scholarly journals Analysis of Marangoni convection of non-Newtonian power law fluids with linear temperature distribution

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 45-52 ◽  
Author(s):  
Yan Zhang ◽  
Liancun Zheng ◽  
Xiaojing Wang ◽  
Guhua Song
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Marangoni Convection ◽  
Approximate Solutions ◽  
Convection Flow ◽  
Linear Temperature ◽  
Power Law Fluids ◽  
Variable Surface ◽  
Power Law Index ◽  
Steady Laminar

The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Pad? approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Yanhai Lin ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Marangoni Convection ◽  
Convection Heat Transfer ◽  
Temperature Fields ◽  
Convection Heat ◽  
Power Law Fluids

This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

scholarly journals Effect of Radiation on Free Convection Flow of Non-Newtonian Power-Law Fluids Along a Power-Law Stretching Sheet

2013 ◽  
Vol 61 (1) ◽  
pp. 97-104
Author(s):  
MA Samad ◽  
MR Hossain ◽  
D Kumar
Keyword(s):  
Differential Equations ◽  
Free Convection ◽  
Power Law ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Convection Heat Transfer ◽  
Simultaneous Action ◽  
Integration Scheme ◽  
Convection Flow ◽  
Power Law Fluids

An analysis is carried out to investigate the effects of MHD free convection heat transfer of power-law non-Newtonian fluids along a stretching sheet. This has been done under the simultaneous action of suction, thermal radiation and uniform transverse magnetic field. The stretching sheet is assumed to continuously moving with a power-law velocity and maintaining a uniform surface heat flux. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The resulting non-linear equations are solved numerically using Nachtsheim-Swigert shooting iterative technique along with sixth order Runge-Kutta integration scheme. Numerical results for the non-dimensional velocity and temperature profiles are shown graphically and discussed. The effects of skin-friction coefficient and the local Nusselt number which are of physical and engineering interest are studied and presented in the form of tables for the variation of different physically important parameters. A comparison of the present study is also performed with the previously published work and found excellent agreement. Dhaka Univ. J. Sci. 61(1): 97-104, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15104

MHD combined convection flow of a non-Newtonian power-law fluid due to a rotating cone or disk

2004 ◽  
Vol 82 (7) ◽  
pp. 531-540 ◽  
Author(s):  
E M Abo-Eldahab ◽  
A M Salem
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Shooting Method ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Power Law Fluid ◽  
Similarity Transformations ◽  
Laminar Mixed Convection ◽  
Power Law Fluids

The problem of laminar mixed convection flow of non-Newtonian power-law fluids from a constantly rotating isothermal cone or disk in the presence of a uniform magnetic field is investigated in this paper. The effect of Joule heating is also considered. The governing partial-differential equations are transformed into ordinary differential equations using similarity transformations. The transformed equations, on the assumption of a small magnetic Reynolds number, are solved numerically by employing the shooting method. Graphical results for the velocity and temperature profiles as well as tabulated results for the skin friction and the Nusselt number for various parametric conditions are presented and discussed. PACS No.: 47.50.td

scholarly journals Series Solutions for Marangoni Convection on a Vertical Surface

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Gabriella Bognár ◽  
Krisztián Hriczó
Keyword(s):  
Power Law ◽  
Marangoni Convection ◽  
Approximate Solutions ◽  
Vertical Surface ◽  
Similarity Solutions ◽  
Convection Flow ◽  
Boundary Layer Equations ◽  
Power Law Exponent ◽  
Power Law Function ◽  
Energy Equations

The problem of steady, laminar, thermal Marangoni convection flow of Newtonian fluid over a flat surface is investigated. The boundary layer equations for the momentum and energy equations are transformed with the similarity solutions to ODEs to obtain the analytical approximate solutions. The analysis assumes that the temperature variation is a power law function of the location. The approximate solutions to the similarity equations are obtained by exponential series. The effects of the power law exponent and Prandtl number on the velocity and temperature profiles are presented.

