scholarly journals Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Imran Siddique ◽  
Sehrish Ayaz ◽  
Dalal Alrowaili ◽  
Sohaib Abdal
Keyword(s):  
Free Convection ◽  
Fourier Transforms ◽  
Special Functions ◽  
Rectangular Channel ◽  
Convection Flow ◽  
Physical Parameters ◽  
Free Convection Flow ◽  
Closed Form Solutions ◽  
Generalized Boundary Conditions ◽  
Short Time

In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.

The Effects of Radiation on Free Convection Flow with Ramped Wall Temperature in Brinkman Type Fluid

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Muhamad Najib Zakaria ◽  
Abid Hussanan ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Laplace Transform ◽  
Vertical Plate ◽  
Convection Flow ◽  
Physical Parameters ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Effects Of Radiation

The present paper is on study of the influence of radiation on unsteady free convection flow of Brinkman type fluid near a vertical plate containing a ramped temperature profile. Using the appropriate variables, the basic governing equations are reduced to nondimensional equations valid with the imposed initial and boundary conditions. The exact solutions are obtained by using Laplace transform technique. The influence of radiation near a ramped temperature plate is also compared with the flow near a plate with constant temperature. The numerical computations are carried out for various values of the physical parameters such as velocity, temperature, skin friction and Nusselt number and presented graphically.

Solutions with special functions for time fractional free convection flow of Brinkman-type fluid

2016 ◽  
Vol 131 (9) ◽  
Author(s):  
Farhad Ali ◽  
Syed Aftab Alam Jan ◽  
Ilyas Khan ◽  
Madeha Gohar ◽  
Nadeem Ahmad Sheikh
Keyword(s):  
Free Convection ◽  
Special Functions ◽  
Convection Flow ◽  
Free Convection Flow

scholarly journals Heat and Mass Transfer of Unsteady Hydromagnetic Free Convection Flow Through Porous Medium Past a Vertical Plate with Uniform Surface Heat Flux

2017 ◽  
Vol 47 (3) ◽  
pp. 25-58 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Aishah S. Yahya
Keyword(s):  
Mass Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Free Convection ◽  
Heat And Mass Transfer ◽  
Transport Model ◽  
Convection Flow ◽  
Physical Parameters ◽  
Free Convection Flow ◽  
Laplace Transform Technique

AbstractSimultaneous effects of thermal and concentration diffusions in unsteady magnetohydrodynamic free convection flow past a moving plate maintained at constant heat flux and embedded in a viscous fluid saturated porous medium is presented. The transport model employed includes the effects of thermal radiation, heat sink, Soret and chemical reaction. The fluid is considered as a gray absorbing-emitting but non-scattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. The dimensionless coupled linear partial differential equations are solved by using Laplace transform technique. Numerical results for the velocity, temperature, concentration as well as the skin friction coefficient and the rates of heat and mass transfer are shown graphically for different values of physical parameters involved.

scholarly journals Effect of Variable Viscosity and Thermal Conductivity on MHD Natural Convection Flow along a Vertical Flat Plate

2021 ◽  
pp. 58-71
Author(s):  
Sree Pradip Kumer Sarker ◽  
Md. M. Alam
Keyword(s):  
Thermal Conductivity ◽  
Free Convection ◽  
Flat Plate ◽  
Variable Viscosity ◽  
Convection Flow ◽  
Physical Parameters ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Local Skin ◽  
Vertical Flat Plate

Free convection flow around a heated vertical flat plate in the presence of a magnetic field is very important from the technical standpoint, and several researchers have studied this issue. The effects of variable viscosity and thermal conductivity on Magneto-Hydrodynamics (MHD) free convection flow over an isothermal vertical plate immersed in a fluid with heat conduction will be studied in this study. The two-dimensional, laminar, and unsteady boundary layer equations are considered in this paper. Using relevant variables, simple governing equations are transformed into non-dimensional governing equations. The implicit finite difference scheme, also known as the Crank-Nicolson scheme, is used to solve these equations numerically. This research looks at viscous incompressible fluids with temperature-dependent viscosity and thermal conductivity. The effect of various parameters on velocity, temperature, local skin friction, and local heat transfer coefficient profiles will be shown in this study, and the results will be compared to those of other researchers. The current numerical results will be compared to the results of previously published works. Figures from the current thesis will be compared to those from previously published works. The outcomes result will be shown in graphs for various values of relevant physical parameters.

scholarly journals Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2313-2326 ◽  
Author(s):  
Abid Hussanan ◽  
Mohd Salleh ◽  
Ilyas Khan ◽  
Razman Tahar
Keyword(s):  
Free Convection ◽  
Closed Form ◽  
Micropolar Fluid ◽  
Closed Form Solution ◽  
Convection Flow ◽  
Physical Parameters ◽  
Newtonian Heating ◽  
Free Convection Flow ◽  
Present Solution ◽  
Laplace Transform Technique

This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.

scholarly journals Magnetohydrodynamics Free Convection Flow of Incompressible Fluids over Corrugated Vibrating Bottom Surface with Hall Currents and Heat and Mass Transfers

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Vincent M. Bulinda ◽  
Giterere P. Kang’ethe ◽  
Phineas R. Kiogora
Keyword(s):  
Free Convection ◽  
Incompressible Fluids ◽  
Bottom Surface ◽  
Convection Flow ◽  
Physical Parameters ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Finite Difference Numerical Method ◽  
Explicit Finite Difference ◽  
Mass Transfers

Magnetohydrodynamics free convection flow of incompressible fluids over corrugated vibrating bottom surface with Hall currents and heat and mass transfers considering heat flux is discussed. The corrugation patterns suggested are sinusoidal in nature. The governing equations are solved by the explicit finite difference numerical method of the forward-time backward-space scheme to obtain the analytical results for velocity, concentration, and temperature profiles. The unsteady resultant velocities, concentration, and temperature for various values of physical parameters are discussed in detail, and it is shown that they have significant effects on the fluid flow, and heat and mass transfers are shown graphically.

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