scholarly journals IMPACT OF SUCTION/INJECTION AND HEAT TRANSFER ON UNSTEADY MHD FLOW OVER A STRETCHABLE ROTATING DISK

2020 ◽  
Vol 50 (3) ◽  
pp. 159-165
Author(s):  
K. V. Prasad ◽  
Hanumesh Vaidya ◽  
O D Makinde ◽  
Kuppalapalle Vajravelu ◽  
V Ramajini
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Rotating Disk ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Optimal Homotopy Analysis Method ◽  
Similarity Transformations

In this article, the unsteady magnetohydrodynamic two-dimensional boundary layer flow and heat transfer over a stretchable rotating disk with mass suction/injection is investigated. Temperature-dependent physical properties and convective boundary conditions are taken into account. The governing coupled nonlinear partial differential equations are transformed into a system of ordinary differential equations by adopting the well-known similarity transformations. Further, the solutions are obtained through the semi-analytical method called an Optimal Homotopy Analysis Method (OHAM). The obtained results are discussed graphically to predict the features of the involved key parameters which are monitoring the flow model. The skin friction coefficient and Nusselt number are also examined. The validation of the present work is verified with the earlier published results and is found to be in excellent agreement. It is noticed that an increase in the viscosity parameter leads to decay in momentum boundary layer thickness, and the inverse trend is observed in the case of the temperature profile.

Effect of Convective Boundary Condition on MHD Carreau Dusty Fluid over a Stretching Sheet with Heat Source

2017 ◽  
Vol 377 ◽  
pp. 233-241 ◽  
Author(s):  
S.U. Mamatha ◽  
Mahesha ◽  
Chakravarthula S.K. Raju ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Dusty Fluid ◽  
Similarity Transformations

The underlying intention of the present study is to analyze the steady incompressible magneto hydrodynamic Carreau Dusty fluid over a stretching sheet with exponentially decaying heat source. Convective conditions are considered to control the thermal boundary layer. Similarity transformations were used to convert partial differential equations (PDEs) to a system of nonlinear ordinary differential equations (NODEs) which are solved numerically by employing Runge-Kutta with Newton’s technique. The effect of pertinent parameters on velocity and temperature profiles of both fluid and dust phase within the boundary layer has been studied by considering various values of controlling parameters. In addition, skin friction coefficient and reduced heat transfer coefficient have been examined for various values of the governing parameters. It is observed that the rate of heat transfer depreciates with space dependent heat generation and enhanced with the existing convective condition.

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.

Double Dispersion for Double Diffusive Boundary Layer in Non-Darcy Saturated Porous Medium Filled by a Nanofluid

2016 ◽  
Vol 32 (4) ◽  
pp. 441-451 ◽  
Author(s):  
A. M. Bouaziz ◽  
S. Hanini
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Saturated Porous Medium ◽  
Nonlinear Partial Differential Equations ◽  
Convective Boundary ◽  
Similarity Transformations ◽  
Governing System ◽  
Double Dispersion ◽  
Double Diffusive

AbstractThis work investigates mainly the double dispersion on the double diffusive convective boundary layer between a vertical plate immersed into a non-Darcy saturated porous medium with a nanofluid. The similarity transformations are involved and the governing system of nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations. Results are displayed graphically to illustrate the influence of δ, and ξ on the velocity, the temperature and concentration of the species profiles. Two interesting cases are treated, isothermal and non-isothermal wall plate. For a nanofluid, the rate of mass transfer is affected strongly by the double dispersion while the rate of heat transfer coefficient is less sensitive to it.

Impact of generalized Fourier’s law and Fick’s law for MHD flow of Ag‒H2O and TiO2‒H2O nanomaterials

2019 ◽  
Vol 15 (6) ◽  
pp. 1075-1099 ◽  
Author(s):  
Sumit Gupta ◽  
Devendra Kumar ◽  
Jagdev Singh ◽  
Sandeep Gupta
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Variable Viscosity ◽  
Mhd Flow ◽  
Field Variable ◽  
Numerical Results ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Optimal Homotopy Analysis Method ◽  
Content Type

Purpose The purpose of this paper is to investigate the effect of inclined magnetic field, variable viscosity and Cattaneo–Christov heat and mass flux theories on the steady MHD free convective boundary layer flow of viscous, incompressible and electrically conducting water-driven silver and titanium-oxide nanofluids over a vertical stretching sheet. Design/methodology/approach The boundary layer equations of momentum, energy and nanoparticle concentration are partial differential equations in nature, which are reduced to nonlinear ordinary differential equations by means of similarity transformations. The resulting nonlinear equations are solved analytically by means of optimal homotopy analysis method. Findings Assessments with numerical results are performed and are found to be in an excellent agreement. Numerical results of the skin friction factor, the local Nusselt number and the local Sherwood number are obtained through tables. The effects of various physical parameters on the velocity, temperature and nanoparticles fraction are incorporated through graphs. The study analyzes the efficiency of heat transfer of nanofluids in cooling plants and rubber sheets. Originality/value No research works have been conducted to evaluate the effects of various physical phenomena on the copper and titanium nanofluids flow.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

