An integrated solution for reducing ill-conditioning and testing the results in non-linear 3D similarity transformations

2017 ◽  
Vol 26 (5) ◽  
pp. 708-727 ◽  
Author(s):  
Orhan Kurt
Keyword(s):  
Similarity Transformations ◽  
Non Linear ◽  
Ill Conditioning ◽  
3D Similarity

scholarly journals Similarity Transformations for Compressor Blading

1991 ◽  
Author(s):  
N. G. Zhu ◽  
L. Xu ◽  
M. Z. Chen
Keyword(s):  
High Speed ◽  
Linear Equations ◽  
Low Speed ◽  
Axial Compressors ◽  
Transformation Rules ◽  
Similarity Transformations ◽  
Non Linear ◽  
Experimental Validations ◽  
Model Compressor ◽  
Global Similarity

Improving the performance of high speed axial compressors through low speed model compressor testing has proved to be economical and effective (Wisler, 1984). The key to this technique is to design low speed blade profiles which are aerodynamically similar to their high speed counterparts. The conventional aerodynamic similarity transformation involves the small disturbance potential flow assumption therefore its application is severely limited and generally not used in practical design. In this paper, a set of higher order transformation rules are presented which can accommodate large disturbances at transonic speed and are therefore applicable to similar transformations between the high speed HP compressor and its low speed model. Local linearization is used in the non–linear equations and the transformation is obtained in an iterative process. The transformation gives the global blading parameters such as camber, incidence and solidity as well as the blade profile. Both numerical and experimental validations of the transformation show that the non–linear similarity transformations do retain satisfactory accuracy for highly loaded blades up to low transonic speeds. Further improvement can be made by only slightly modifing profiles numerically without altering the global similarity parameters.

Cross-Diffusion Effects on MHD Cattaneo-Christov Flow of Casson Fluid Past a Convective Linear/Non-Linear Stretching Sheet

2018 ◽  
Vol 388 ◽  
pp. 96-113 ◽  
Author(s):  
Bujula Ramadevi ◽  
Janke Venkata Ramana Reddy ◽  
Vangala Sugunamma
Keyword(s):  
Heat Transfer ◽  
Stretching Sheet ◽  
Casson Fluid ◽  
Transfer Coefficients ◽  
Convective Boundary ◽  
Flow Equations ◽  
Cross Diffusion ◽  
Similarity Transformations ◽  
Flow Past ◽  
Non Linear

Through this article, we presented a comparative study for the MHD non- Newtonian fluid flow past a stretching sheet using Cattaneo-Christov heat flux model. The flow equations and the related convective boundary conditions have been altered as dimensionless ODEs by suitable similarity transformations. Further, these are resolved by employing fourth order Runge-Kutta method along with shooting technique. The influence of all flow regulating parameters on velocity, thermal and mass diffusive boundary layers are perceived through graphs. Also the variation in skin friction, mass and heat transfer coefficients for the same parameters are perceived via numerical values. The velocity of the flow past a linear stretching sheet is higher than that of the flow past a non-linear stretching sheet. But heat transfer performance in the flow via non-linear surface is better than that of flow via linear surface.

Numerical exploration of the combined effects of non-linear thermal radiation and variable thermo-physical properties on the flow of Casson nanofluid over a wedge

2017 ◽  
Vol 13 (4) ◽  
pp. 628-647 ◽  
Author(s):  
Archana M. ◽  
Gireesha B.J. ◽  
Prasannakumara B.C. ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Physical Properties ◽  
Physical Parameters ◽  
Content Type ◽  
Casson Nanofluid ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Non Linear ◽  
Thermo Physical Properties

Purpose The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue. Design/methodology/approach Selected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique. Findings The velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail. Research limitations/implications This study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies. Originality/value It is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.

