MHD mixed convection flow of a viscoelastic fluid over an inclined surface with a nonuniform heat source/sink

2013 ◽  
Vol 91 (12) ◽  
pp. 1074-1080 ◽  
Author(s):  
G.K. Ramesh ◽  
Ali J. Chamkha ◽  
B.J. Gireesha
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Viscoelastic Fluid ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Different Types ◽  
Layer Flow ◽  
Source Sink ◽  
Inclined Surface

The steady mixed convection boundary layer flow over an inclined stretching surface immersed in an incompressible viscoelastic fluid is considered in this paper. Employing suitable similarity transformations, the governing partial differential equations are transformed into ordinary differential equations, and the transformed equations are solved numerically using Runge–Kutta–Fehlberg method. Herein, two different types of heating processes are considered, namely, (i) prescribed surface temperature and (ii) prescribed wall heat flux. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that velocity decreases and temperature increases with an increase in the value of angle of inclination.

g-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Noraihan Afiqah Rawi ◽  
Abdul Rahman Mohd Kasim ◽  
Mukheta Isa ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Keller Box Method ◽  
Unsteady Mixed Convection ◽  
Layer Flow

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

scholarly journals Mixed Convection Flow Along Vertical Thin Needles Containing Gyrotactic Microorganism with Variable Heat, Mass and Motile Microorganism Flux

2021 ◽  
Author(s):  
Nayema Islam Nima ◽  
Bader Alshuraiaan ◽  
M. Ferdows
Keyword(s):  
Mixed Convection ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Needle Size ◽  
Similarity Transformations ◽  
Laminar Mixed Convection ◽  
Variable Surface ◽  
Fluid Concentration ◽  
Layer Flow ◽  
Gyrotactic Microorganism

Abstract The problem of steady laminar mixed convection boundary layer flow along vertical thin needle with variable surface heat, mass and motile microorganism flux in the presence of gyrotactic microorganism is considered in this study. The dimensionless leading equations of continuity, momentum, concentraton and motile microorganism conservation are reduced to ordinary differential equations with the help of similarity transformations. The transformed governing equations are then numerically solved by using MATLAB BVP4C function. The research is reached to excellent argument by comparison in few cases between the results obtained from MATLAB and Maple algorithm with the help of dsolve command. Numerical calculations are carried out for various values of the dimensionless parameters of the problem which includes mixed convection parameter λ, power law index m, buoyancy parameters N1, N2 Lewis parameter Le, bioconvection lewis parameter Lb, Bioconvection peclet number Pe and also the parameter a representing the needle size. It is also shown from the results that the surface (wall) temperature, surface fluid concentration, surface motile microorganism concentration and the corresponding velocity, temperature, concentration and motile microorganism profiles are significantly induced by these parameters. The results are pictured and discussed in detail.

scholarly journals MHD Mixed Convection Flow of Viscoelastic Fluid Embedded in Porous Medium

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
A.R.M. Kasim ◽  
N.F. Mohammad ◽  
Aurangzaib Aurangzaib ◽  
S. Shafie
Keyword(s):  
Porous Medium ◽  
Mixed Convection ◽  
Viscoelastic Fluid ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Local Skin ◽  
Viscoelastic Parameter ◽  
Keller Box Method ◽  
Local Skin Friction ◽  
Layer Flow

An analysis has been carried out to investigate the effect of magnetic field presence on the mixed convection boundary layer flow of viscoelastic fluid over a horizontal circular cylinder in a porous medium. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method. Some important parameters have been discussed in this study which include the Prandtl number (Pr), magnetic parameter (M), viscoelastic parameter (K), porosity parameter (γ) and the mixed convection parameters (λ). The results show the values of the velocity decrease when the value of viscoelastic parameter increase and the reverse trend were observe for temperature profile. Numerical results of local skin friction as well as local Nusselt number are also presented in tabular form.

Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Haliza Rosali ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Boundary Layer Flow ◽  
Thermal Conductivity Ratio ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

Mixed convection boundary layer flow past a vertical flat plate embedded in a non-Darcy porous medium saturated by a nanofluid

2014 ◽  
Vol 24 (5) ◽  
pp. 970-987 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Teodor Groşan ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Flat Plate ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Content Type ◽  
Layer Flow ◽  
Vertical Flat Plate

Purpose – The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used. Design/methodology/approach – Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed. Findings – Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (λ<0). The stability analysis indicates that for the opposing flow case, the lower solution branch is unstable, while the upper solution branch is stable. In addition, it is shown that for a regular fluid (φ=0) a very good agreement exists between the present numerical results and those reported in the open literature. Research limitations/implications – The problem is formulated for three types of nanoparticles, namely, copper (Cu), alumina (Al2O3) and titania (TiO2). However, the paper present results here only for the Cu nanoparticles. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved. Practical implications – Nanofluids have many practical applications, for example, the production of nanostructured materials, engineering of complex fluids, for cleaning oil from surfaces due to their excellent wetting and spreading behavior, etc. Social implications – Nanofluids could be applied to almost any disease treatment techniques by reengineering the nanoparticle properties. Originality/value – The present results are original and new for the boundary-layer flow and heat transfer past a vertical flat plate embedded in a porous medium saturated by a nanofluid. Therefore, this study would be important for the researchers working in porous media in order to become familiar with the flow behavior and properties of such nanofluids.

scholarly journals Numerical investigation of mixed convection boundary layer flow for nanofluids under quasilinearization technique

2021 ◽  
Vol 3 (11) ◽  
Author(s):  
Srimanta Maji ◽  
Akshaya K. Sahu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Nonlinear Pdes ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Layer Flow

AbstractThe study of boundary layer flow under mixed convection has been investigated numerically for various nanofluids over a semi-infinite flat plate which has been placed vertically upward for both buoyancy-induced assisting and buoyancy-induced opposing flow cases. To facilitate numerical calculations, a suitable transformation has been made for the governing partial differential equations (PDEs). Then, similarity method has been applied locally to approximate the nonlinear PDEs into a coupled nonlinear ordinary differential equations (ODEs). Then, quasilinearization method has been taken for linearizing the nonlinear terms which are present in the governing equations. Thereafter, implicit trapezoidal rule has been taken for integration numerically along with principle of superposition. The effect of physical parameters which are involved in the study are analyzed on the flow and heat transfer characteristics. This study reveals the presence of dual solutions in case of opposing flow. Further, this study shows that with increasing $$\phi$$ ϕ and Pr, the range of existence of dual solutions becomes wider. Also, it has been noted that nanofluids enhance the process of heat transfer for buoyancy assisting flow and it delays the separation point in case of opposing flow.

scholarly journals Mixed convection flow of Jeffrey fluid along an inclined stretching cylinder with double stratification effect

2017 ◽  
Vol 21 (2) ◽  
pp. 849-862 ◽  
Author(s):  
Tasawar Hayat ◽  
Sajid Qayyum ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi ◽  
Muhammad Ayub
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Variable Temperature ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Convection Boundary Layer ◽  
Stretching Cylinder ◽  
Double Stratification ◽  
Non Linear

This paper addresses double stratified mixed convection boundary layer flow of Jeffrey fluid due to an impermeable inclined stretching cylinder. Heat transfer analysis is carried out with heat generation/absorption. Variable temperature and concentration are assumed at the surface of cylinder and ambient fluid. Non-linear partial differential equations are reduced into the non-linear ordinary differential equations after using the suitable transformations. Convergent series solutions are computed. Effects of various pertinent parameters on the velocity, temperature, and concentration distributions are analyzed graphically. Numerical values of skin friction coefficient, Nusselt, and Sherwood numbers are also computed and discussed.

scholarly journals The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
D. R. V. S. R. K. Sastry ◽  
A. S. N. Murti ◽  
T. Poorna Kantha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Layer Flow

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

2014 ◽  
Vol 6 (3) ◽  
pp. 359-375 ◽  
Author(s):  
Antonio Mastroberardino
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Electrically Conducting ◽  
Homotopy Analysis ◽  
Layer Flow

AbstractAn investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

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