Existence of Dual Solutions and Melting Phenomenon in Unsteady Nanofluid Flow and Heat Transfer over a Stretching Surface

2019 ◽  
Vol 35 (5) ◽  
pp. 705-717
Author(s):  
S. Ghosh ◽  
S. Mukhopadhyay ◽  
K. Vajravelu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Stretching Surface ◽  
Melting Phenomenon ◽  
Runge Kutta Method ◽  
Layer Flow

ABSTRACTThe problem of unsteady boundary layer flow of a nanofluid over a stretching surface is studied. Heat transfer due to melting is analyzed. Using a similarity transformation the governing coupled nonlinear partial differential equations of the model are reduced to a system of nonlinear ordinary differential equations, and then solved numerically by a Runge-Kutta method with a shooting technique. Dual solutions are observed numerically and their characteristics are analyzed. The effects of the pertinent parameters such as the acceleration parameter, the Brownian motion parameter, the thermophoresis parameter, the Prandtl number and the Lewis number on the velocity, temperature and concentration fields are discussed. Also the effects of these parameters on the skin friction coefficient, the Nusselt number and the Sherwood number are analyzed through graphs. It is observed that the melting phenomenon has a significant effect on the flow, heat and mass transfer characteristics.

Steady Laminar Convective Flow with Variable Properties Due to a Porous Rotating Disk

2005 ◽  
Vol 127 (12) ◽  
pp. 1406-1409 ◽  
Author(s):  
Kh. Abdul Maleque ◽  
Md. Abdus Sattar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Disk ◽  
Polar Coordinates ◽  
Shooting Methods ◽  
Variable Properties ◽  
Relative Temperature ◽  
Flow And Heat Transfer ◽  
Steady Laminar

The present paper investigates the effects of variable properties (density (ρ), viscosity (μ), and thermal conductivity (κ)) on steady laminar flow and heat transfer for a viscous fluid due to an impulsively started rotating porous infinite disk. These properties ρ, μ and κ are taken to be the functions of temperature. The system of axisymmetric nonlinear partial differential equations governing the steady flow and heat transfer are written in cylindrical polar coordinates and are reduced to nonlinear ordinary differential equations by introducing suitable similarity parameters. The resulting steady equations are solved numerically by using Runge-Kutta and Shooting methods, and the effects of the relative temperature difference and suction/injection parameters are examined.

scholarly journals Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

2021 ◽  
Vol 50 (12) ◽  
pp. 3753-3764
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Theoretical Investigations ◽  
Suitable Form ◽  
Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

scholarly journals Entropy Generation and Bejan Number Analysis of MHD Casson Fluid Flow in a Micro-Channel with Navier Slip and Convective Boundary Conditions

2020 ◽  
Vol 7 (4) ◽  
Author(s):  
M. Venkateswarlu ◽  
P. Bhaskar
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Bejan Number ◽  
Micro Channel ◽  
Convective Boundary Conditions ◽  
Convective Boundary

The analysis of MHD flow has been a concern of consideration for research scientists and engineers. In this treatise, the steady MHD flow of an incompressible and electrically conducting Casson fluid in a micro-channel with heat generation and viscous dissipation, in the presence of hydrodynamic slip and convective boundary conditions, is examined. Exact solutions of non-dimensional steady governing equations are obtained in closed form. Transient fluid velocity, temperature, entropy generation, and Bejan number are depicted by the line graphs whereas rate of heat transfer and skin-friction coefficient are computed in tabular form for pertinent flow parameters. It is established that the entropy generation rate and Bejan number increases for increasing values of the Casson parameter and heat generation parameter. In particular, the Casson parameter accelerates the skin-friction coefficient while it provides resistance to the rate of heat transfer near the channel walls. Casson fluid finds significant applications in biomechanics, polymer processing industries, and food processing.

scholarly journals Magnetohydrodynamic stagnation point on a Casson nanofluid flow over a radially stretching sheet

2020 ◽  
Vol 11 ◽  
pp. 1303-1315
Author(s):  
Ganji Narender ◽  
Kamatam Govardhan ◽  
Gobburu Sreedhar Sarma
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Casson Nanofluid ◽  
Similarity Transformations ◽  
Program Language ◽  
The Impact

This article proposes a numerical model to investigate the impact of the radiation effects in the presence of heat generation/absorption and magnetic field on the magnetohydrodynamics (MHD) stagnation point flow over a radially stretching sheet using a Casson nanofluid. The nonlinear partial differential equations (PDEs) describing the proposed flow problem are reduced to a set of ordinary differential equations (ODEs) via suitable similarity transformations. The shooting technique and the Adams–Moulton method of fourth order are used to obtain the numerical results via the computational program language FORTRAN. Nanoparticles have unique thermal and electrical properties which can improve heat transfer in nanofluids. The effects of pertinent flow parameters on the nondimensional velocity, temperature and concentration profiles are presented. Overall, the results show that the heat transfer rate increases for higher values of the radiation parameter in a Casson nanofluid.

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