scholarly journals Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion

2022 ◽  
Vol 2022 ◽  
pp. 1-20
Author(s):  
Ndolane Sene
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Special Functions ◽  
Error Function ◽  
Mass Diffusion ◽  
Incompressible Viscous Fluid ◽  
Convection Flow ◽  
Fractional Operator ◽  
Newtonian Heating ◽  
Proposed Model

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Magnetohydrodynamic Natural Convection Flow with Newtonian Heating and Mass Diffusion over an Infinite Plate that Applies Shear Stress to a Viscous Fluid

2014 ◽  
Vol 69 (12) ◽  
pp. 714-724 ◽  
Author(s):  
Dumitru Vieru ◽  
Corina Fetecau ◽  
Constantin Fetecau ◽  
Niat Nigar
Keyword(s):  
Shear Stress ◽  
Natural Convection ◽  
Exact Solutions ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Boussinesq Approximation ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Newtonian Heating ◽  
Natural Convection Flow

AbstractUnsteady magnetohydrodynamic natural convection flow with Newtonian heating and constant mass diffusion over an infinite vertical plate that applies an arbitrary time-dependent shear stress to a viscous optically thick fluid is studied in the presence of a heat source. Radiative effects are taken into consideration and exact solutions for the dimensionless velocity and temperature are established under Boussinesq approximation. The solutions that have been obtained, uncommon in the literature, satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion problem with technical relevance of this type. For illustration, a special case is considered and the influence of pertinent parameters on the fluid motion is graphically underlined.

scholarly journals Heat Transfer Analysis for Viscous Fluid Flow with the Newtonian Heating and Effect of Magnetic Force in a Rotating Regime

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Rashid Ayub ◽  
Shahzad Ahmad ◽  
Muhammad Imran Asjad ◽  
Mushtaq Ahmad
Keyword(s):  
Viscous Fluid ◽  
Fluid Motion ◽  
Velocity Fields ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Newtonian Heating ◽  
Flow Parameters ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

In this article, an unsteady free convection flow of MHD viscous fluid over a vertical rotating plate with Newtonian heating and heat generation is analyzed. The dimensionless governing equations for temperature and velocity fields are solved using the Laplace transform technique. Analytical solutions are obtained for the temperature and components of velocity fields. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are presented graphically.

EFFECTS OF NEWTONIAN HEATING AND MASS DIFFUSION ON MHD FREE CONVECTION FLOW OVER VERTICAL PLATE WITH SHEAR STRESS AT THE WALL

2016 ◽  
Vol 78 (3-2) ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Shear Stress ◽  
Free Convection ◽  
Vertical Plate ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Newtonian Heating ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Set Up ◽  
Energy Equations

Effects of Newtonian heating and mass diffusion on magnetohydrodynamic free convection flow over a vertical plate that applies arbitrary shear stress to the fluid is studied. The fluid is considered electrically conducting and passing through a porous medium. The influence of thermal radiation in the energy equations is also considered. General solutions of the problem are obtained in closed form using the Laplace transform technique. They satisfy the governing equations, initial and boundary conditions and can set up a huge number of exact solutions correlatives to various fluid motions. The effects of various parameters on velocity profiles are shown graphically and discussed in details

Exact Solutions on Mixed Convection Flow of Accelerated Non-Coaxial Rotation of MHD Viscous Fluid with Porosity Effect

2020 ◽  
Vol 399 ◽  
pp. 26-37
Author(s):  
Ahmad Qushairi Mohamad ◽  
Zulkhibri Ismail ◽  
Nur Fatihah Mod Omar ◽  
Muhammad Qasim ◽  
Muhamad Najib Zakaria ◽  
...  
Keyword(s):  
Viscous Fluid ◽  
Mixed Convection ◽  
Exact Solutions ◽  
Initial Conditions ◽  
Convection Flow ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Porosity Effect ◽  
Prandtl Numbers ◽  
Physical Boundary

Mixed convection of unsteady non-coaxial rotation flow of viscous fluid over an accelerated vertical disk is investigated. The motion in the fluid is induced due to the rotating and buoyancy force effects. The problem is formulated and extended in terms of coupled partial differential equations with some physical boundary and initial conditions. The non-dimensional equations of the problem are obtained by using the suitable non-dimensional variables. The exact solutions of non-coaxial velocity and temperature profiles are obtained by using Laplace transform method which are satisfying all the initial and boundary conditions. The physical significance of the mathematical results is shown in various plots and is discussed for Grashof and Prandtl numbers as well as magnetic, porosity and accelerated parameters. It is found that, the velocity with the effect of acceleration is higher compared to constant velocity. In limiting sense, the present solutions are found identical with published results.

Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Incompressible Viscous Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Shear Stresses ◽  
Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

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