Transient free convective hydromagnetic flow in an infinite vertical cylinder with Hall current and heat source/sink

2020

Self Cite

The intention of the present article is to examine the transient effect on the free convection of the second‐grade fluid flowing in a vertical cylinder. We have found the analytical solution of the derived governing partial differential equations in nondimensional form corresponding to the velocity as well as the temperature fields by applying the Laplace transformation method in terms of the Bessel function of the first kind. To obtain the impacts of the appropriate parameters related to the given equations, such as the second‐grade fluid parameter and the Prandtl number, the numerical values of the velocity are discussed and displayed in graphs. Furthermore, the mass flow rate and the skin friction at the inner surface of the cylinder are given in a tabular form. The influence of the second‐grade fluid parameter is to decelerate the velocity as well as the mass flow rate and to enhance the steady‐state time.

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transient free convection of a second‐grade fluid flowing in a vertical cylinder

Dwivedi

2020

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“…Recently, Dwivedi and Singh 43 have presented in detailed the analysis corresponding to Equation (13); thus, its analysis will be not presented here. Deputing the mathematical expression of

\bar{θ} false(r, p false)

from Equation (13) in (10) and then solving by employing the border circumstances given in Equation (12),

\overset{U}{true} (r, p)

is obtained as follows:

\bar{U} false(r, p false) = A_{1} true{\frac{J_{0} true(ir \sqrt{\frac{1}{M} true(p + \frac{1}{italicDa} true)} true)}{J_{0} true(i \sqrt{\frac{1}{M} true(p + \frac{1}{italicDa} true)} true)} - \frac{J_{0} false(r \sqrt{S - pPr} false)}{J_{0} false(\sqrt{S - italicpPr} false)} true} .

…”

Section: Mathematical Analysismentioning

confidence: 99%

“…The detailed analysis of Equation (21) will be not presented here, as it has been already discussed by Dwivedi and Singh 43 recently.…”

Section: Mathematical Analysismentioning

confidence: 99%

“…Recently, Dwivedi and Singh 43 have presented in detailed the analysis corresponding to Equation ( 13); thus, its analysis will be not presented here. Deputing the mathematical expression of θ r p ( , ) from Equation ( 13) in ( 10) and then solving by employing the border circumstances given in Equation ( 12), U r p ̅ ( , ) is obtained as follows:…”

Section: Mathematical Analysismentioning

confidence: 99%

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Role of heat source/sink in transient free convective flow through a vertical cylinder filled with a permeable medium: An analytical approach

2020

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In this study, an investigation is performed to analyze the impact of the heat source/sink parameter on the laminar transient free convective flow through a vertical cylinder filled with a permeable medium. The governing nondimensional PDEs of the mathematical model along with their appropriate initial and boundary conditions are solved analytically by incorporating the Laplace transform scheme. Moreover, we explored the impact of emerging physical parameters of the considering model in the presence of the source/sink on the velocity profiles by graphs and tables. It is found that the velocity profile has a increasing tendency with enhancement in the numerical values of the time, which finally attains its steady‐state solution in the presence of heat source/sink. Moreover, the Prandtl number, sink parameter, and viscosity ratio parameter lead to a decrease in the velocity profiles, whereas the reverse phenomenon occurs with the Darcy number and source parameter. Finally, the numerical values of the Nusselt number, skin friction, and mass flux are given in the tabular forms. The main result obtained in this paper is that the velocity is higher in the case of the source parameter, whereas an opposite behavior is observed in the case of the sink parameter.

Significance of time‐dependent magnetohydrodynamic transient free convective flow in vertical annuli: An analytical approach with the finite Hankel transform

Maurya

2021

An analytical study is accomplished by using the Finite Hankel Transform Technique for the variation of the temperature and the velocity profile with several nondimensional parameters. In this problem, an electrically conducting fluid has been considered in the vertical concentric annulus, with a perpendicular radial magnetic field. Furthermore, a closed and exact type of expression for the velocity and the temperature are received in the form of Bessel functions of both kinds (first and second). The impact of emerging parameters in this model, such as time, Hartmann number, Prandtl number, and the annular gap between the cylinders, is discussed through graphs, whereas the numerical values of the skin friction, mass flux, and the Nusselt number are given in the tabular form. As a consequence of this, it is detected that the velocity and temperature distributions are increasing continuously with an enhanced time scale. Eventually, it gains its steady state very quickly. Moreover, the impact of the Prandtl number and the Hartmann number leads to a decrease in the velocity profiles.