scholarly journals Flow of Brinkman Fluid with Heat Generation and Chemical Reaction

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Ramzan ◽  
Zaib Un Nisa ◽  
M. Ahmad ◽  
M. Nazar
Keyword(s):  
Chemical Reaction ◽  
Heat Generation ◽  
Vertical Plate ◽  
Magnetic Parameter ◽  
Mhd Flow ◽  
Velocity Fields ◽  
Temperature Profiles ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform

Unsteady magnetohydrodynamics (MHD) flow of fractionalized Brinkman-type fluid over a vertical plate is discussed. In the model of problem, additional effects such as heat generation/absorption and chemical reaction are also considered. The model is solved by using the Caputo fractional derivative. The governing dimensionless equations for velocity, concentration, and temperature profiles are solved using the Laplace transform method and compared graphically. The effects of different parameters like fractional parameter, heat generation/absorption Q , chemical reaction R, and magnetic parameter M are discussed through numerous graphs. Furthermore, comparison among ordinary and fractionalized velocity fields are also drawn. From the figures, it is observed that chemical reaction and magnetic field have decreasing effect on velocity profile, whereas thermal radiation and mass Grashof numbers have increasing effect on the velocity of the fluid.

scholarly journals Impacts of Chemical Reaction, Diffusion-Thermo and Radiation on Unsteady Natural Convective Flow past an Inclined Vertical Plate under Aligned Magnetic Field

2021 ◽  
Vol 11 (5) ◽  
pp. 13252-13267
Keyword(s):  
Magnetic Field ◽  
Chemical Reaction ◽  
Vertical Plate ◽  
Closed Form Solution ◽  
Reaction Diffusion ◽  
Form Solution ◽  
Transform Method ◽  
The Laplace Transform ◽  
First Order Chemical Reaction ◽  
Aligned Magnetic Field

In this article, diffusion-thermo, thermal radiation, and first-order chemical reaction effects are studied analytically when the aligned magnetic field set to the fluid/ the plate on the unsteady, free convective fluid passing through an inclined vertical plate by flexible surface conditions, concentration diffusion under the action of a coaxial magnetic field. The governing PDE's are derived from the physical model and transformed into dimensionless form. Then a closed-form solution is obtained using the Laplace transform method. The effects of controlling parametric quantities like M, R, Sc, Pr, Du, Gr, Gm are analyzed through graphs for fluid properties. A comparative study has been made with published results in the absence of some non-dimensional parameters for a particular case (aligned magnetic field set to the fluid) found in good agreement.

scholarly journals MHD flow past a parabolic flow past an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction

2016 ◽  
Vol 21 (1) ◽  
pp. 95-105 ◽  
Author(s):  
R. Muthucumaraswamy ◽  
P. Sivakumar
Keyword(s):  
Thermal Radiation ◽  
Chemical Reaction ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Convection Flow ◽  
Grashof Number ◽  
Linear Partial Differential Equations ◽  
Flow Past ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Abstract The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.

UNSTEADY MHD FLOW OF SOME NANOFLUIDS PAST AN ACCELERATED VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Abid Hussanan ◽  
Ilyas Khan ◽  
Hasmawani Hashim ◽  
Muhammad Khairul Anuar ◽  
Nazila Ishak ◽  
...  
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Vertical Plate ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
The Laplace Transform ◽  
Infinite Vertical Plate

The present paper deals with the unsteady magnetohydrodynamics (MHD) flow and heat transfer of some nanofluids past an accelerating infinite vertical plate in a porous medium. Water as conventional base fluid containing three different types of nanoparticles such as copper (Cu), aluminum oxide (Al2O3) and titanium oxide (TiO2) are considered. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy are converted into linear ordinary differential equations. Exact solutions of these equations are obtained with the Laplace Transform method. The influence of pertinent parameters on the fluid motion is graphically underlined. It is found that the temperature of Cu-water is higher than those of Al2O3-water and TiO2-water nanofluids.   

Soret Effect on Unsteady MHD Free Convection Flow Past an Impulsively Started Vertical Plate with Chemical Reaction

2018 ◽  
Vol 2 (01) ◽  
Author(s):  
N. K. Gupta ◽  
U. S. Rajput
Keyword(s):  
Magnetic Field ◽  
Free Convection ◽  
Chemical Reaction ◽  
Vertical Plate ◽  
Soret Effect ◽  
Mhd Flow ◽  
Convection Flow ◽  
Transform Method ◽  
Grashof Number ◽  
Flow Past

In this paper, we are analyzing Soret effect and inclined magnetic field on unsteady free convection MHD flow past an impulsively started vertical plate with chemical reaction. Fluid considered is electrically conducting. The Laplace transform method has been used to find the exact solutions for the concentration, momentum and energy equations. The flow model consists of a magnetic field inclined from vertical by an angle . The flow is considered unsteady and heat is transferred through free convection. The velocity profiles are discussed with the help of graphs drawn for different parameters like thermal Grashof number, the Soret number, the Prandtl number, the chemical reaction parameter, the Hartmann number, the Schmidt number, the mass Grashof number, time and inclination of magnetic field. The numerical values of skin friction have been discussed with the help of table for different parameters.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

scholarly journals Hall Current And Dufour Effects On Mhd Flow Of A Micropolar Fluid Past A Vertical Plate In The Presence Of Radiation Absorption And Chemical Reaction

2014 ◽  
Vol 10 (4) ◽  
pp. 106-121 ◽  
Author(s):  
K. Surya Narayana Reddy ◽  
◽  
M. Sreedhar Babu ◽  
S. Vijaya Kumar Varma ◽  
N. Bhaskar Reddy
Keyword(s):  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Vertical Plate ◽  
Hall Current ◽  
Mhd Flow ◽  
Radiation Absorption

The Laplace Transform Method

2016 ◽  
pp. 321-373
Author(s):  
Svetlin G. Georgiev
Keyword(s):  
Laplace Transform ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform
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