scholarly journals Effect of variable viscosity on free flow of non-Newtonian power-law fluids along a vertical surface with thermal stratification

2011 ◽  
Vol 33 (4) ◽  
pp. 109-121 ◽  
Author(s):  
M.B.K. Moorthy ◽  
K. Senthilvadivu
Keyword(s):  
Power Law ◽  
Thermal Stratification ◽  
Variable Viscosity ◽  
Saturated Porous Medium ◽  
Vertical Surface ◽  
Convection Flow ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Power Law Fluids ◽  
Power Law Index

Abstract The aim of this paper is to investigate the effect of thermal stratification together with variable viscosity on free convection flow of non- Newtonian fluids along a nonisothermal semi infinite vertical plate embedded in a saturated porous medium. The governing equations of continuity, momentum and energy are transformed into nonlinear ordinary differential equations using similarity transformations and then solved by using the Runge-Kutta-Gill method along with shooting technique. Governing parameters for the problem under study are the variable viscosity, thermal stratification parameter, non-Newtonian parameter and the power-law index parameter.The velocity and temperature distributions are presented and discussed. The Nusselt number is also derived and discussed numerically.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

scholarly journals On power-law fluids with the power-law index proportional to the pressure

2016 ◽  
Vol 62 ◽  
pp. 118-123 ◽  
Author(s):  
J. Málek ◽  
K.R. Rajagopal ◽  
J. Žabenský
Keyword(s):  
Power Law ◽  
Power Law Fluids ◽  
Power Law Index

Dynamics of Marangoni convection in radiative flow of power-law fluid with entropy optimization

2021 ◽  
pp. 2150280
Author(s):  
Hunida Malaikah ◽  
M. Ijaz Khan
Keyword(s):  
Power Law ◽  
Marangoni Convection ◽  
Mhd Flow ◽  
Transfer Characteristic ◽  
Radiation Parameter ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Newtonian Liquids ◽  
Power Law Index

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

Unsteady Flow of Power Law Fluids With Wall Slip in Microducts

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer ◽  
M'hamed Boutaous
Keyword(s):  
Power Law ◽  
Nonlinear Partial Differential Equation ◽  
Slip Flow ◽  
Wall Slip ◽  
Nonlinear Boundary Conditions ◽  
Velocity Profiles ◽  
Momentum Balance ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Pseudo Spectral

Unsteady laminar nonlinear slip flow of power law fluids in a microchannel is investigated. The nonlinear partial differential equation resulting from the momentum balance is solved with linear as well as nonlinear boundary conditions at the channel wall. We prove the existence of the weak solution, develop a semi-analytical solution based on the pseudo-spectral-Galerkin and Tau methods, and discuss the influence and effect of the slip coefficient and power law index on the time-dependent velocity profiles. Larger slip at the wall generates increased velocity profiles, and this effect is further enhanced by increasing the power law index. Comparatively, the velocity of the Newtonian fluid is larger and smaller than that of the power law fluid for the same value of the slippage coefficient if the power index is smaller and larger, respectively, than one.

Numerical Simulation for Heat Transfer of Nanofluid in a Rotating Circular Groove Using a Continuous Finite Element Scheme

2014 ◽  
Vol 1081 ◽  
pp. 175-179 ◽  
Author(s):  
Yong Yue Jiang ◽  
Ping Lin ◽  
Bo Tong Li ◽  
Lin Li
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Power Law ◽  
Initial Time ◽  
The Finite Element Method ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Circular Groove ◽  
Power Law Fluids ◽  
Power Law Index

In this paper, we investigate the heat transfer of the power-law-fluids-based nanofluids in a rotating circular groove. The circular groove rotates with a constant speed and the temperature on the wall of the groove is different from the temperature inside in the initial time. The effects of thermophoresis and Brownian are considered. The thermal conductivity of the nanofluids is taken as a constant. We solve the model with the finite element method directly and discretize them using a continuous finite element scheme in space and a modified midpoint scheme in time. From the results we can find that the heat transfer enhancement of the nanofluids increases as the power law index of the base fluid decreases.

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