Magneto-hydrodynamic Blasius flow and heat transfer from a flat plate in the presence of suspended carbon nanofluids

2017 ◽  
Vol 232 (1) ◽  
pp. 31-40
Author(s):  
Mahantesh M Nandeppanavar ◽  
Rama Subba Reddy Gorla ◽  
S Shakunthala
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
External Magnetic Field ◽  
Flat Plate ◽  
Linear Partial Differential Equation ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Non Linear

In this article, we have discussed the effect of external magnetic field and other governing parameters on the flow and heat transfer in the presence of suspended carbon nanotubes over a flat plate. The governing equations of flow and heat transfer are derived from the Navier–Stokes and Prandtl boundary layer concept. The derived governing equations of flow and energy are non-linear partial differential equation, and these equations are converted into non-linear ordinary differential equations with corresponding boundary conditions using some suitable similarity transformations and are solved numerically using fourth-order Runge–Kutta method with efficient shooting technique. Effects of governing parameters on flow and heat transfer are shown through various graphs and explained with physical interpretation in detail. This study has applications in glass-fiber production and technology. On observing the results of this study, we can conclude that external magnetic field shows opposite behaviors on velocity and temperature and it enhances the rate of heat transfer.

Non-linear radiative squeezed flow in a rotating frame

2017 ◽  
Vol 34 (8) ◽  
pp. 2450-2462 ◽  
Author(s):  
Naveed Ahmed ◽  
Umar Khan ◽  
Syed Tauseef Mohyud-Din ◽  
Saeed Ullah Jan
Keyword(s):  
Total Error ◽  
Coupled System ◽  
Reduced Form ◽  
Rotating Frame ◽  
Content Type ◽  
Similarity Transformations ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Squeezed Flow ◽  
Linear Radiation

Purpose In this current study, the authors aim to analyze non-linear radiative squeezed flow in a rotating frame of viscous fluid. Design/methodology/approach The Radioactive nature of the fluid is taken into consideration. The reduced form of equations governing the flow are developed by the implementation of similarity transformations. The coupled system thus obtained is solved by using the homotopy analysis method (HAM). Findings Augmentation in velocity and temperature profiles is discussed graphically by varying various involved parameters. The total error of the system is discussed in Table I. The cases of linear radiation and non-linear radiation are also discussed in Tables II and III. Originality/value The study presented in this paper is original and it has not been submitted to any other journal for publication purpose. The contents are original and proper references have been provided wherever applicable.

scholarly journals Chemically reacting on MHD boundary-layer flow of nanofluids over a non-linear stretching sheet with heat source/sink and thermal radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 495-506 ◽  
Author(s):  
Oluwole Makinde ◽  
Fazle Mabood ◽  
Mohammed Ibrahim
Keyword(s):  
Boundary Layer ◽  
Heat Source ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Non Linear ◽  
Linear Ode ◽  
Source Sink

In this paper, steady 2-D MHD free convective boundary-layer flows of an electrically conducting nanofluid over a non-linear stretching sheet taking into account the chemical reaction and heat source/sink are investigated. The governing equations are transformed into a system of non-linear ODE using suitable similarity transformations. Analytical solution for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat and mass transfer rates are obtained by using homotopy analysis method. The obtained results show that the flow field is substantially influenced by the presence of chemical reaction, radiation, and magnetic field.

Non-Linear Radiation and Chemical Reaction Impacts on Hydromagnetic Particle Suspension Flow in Non-Newtonian Fluids

2018 ◽  
Vol 16 (6) ◽  
Author(s):  
M. Gnaneswara Reddy ◽  
M.V.V.N.L. Sudha Rani ◽  
C. Prasannakumara
Keyword(s):  
Boundary Layer ◽  
Temperature Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Graphical Analysis ◽  
Two Phase ◽  
Similarity Transformations ◽  
Non Linear ◽  
Dynamical Flow ◽  
Linear Radiation

