Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The natural convection flow and heat transfer between two enclosures that communicate through a vertical opening is studied by considering the evolution of an enclosed fluid in which the left half is originally at a different temperature than the right half. Numerical experiments show that at sufficiently high Rayleigh numbers the ensuing flow is oscillatory. This and other features are anticipated on the basis of scale analysis. The time scales of the oscillation, the establishment of thermal stratification, and eventual thermal equilibrium are determined and tested numerically. At sufficiently high Rayleigh numbers the heat transfer between the communicating zones is by convection, in accordance with the constant-Stanton-number trend pointed out by Jones and Otis (1986). The range covered by the numerical experiments is 102 < Ra < 107, 0.71 < Pr < 100, and 0.25 < H/L < 1.

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Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

MATEMATIKA ◽

10.11113/matematika.v34.n2.1016 ◽

2018 ◽

Vol 34 (2) ◽

pp. 393-417 ◽

Cited By ~ 2

Author(s):

Yahaya Shagaiya Daniel ◽

Abdul Aziz Zainal ◽

Zuhaila Ismail ◽

Faisal Salah

Keyword(s):

Natural Convection ◽

Differential Equations ◽

Thermal Radiation ◽

Heat Generation ◽

Thermal Stratification ◽

Nonlinear Partial Differential Equations ◽

Convection Flow ◽

Natural Convection Flow ◽

Reaction Heat ◽

Radiation Chemical

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

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Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface

Symmetry ◽

10.3390/sym13020175 ◽

2021 ◽

Vol 13 (2) ◽

pp. 175

Author(s):

Mina B. Abd-el-Malek ◽

Nagwa A. Badran ◽

Amr M. Amin ◽

Anood M. Hanafy

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Symmetry Group ◽

Transformation Method ◽

Vertical Surface ◽

Lie Symmetry ◽

Convection Boundary Layer ◽

Group Transformation ◽

Layer Flow ◽

Lie Symmetry Group Transformation

The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transformation was applied twice consecutively to convert the motion governing equations into a system of ordinary differential equations. The obtained system of ordinary differential equations was solved numerically using the Lobatto IIIA formula (implicit Runge–Kutta method). The effect of the Prandtl number on the temperature and velocity profiles is illustrated graphically.

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