Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium

Kulkarni, Ameya; Jacobs, Hans; Hwang, Jen-Jyh

doi:10.1016/0017-9310(87)90199-2

Cited by 62 publications

(36 citation statements)

References 9 publications

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“…Also, temperature becomes negative in presence of dense stratified fluid. This type of behaviour has also been observed by earlier investigators (Kulkarni et al [26], Loganathan and Ganesan [14], and Deka and Paul [24]). This is because the fluid with dense stratification near the cylinder can have temperature and concentration lower than the ambient.…”

Section: Resultssupporting

confidence: 87%

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

Paul

Deka

2017

International Journal of Engineering Mathematics

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This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times.

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Section: Resultssupporting

confidence: 87%

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

Paul

Deka

2017

International Journal of Engineering Mathematics

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“…Deka and Neog [7] studied unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid. Kulkarni et al [8] presented the similarity solutions for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium. Gurminder Singh et al [9] examined the impacts of thermally stratified ambient fluid on MHD convective along a moving non-isothermal vertical plate using Runge-Kutta fourth order method along with shooting technique.…”

Section: Introductionmentioning

confidence: 99%

Unsteady MHD Natural Convective Flow over Vertical Plate in Thermally Stratified Media with Variable Viscosity and Thermal Conductivity

Iranian¹,

Loganathan²,

Ganesan³

2015

IJCA

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The effects of exponentially varying viscosity and linearly varying thermal conductivity on unsteady MHD natural convective flow past a semi infinite vertical plate in a thermally stratified medium is studied. The variables of both viscosity and thermal conductivity are considered only a function of temperature. The governing boundary layer equations of continuity, momentum and energy have been transformed into dimensionless coupled and nonlinear equations and after that solved by implicit finite-difference method of Crank-Nicolson type. The effects of the varying viscosity, thermal conductivity and stratification parameter at various times are discussed with velocity and temperature profiles and additionally the skin-friction and the rate of heat transfer. KeywordsUnsteady, vertical plate, variable viscosity, thermal conductivity, thermal stratification. NOMENCLATURE INTRODUCTIONFree convection flows are of great interest in a number of industrial applications, for example, geothermal frameworks, fiber and granular insulation etc. Buoyancy is also of importance in an environment where differences between land and air temperatures can give rise to complicated flow patterns. Heat transfer on fluid flow due to free convection in the presence of magnetic field finds subsidiary applications in different branches of Science and Technology such as atomic science, fire engineering, computational astrophysics, the magnetic behavior of plasmas in fusion reactors, liquid-metal cooling of nuclear reactors and electromagnetic casting. The problem of free convection flow past an infinite vertical plate under different plate conditions was studied by numerous researchers. Soundalgekar [1] studied the free convection effects on the Stokes problem for an infinite vertical plate by using Laplace transform method. Hellums and Churchill [2] were the first to present unsteady natural convective flow past a semi-infinite isothermal vertical plate by using an explicit finite-difference scheme. As explicit finite-difference scheme has its own particular lacks, later, Soundalgekar and Ganesan [3] have solved free convection flow past a vertical plate with mass transfer using implicit finite difference method of Crank-Nicolson type which is unconditionally stable and convergent.

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“…Many principal past studies concerning natural convection flows over a semi-infinite vertical plate immersed in an ambient fluid where the flow is induced by both heat and chemical diffusion mechanisms have been found in the literature [5,8,12,18]. An interesting extension of this problem is the study of effects caused by the inclusion of general chemical reaction of order n. In particular, this study is concerned mainly with the steady-state behaviour of the same binary system composed of a semi-infinite plate and ambient fluid, each initially at different concentrations of a given species, but between which a homogeneous, irreversible, isothermal chemical reaction of order n is assumed to occur.…”

mentioning

confidence: 99%

“…For this, it is convenient to consider the idealised system composed of a semi-infinite plate set in a fluid of infinite extent. Such a model has been commonly used in previous work [11,12,18,21] and permits the application of classical boundary-layer analysis in the mathematical formulation. In the analysis, steady two-dimensional laminar viscous flow over the semi-infinite vertical plate is examined.…”

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confidence: 99%

Similarity analysis for natural convection from a vertical plate with distributed wall concentration

Mulolani

Rahman

2000

International Journal of Mathematics and Mathematical Sciences

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Abstract. Steady laminar natural convection flow over a semi-infinite vertical plate is examined in this paper. It is assumed that the concentration of a species along the plate follows some algebraic law with respect to chemical reaction. Similarity solutions may then be obtained for different orders of reaction. The fundamental parameters of this problem are the Schmidt number, Sc, and reaction order, n. Numerical results, based on the fourth order Runge-Kutta method, for Schmidt number ranging from 0.0 to 100.0 and reaction order from 0.0 to 1.5 are presented. When chemical reaction occurs, diffusion and velocity domains are seen to expand out from the plate. For large values of n, one may expect a smaller diffusion layer which, at fixed Schmidt number, is associated with increased velocity and reduced convection-layer.

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Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium

Cited by 62 publications

References 9 publications

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

Unsteady MHD Natural Convective Flow over Vertical Plate in Thermally Stratified Media with Variable Viscosity and Thermal Conductivity

Similarity analysis for natural convection from a vertical plate with distributed wall concentration

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