Abstract A two dimensional (2D) boundary layer two-phase MHD (magneto hydrodynamics) flow of Maxwell and Oldroyd-B fluid over a stretching sheet has been explored. Heat and mass transfer phenomena is inspected through Non-linear radiation, viscous dissipation, joule heating, Soret (thermo-diffusion) and Dufour (diffusion-thermo) Impact. The boundary layer governing differential equations are modelled and transformed to a system of ODE’S with the aid of similarity transformations. The final controlled equations along boundary restrictions are resolved numerically by Runge-Kutta Felhberg method. The graphical analysis has been emphasized for the fluid and dust phase velocity, temperature and concentration fields to the influence of sundry dynamical flow quantities. Furthermore, for authentication of the present computation, the achieved results are distinguished with earlier research works in specific cases and marvellous agreement has been noted. The outcomes conveyed here manifest that velocity and boundary layer thickness escalate with boost up the values of ${K_1}$ . Velocity and boundary layer thickness declines with boost up the values of $M$ . Opposite trend is seen in temperature and concentration profiles. The specific heat ratio parameter $\gamma$ enhances the temperature profile declines. Boost up the values of Soret number $Sr$ temperature profile declines and concentration profile enhances. Skin friction factor declines with increasing values $\beta _v$ verses $M$ .

scholarly journals A Magnetite–Water-Based Nanofluid Three-Dimensional Thin Film Flow on an Inclined Rotating Surface with Non-Linear Thermal Radiations and Couple Stress Effects

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5531
Author(s):  
Asad Ullah ◽  
Ikramullah ◽  
Mahmoud M. Selim ◽  
Thabet Abdeljawad ◽  
Muhammad Ayaz ◽  
...  
Keyword(s):  
Couple Stress ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Fluid Temperature ◽  
Thin Film Flow ◽  
Similarity Transformations ◽  
Water Based ◽  
Non Linear ◽  
Rotating Surface ◽  
Thermal Radiations

This study is related to the heat energy transfer during 3D nanofluid (water-based) motion over a rotating surface by incorporating the combined impacts of thermal radiations and couple stress. The flow is modeled by a set of non-linear coupled PDEs, which is converted to a set of coupled non-linear ODEs by using suitable similarity transformations. The transformed equations are solved with the built-in NDSolve command. The effects of relevant interesting parameters on the nanofluid velocity components and temperature distribution are explained through various graphs. It is found that the velocity component f(η) is increased with higher values of γ and A0 while it drops with an increasing rotation parameter and nanoparticle volume fraction. The fluid temperature increases with higher αnf, Rd, ϵ2, ϵ3, A1 and drops with increasing Pr, ϵ1 and couple stress parameter (A0). The Nusselt number remains constant at a fixed Pr and Rd, whereas it increases with increasing Pr and is reduced with rising Rd. A comparison between the achieved results is carried out with the analytical results through different tables. An excellent agreement is observed between these results.

scholarly journals Influence of Joule Heating and Non-Linear Radiation on MHD 3D Dissipating Flow of Casson Nanofluid past a Non-Linear Stretching Sheet

2019 ◽  
Vol 8 (1) ◽  
pp. 661-672
Author(s):  
Pandikunta Sreenivasulu ◽  
Tamalapakula Poornima ◽  
Nandanoor Bhaskar Reddy
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Skin Friction Coefficient ◽  
Casson Nanofluid ◽  
Similarity Transformations ◽  
Non Linear

Abstract Present analysis is to study the combined effects of viscous dissipation and Joule heating on MHD three-dimensional laminar flow of a viscous incompressible non-linear radiating Casson nanofluid past a nonlinear stretching porous sheet. Present model describes that flow generated by bi-directional non-linear stretching sheet with thermophoresis and Brownian motion effects. The governing nonlinear partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations by similarity transformations and then solved by employing shooting method. The effects of the flow parameters on the velocity, temperature and concentration as well as the skin friction coefficient, Nusselt number and Sherwood number near the wall are computed for various values of the fluid properties. This study reveals that the temperature of Casson nanofluid increases with combination of viscous dissipation and Joule heating. Increasing thermophoresis parameter increases the species concentration of the nanoflow. The comparison of present results have been made with the published work and the results are found to be very good agreement.

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