scholarly journals Explicit Solutions of a Gravity-Induced Film Flow along a Convectively Heated Vertical Wall

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ammarah Raees ◽  
Hang Xu
Keyword(s):  
Film Flow ◽  
Vertical Wall ◽  
Boussinesq Approximation ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Reduced Equations ◽  
Homotopy Analysis ◽  
Gravity Driven ◽  
The Mathematical Model

The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). The resulting solutions are investigated for heat transfer effects on velocity and temperature profiles.

scholarly journals Numerical study of bio-convection flow of magneto-cross nanofluid containing gyrotactic microorganisms with activation energy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qiu-Hong Shi ◽  
Aamir Hamid ◽  
M. Ijaz Khan ◽  
R. Naveen Kumar ◽  
R. J. Punith Gowda ◽  
...  
Keyword(s):  
Radiation Effects ◽  
Numerical Study ◽  
Source Parameters ◽  
Lewis Number ◽  
Convective Boundary Condition ◽  
Convection Flow ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Cross Nanoliquid ◽  
Source Sink

AbstractIn this study, a mathematical model is developed to scrutinize the transient magnetic flow of Cross nanoliquid past a stretching sheet with thermal radiation effects. Binary chemical reactions and heat source/sink effects along with convective boundary condition are also taken into the consideration. Appropriate similarity transformations are utilized to transform partial differential equations (PDE’s) into ordinary ones and then numerically tackled by shooting method. The impacts of different emerging parameters on the thermal, concentration, velocity, and micro-rotation profiles are incorporated and discussed in detail by means of graphs. Results reveal that, the escalation in magnetic parameter and Rayleigh number slowdowns the velocity and momentum of the fluid. The increase in Biot number, radiation and heat sink/source parameters upsurges the thermal boundary but, converse trend is seen for escalating Prandtl number. The density number of motile microorganisms acts as a growing function of bioconvection Lewis number and declining function of bioconvection Peclet number.

Slip flow over a non-Newtonian fluid through a Darcy–Forchheimer medium: Numerical approach

2019 ◽  
Vol 33 (35) ◽  
pp. 1950448
Author(s):  
K. Ganesh Kumar ◽  
M. N. Khan ◽  
M. Osman ◽  
Abdulaziz R. Alharbi ◽  
Mohammad Rahimi-Gorji ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Convective Boundary Condition ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Liquid Suspension

This work focused on slip flow over a non-Newtonian nanofluid fluid flow past a stretching sheet with particles–liquid suspension. The convective boundary condition is taken into account. Similarity transformations are utilized to reduce the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Runge–Kutta–Fehlberg scheme is used to get the numerical solution. Important parameters are analyzed through graphs and skin friction coefficient. Nusselt numbers are presented in tables. Investigation reveals that slip parameter decreases the velocity field and Biot number increases the temperature field.

Effects of Arrhenius Activation Energy and Binary Chemical Reaction on Convective Flow of a Nanofluid over Frustum of a Cone with Convective Boundary Condition

2017 ◽  
Vol 16 (3) ◽  
Author(s):  
RamReddy Chetteti ◽  
Venkata Rao Chukka
Keyword(s):  
Activation Energy ◽  
Boundary Condition ◽  
Chemical Reaction ◽  
Convective Flow ◽  
Volume Fraction ◽  
Convective Boundary Condition ◽  
Complex Flow ◽  
Arrhenius Activation Energy ◽  
Convective Boundary ◽  
Similarity Transformations

AbstractIn this article, we investigate the effects of Arrhenius activation energy with binary chemical reaction and convective boundary condition on natural convective flow over vertical frustum of a cone in a Buongiorno nanofluid under the presence of thermal radiation. The zero nanoparticle flux condition is used at the surface of frustum of a cone rather than the uniform wall condition to execute physically applicable results. For this complex flow model, a suitable non-similarity transformations are used initially and then Bivariate pseudo-spectral local linearisation method is used to solve the non-similar, coupled partial differential equations. Further, the convergence test and error analysis are conducted to verify the accuracy of numerical method. The effects of flow influenced parameters on the non-dimensional velocity, temperature, nanoparticle volume fraction and regular concentration profiles as well as on the skin friction, heat transfer rate, nanoparticle and regular mass transfer rates are analyzed.

