scholarly journals Irreversibility Analysis of Dissipative Fluid Flow Over A Curved Surface Stimulated by Variable Thermal Conductivity and Uniform Magnetic Field: Utilization of Generalized Differential Quadrature Method

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 943 ◽  
Author(s):  
Muhammad Afridi ◽  
Abderrahim Wakif ◽  
Muhammad Qasim ◽  
Abid Hussanan
Keyword(s):  
Thermal Conductivity ◽  
Entropy Generation ◽  
Differential Quadrature Method ◽  
Variable Thermal Conductivity ◽  
Differential Quadrature ◽  
Curved Surface ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Self Similar ◽  
Generalized Differential

The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the energy equation. Appropriate transformations are used to develop the self-similar equations from the governing equations of momentum and energy. The resulting self-similar equations are then solved by the Generalized Differential Quadrature Method (GDQM). For the validation and precision of the developed numerical solution, the resulting equations are also solved numerically using the Runge-Kutta-Fehlberg method (RKFM). An excellent agreement is found between the numerical results of the two methods. To examine the impacts of emerging physical parameters on velocity, temperature distribution and entropy generation, the numerical results are plotted against the various values of physical flow parameters and discussed physically in detail.

Numerical Examination of the Entropic Energy Harvesting in a Magnetohydrodynamic Dissipative Flow of Stokes’ Second Problem: Utilization of the Gear-Generalized Differential Quadrature Method

2019 ◽  
Vol 44 (4) ◽  
pp. 385-403 ◽  
Author(s):  
Abderrahim Wakif ◽  
Muhammad Qasim ◽  
Muhammad Idrees Afridi ◽  
Salman Saleem ◽  
M. M. Al-Qarni
Keyword(s):  
Entropy Generation ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Temperature Fields ◽  
Bejan Number ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Velocity And Temperature Fields ◽  
Generalized Differential ◽  
Stokes Second Problem

Abstract The main purpose of this numerical investigation is to estimate energetically the thermo-magnetohydrodynamic (MHD) irreversibility arising in Stokes’ second problem by successfully applying the first and second thermodynamic laws to the unsteady MHD free convection flow of an electrically conducting dissipative fluid. This fluid flow is assumed to originate periodically in time over a vertical oscillatory plate which is heated with uniformly distributed temperature and flowing in the presence of viscous dissipation and Ohmic heating effects. Moreover, the mathematical model governing the studied flow is formulated in the form of dimensional partial differential equations (PDEs), which are transformed into non-dimensional ones with the help of appropriate mathematical transformations. The expressions of entropy generation and the Bejan number are also derived formally from the velocity and temperature fields. Mathematically, the resulting momentum and energy conservation equations are solved accurately by utilizing a novel hybrid numerical procedure called the Gear-Generalized Differential Quadrature Method (GGDQM). Furthermore, the velocity and temperature fields obtained numerically by the GGDQM are exploited thereafter for computing the entropy generation and Bejan number. Finally, the impacts of the various emerging flow parameters are emphasized and discussed in detail with the help of tabular and graphical illustrations. Our principal result is that the entropy generation is maximum near the oscillating boundary. In addition, this thermodynamic quantity can rise with increasing values of the Eckert number and the Prandtl number, whereas it can be reduced by increasing the magnetic parameter and the temperature difference parameter.

scholarly journals Second Law Analysis of Unsteady MHD Viscous Flow over a Horizontal Stretching Sheet Heated Non-Uniformly in the Presence of Ohmic Heating: Utilization of Gear-Generalized Differential Quadrature Method

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 240 ◽  
Author(s):  
Muhammad Qasim ◽  
Muhammad Idrees Afridi ◽  
Abderrahim Wakif ◽  
T. Nguyen Thoi ◽  
Abid Hussanan
Keyword(s):  
Entropy Generation ◽  
Ohmic Heating ◽  
Differential Quadrature Method ◽  
Relaxation Method ◽  
Differential Quadrature ◽  
Bejan Number ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Special Cases ◽  
Generalized Differential

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport equations are altered into dimensionless self-similar partial differential equations (PDEs) through suitable transformations. The reduced momentum and energy equations are then worked out numerically by employing a new hybrid method called the Gear-Generalized Differential Quadrature Method (GGDQM). The obtained numerical results are incorporated in the calculation of the Bejan number and dimensionless entropy generation. Quantities of physical interest, like velocity, temperature, shear stress and heat transfer rate, are illustrated graphically as well as in tabular form. Impacts of involved parameters are examined and discussed thoroughly in this investigation. Exact and GGDQM solutions are compared for special cases of initial unsteady flow and final steady state flow. Furthermore, a good harmony is observed between the results of GGDQM and those given previously by the Spectral Relaxation Method (SRM), Spectral Quasilinearization Method (SQLM) and Spectral Perturbation Method (SPM).

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

2019 ◽  
Vol 55 (1-2) ◽  
pp. 42-52
Author(s):  
Milad Ranjbaran ◽  
Rahman Seifi
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

This article proposes a new method for the analysis of free vibration of a cracked isotropic plate with various boundary conditions based on Kirchhoff’s theory. The isotropic plate is assumed to have a part-through surface or internal crack. The crack is considered parallel to one of the plate edges. Existence of the crack modified the governing differential equations which were formulated based on the line-spring model. Generalized differential quadrature method discretizes the obtained governing differential equations and converts them into an algebraic system of equations. Then, an eigenvalue analysis was used to determine the natural frequencies of the cracked plates. Some numerical results are given to demonstrate the accuracy and convergence of the obtained results. To demonstrate the efficiency of the method, the results were compared with finite element solutions and available literature. Also, effects of the crack depth, its location along the thickness, the length of the crack and different boundary conditions on the natural frequencies were investigated.

Sign in / Sign up

Export Citation Format

Share Document