scholarly journals An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3396
Author(s):  
Yasir Nawaz ◽  
Muhammad Shoaib Arif ◽  
Wasfi Shatanawi ◽  
Amna Nazeer

The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding implicit compact scheme to find solutions of nonlinear and linear convection–diffusion type equations because the implicit existing compact scheme fails to obtain the solution. In addition, the present scheme provides fourth-order accuracy in space and second-order accuracy in time, and is constructed on three grid points and three time levels. It is a compact multistep scheme and conditionally stable, while the existing multistep scheme developed on three time levels is unconditionally unstable for parabolic and considered a type of equations. The mathematical model of the heat transfer in a mixed convective radiative fluid flow over a flat plate is also given. The convergence conditions of dimensionless forms of these equations are given, and also the proposed scheme solves equations, and results are compared with two existing schemes. It is hoped that the results in the current report are a helpful source for future fluid-flow studies in an industrial environment in an enclosure area.

Author(s):  
Xiuling Yin ◽  
Chengjian Zhang ◽  
Jingjing Zhang

AbstractThis paper proposes two schemes for a nonlinear Schrödinger equation with four-order spacial derivative by using compact scheme and discrete gradient methods. They are of fourth-order accuracy in space. We analyze two discrete invariants of the schemes. The numerical experiments are implemented to investigate the efficiency of the schemes.


Author(s):  
A. D. Gosman ◽  
M. L. Koosinlin ◽  
F. C. Lockwood ◽  
D. B. Spalding

A calculation procedure has been developed for predicting fluid-flow and heat-transfer phenomena in axisymmetrical, rotating, turbulent, steady flows, with special reference to those mainly confined within cavities. The procedure has been used for predicting boundary-layer flow between a rotating disk and a stationary one, and flow and heat transfer in a shrouded-disk system. Agreement with experimental measurements is satisfactory.


2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jun-Jie Cao ◽  
Xiang-Gui Li ◽  
Jing-Liang Qiu ◽  
Jing-Jing Zhang

Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.


Author(s):  
Noreen Akbar ◽  
z Khan ◽  
S Nadeem ◽  
W khan

Purpose – The purpose of this paper, is to study the MHD double-diffusive natural convection of a nanofluid over a linearly stretching sheet using the Buongiorno model. Design/methodology/approach – The transport equations are transformed into coupled similarity equations. The numerical self-similar solutions are compared with the literature for the special case of pure fluid flow and found to be in good agreement. Graphical results are presented to illustrate the effects of various fluid flow, heat transfer and nano concentration parameters for both assisting and opposing flows. Findings – It is found that the heat transfer rate increases as nanoparticles and salt are suspended in water. It is also found that dual solutions exist for the stretching parameter. Originality/value – First paper on this model for stretching sheet.


2017 ◽  
Vol 20 (4) ◽  
pp. 58-63
Author(s):  
K. Maksymenko-Sheiko ◽  
◽  
Yu. Litvinova ◽  
T. Sheyko ◽  
M. Khazhmuradov ◽  
...  

2015 ◽  
Vol 9 (3) ◽  
pp. 242 ◽  
Author(s):  
Efstathios Kaloudis ◽  
Dimitris Siachos ◽  
Konstantinos Stefanos Nikas

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