Study on Sakiadis and Blasius flows of Williamson fluid with convective boundary condition

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
G.K. Ramesh ◽  
B.J. Gireesha ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary ◽  
Williamson Fluid ◽  
Blasius Flow ◽  
Similarity Transformations ◽  
Sakiadis Flow ◽  
Fifth Order

AbstractThe present analysis reports the behaviour of Sakiadis and Blasius flow of Williamson fluid with convective boundary condition. Using boundary layer approximations and suitable similarity transformations the governing partial differential equations along with the boundary conditions are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved numerically with the help of fourth and fifth order Runge-Kutta-Fehlberg method. It is found that the Blasius flow provides a thicker thermal boundary layerwhen compared with the Sakiadis flow.

Analytical and Numerical Study on Cross Diffusion Effects on Magneto-Convection of a Chemically Reacting Fluid with Suction/Injection and Convective Boundary Condition

2020 ◽  
Vol 401 ◽  
pp. 63-78
Author(s):  
Sheniyappan Eswaramoorthi ◽  
Marimuthu Bhuvaneswari ◽  
S. Sivasankaran ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Condition ◽  
Heat Generation ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Soret And Dufour Effects ◽  
Cross Diffusion ◽  
Similarity Transformations ◽  
Fourth Order Method

The purpose of this paper is to investigate the Soret and Dufour effects on unsteady mixed convective boundary layer flow of a viscous fluid over a stretching surface in a porous medium in the presence of magnetic field with heat generation/absorption, chemical reaction, suction/injection and convective boundary condition. The governing time-dependent partial differential equations are transformed into non-linear ordinarydifferential equations using similarity transformations. These equations subject to the appropriate boundary conditions are solved analytically by homotopy analysis method (HAM) and numerically by Runge-Kutta fourth order method and shooting technique.The numerical solution is compared with analytical solution. The influence of the different parameters on velocity, temperature and concentration profiles are discussed in graphical as well as in tabular form. It is observed that the fluid velocity and temperature increase on increasing the buoyancy ratio parameter and heat generation/absorption parameter. Also found that the surface heat and mass transfer rates increase on increasingthe suction/injection and heat generation/absorption parameters.

scholarly journals Numerical study of bio-convection flow of magneto-Cross nanofluid containing gyrotactic microorganisms with effective Prandtl number approach

2021 ◽  
Author(s):  
Aamir Hamid ◽  
M. Ijaz Khan ◽  
R. Naveen Kumar ◽  
R. J. Punith Gowda ◽  
B.C. Prasannakumara
Keyword(s):  
Prandtl Number ◽  
Radiation Effects ◽  
Numerical Study ◽  
Source Parameters ◽  
Lewis Number ◽  
Convective Boundary Condition ◽  
Convection Flow ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Cross Nanoliquid

Abstract In this study, a mathematical model is developed to scrutinize the transient magnetic flow of Cross nanoliquid past a stretching sheet with thermal radiation effects. Binary chemical reactions and heat source/sink effects along with convective boundary condition are also taken into the consideration. Apposite similarity transformations are utilized to transform partial differential equations (PDE’s) into ordinary ones and then numerically tackled by shooting method. The Impacts of different emerging parameters on the thermal, concentration, velocity, and micro-rotation profiles are incorporated and discussed in detail by means of graphs. Results reveals that, the escalation in Magnetic parameter and Rayleigh number slowdowns the velocity and momentum of the fluid. The increase in Biot number, radiation and Heat sink/source parameters upsurges the thermal boundary but, converse trend is seen for escalating Prandtl number. The density number of motile microorganisms acts as a growing function of bioconvection Lewis number and declining function of bioconvection Peclet number.

Simultaneous Convection of Carreau Fluid with Radiation Past a Convectively Heated Moving Plate

2018 ◽  
Vol 389 ◽  
pp. 60-70 ◽  
Author(s):  
Oluwole Daniel Makinde ◽  
B.C. Prasanna Kumara ◽  
G.K. Ramesh ◽  
Bijjanal Jayanna Gireesha
Keyword(s):  
Numerical Solutions ◽  
Convective Boundary Condition ◽  
Temperature Fields ◽  
Practical Significance ◽  
Integration Scheme ◽  
Moving Plate ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Effects Of Radiation ◽  
Energy Equations

In the present analysis, we extended Blasius and Sakiadis problems in Carreau fluids by considering a uniform free stream parallel to a fixed or moving flat plate, which has more practical significance. The effects of radiation and convective boundary condition are also taken into account. The resulting nonlinear momentum and energy equations are simplified using similarity transformations. Numerical solutions have been obtained for the velocity and temperature profiles by employing shooting method coupled with Runge-Kutta-Fehlberg integration scheme. Graphical results for the velocity and temperature fields are sketched and discussed. It is found that temperature of the Blasius problem is always higher than the Sakiadis problem.

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