimilarity procedures are applied to transform the set of nondimensional partial differential equations into set of ordinary differential equations and then the resulting system of equations are solved by Chebyshev spectral collocation method along with the successive linearization. The effect of pertinent parameters, namely, Biot number, mixed convection parameter, and thermal dispersion on velocity, temperature, entropy generation rate, and heat transfer rate are displayed graphically and the salient features are explored in detail.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application

2006 ◽  
Vol 128 (4) ◽  
pp. 946-959 ◽  
Author(s):  
Nhan Nguyen ◽  
Mark Ardema
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Control Problem ◽  
Boundary Control ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

Some non-local logistic population model with non-zero boundary condition

2018 ◽  
Vol 20 (08) ◽  
pp. 1750075 ◽  
Author(s):  
Patricio Cerda ◽  
Marco Souto ◽  
Pedro Ubilla
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Population Model ◽  
A Priori ◽  
Partial Differential ◽  
Non Local

In this paper, we study some type of equations which may model the behavior of species inhabiting in some habitat. For our purpose, using a priori bounded techniques, we obtain a positive solution to a family of non-local partial differential equations with non-homogeneous boundary conditions.

Analysis of Heat Transfer and Entropy Generation in a Channel Partially Filled With N-Layer Porous Media

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Kun Yang ◽  
Hao Chen ◽  
Jiabing Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Porous Media ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Free Fluid ◽  
Bejan Number ◽  
Stress Jump

Convective heat transfer in a channel partially filled with porous medium has received a lot of attention due to its wide engineering applications. However, most researches focused on a channel partially filled with single layer porous medium. In this paper, we will analyze the heat transfer and entropy generation inside a channel partially filled with N-layer porous media. The flow and the heat transfer in the porous region are described by the Darcy–Brinkman model and the local thermal nonequilibrium model, respectively. At the porous-free fluid interface, the momentum and the heat transfer are described by the stress jump boundary condition and the heat flux jump boundary condition, respectively; while at the interface between two different porous layers, the momentum and the heat transfer are described by the stress continuity boundary condition and the heat flux continuity boundary condition, respectively. The analytical solutions for the velocity and temperature in the channel are derived and used to calculate the overall Nusselt number, the total entropy generation rate, the Bejan number, and the friction factor. Furthermore, the performances of the flow and heat transfer of a channel partially filled with third-layer porous media are studied.

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