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

Heat Transfer ◽  
2021 ◽  
Author(s):  
Anurag ◽  
J. P. Maurya ◽  
A. K. Singh
Keyword(s):  
Convective Flow ◽  
Analytical Approach ◽  
Hankel Transform ◽  
Time Dependent ◽  
Free Convective Flow ◽  
Finite Hankel Transform ◽  
Vertical Annuli

Couette Flow of a Generalized Oldroyd-B Fluid due to Constantly Accelerated Shear Stress Coupled with the Pressure Gradient

2011 ◽  
Vol 354-355 ◽  
pp. 179-182
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang ◽  
Jia Jia Niu
Keyword(s):  
Shear Stress ◽  
Laplace Transform ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Hankel Transform ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Finite Hankel Transform

This paper presented an analysis for the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress with the influence of the internal constantly decelerated pressure gradient. The exact solutions are established by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform and presented by integral and series form in terms of the Mittag-Leffler function. Moreover, the effects of various parameters are analyzed in detail by graphical illustrations.

scholarly journals Role of heat source/sink on time dependent free convective flow in a coaxial cylinder filled with porous material: a semi analytical approach

2020 ◽  
Vol 9 (1) ◽  
pp. 67 ◽  
Author(s):  
Taiwo S. Yusuf ◽  
Gambo Dauda
Keyword(s):  
Heat Source ◽  
Time Domain ◽  
Convective Flow ◽  
Viscosity Ratio ◽  
Darcy Number ◽  
Coaxial Cylinder ◽  
Time Dependent ◽  
Free Convective Flow ◽  
Laplace Domain ◽  
Source Sink

In this article, the semi analytical solution for a fully developed time dependent free convective flow of a viscous incompressible fluid with heat source/sink in an infinite vertical coaxial cylinder saturated with porous material has been analyzed. The flow was induced by buoyancy forces due to temperature differences caused by the thermal insulation of the inner wall and constant heating of the outer wall. The Laplace transform technique was employed to transform the governing equation from time domain to the Laplace domain. Notwithstanding, a numerical inversing scheme known as Riemann-sum approximation (RSA), renowned for its precision has been utilized to transform the Laplace domain solution to time domain. The accuracy of the numerical technique employed was tested by presenting a comparison with the numerical values obtained using RSA, PDEPE, and steady state solution at large time. The effects of the various flow parameters on the flow formation are exhibited graphically. It is interesting to note that the fluid temperature and velocity increases as time passes. In addition, the velocity can be enhanced and minimized by gradually increasing Darcy number and the viscosity ratio respectively. However, the increase is seen to be more prominent when heat source is applied. The drag on both walls are seen to increase with increase in Darcy number, the reverse trend is observed with increase in the viscosity ratio.

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