scholarly journals Non-linear radiation influence on oblique stagnation point flow of Maxwell fluid

2018 ◽  
Vol 64 (4) ◽  
pp. 420 ◽  
Author(s):  
Abuzar Ghaffari ◽  
T. Javed ◽  
I. Mustafa
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Maxwell Fluid ◽  
Stagnation Point Flow ◽  
Non Linear ◽  
Linear Radiation

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged through streamlines graphs. It is also observed that oblique stagnation point flow behaves like orthogonal stagnation point flow, when free stream velocity is very large as compared to stretching velocity.

Mixed Convection Falkner–Skan Flow of a Maxwell Fluid

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
T. Hayat ◽  
M. Farooq ◽  
Z. Iqbal ◽  
A. Alsaedi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Maxwell Fluid ◽  
Series Solutions ◽  
Newtonian Heating ◽  
Transformation Procedure

We performed a study for the effect of Newtonian heating on the nonsimilar mixed convection Falkner–Skan flow of a Maxwell fluid. Transformation procedure is adopted in obtaining the ordinary differential equations. Homotopic approach is adopted for the series solutions of velocity and temperature. Special emphasis is given to the effects of Prandtl number (Pr) and conjugate parameter (γ) which measure the strength of surface heating. It is observed that temperature and heat transfer rate are enhanced by increasing the conjugate parameter.

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

2011 ◽  
Vol 66 (8-9) ◽  
pp. 495-499 ◽  
Author(s):  
Khamisah Jafar ◽  
Anuar Ishak ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Stagnation Point Flow ◽  
Bottom Surface ◽  
Stream Velocity ◽  
Surface Boundary ◽  
Convective Parameter

Abstract This study analyzes the steady laminar two-dimensional stagnation point flow and heat transfer of an incompressible viscous fluid impinging normal to a horizontal plate, with the bottom surface of the plate heated by convection from a hot fluid. A uniform magnetic field is applied in a direction normal to the flat plate, with a free stream velocity varying linearly with the distance from the stagnation point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The analysis includes the effects of the magnetic parameter, the Prandtl number, and the convective parameter on the heat transfer rate at the surface. Results showed that the heat transfer rate at the surface increases with increasing values of these quantities.

Non-linear Radiation Effects in Mixed Convection Stagnation Point Flow along a Vertically Stretching Surface

2017 ◽  
Vol 15 (1) ◽  
Author(s):  
S. T. Hussain ◽  
Rizwan Ul Haq ◽  
N. F. M. Noor ◽  
S. Nadeem
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Stagnation Point Flow ◽  
Stretching Surface ◽  
Significant Difference ◽  
Non Linear ◽  
Linear Radiation

Abstract Present phenomenon is dedicated to analyze the combine effects of linear and non-linear Rosseland thermal radiations for stagnation point flow along a vertically stretching surface. For better variation in fluid flow and heat transfer, mixed convection is also considered to sustain this mechanism for significant influence. After incorporating these effects, the pertinent mathematical model is constructed in the form of non-linear partial differential equations and then be transformed into the system of coupled ordinary differential equations with the help of similarity transformation to be further solved numerically. Significant difference in the heat transfer enhancement can be observed through temperature profiles and tables of Nusselt number. Though histogram and isotherms plots, finally it is concluded that non-linear radiation provides better heat transfer rate at the surface of sheet as compare to the linear or absence of radiation effects.

scholarly journals Stagnation Point Flow of a Nanofluid toward an Exponentially Stretching Sheet with Nonuniform Heat Generation/Absorption

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
A. Malvandi ◽  
F. Hedayati ◽  
G. Domairry
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Heat Generation ◽  
Transfer Rate ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Brownian Diffusion ◽  
Exponentially Stretching Sheet ◽  
Exponentially Stretching

This paper deals with the steady two-dimensional stagnation point flow of nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via similarity variables and solved analytically via HAM. Effects of governing parameters such as heat generation/absorption λ, stretching parameter ε, thermophoresis , Lewis number Le, Brownian motion , and Prandtl number Pr on heat transfer and concentration rates are investigated. The obtained results indicate that in contrast with heat transfer rate, concentration rate is very sensitive to the abovementioned parameters. Also, in the case of heat generation , despite concentration rate, heat transfer rate decreases. Moreover, increasing in stretching parameter leads to a gentle rise in both heat transfer and concentration rates.

scholarly journals Mixed Convective Stagnation Point Flow towards a Vertical Riga Plate in Hybrid Cu-Al2O3/Water Nanofluid

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 912 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Boundary Layer Separation ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Volumetric Concentration ◽  
Nonlinear Odes ◽  
Riga Plate

The present work highlights the stagnation point flow with mixed convection induced by a Riga plate using a Cu-Al 2 O 3 /water hybrid nanofluid. The electromagnetohydrodynamic (EMHD) force generated from the Riga plate was influential in the heat transfer performance and applicable to delay the boundary layer separation. Similarity transformation was used to reduce the complexity of the governing model. MATLAB software, through the bvp4c function, was used to compute the resulting nonlinear ODEs. Pure forced convective flow has a distinctive solution, whereas two similarity solutions were attainable for the buoyancy assisting and opposing flows. The first solution was validated as the physical solution through the analysis of flow stability. The accretion of copper volumetric concentration inflated the heat transfer rate for the aiding and opposing flows. The heat transfer rate increased approximately up to an average of 10.216% when the copper volumetric concentration increased from 0.005 ( 0.5 % ) to 0.03 ( 3 % ) .

Mathematical Solution on MHD Stagnation Point Flow of Ferrofluid

2020 ◽  
Vol 399 ◽  
pp. 38-54
Author(s):  
Siti Hanani Mat Yasin ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Keller Box Method ◽  
Non Linear

This study presents a numerical investigation on the magnetohydrodynamic (MHD) stagnation point flow of a ferrofluid with Newtonian heating. The black oxide of iron, magnetite (Fe3O4) which acts as magnetic materials and water as a base fluid are considered. The two dimensional stagnation point flow of cold ferrofluid against a hot wall under the influence of the uniform magnetic field of strength is located some distance behind the stagnation point. The effect of magnetic and volume fraction on the velocity and temperature boundary layer profiles are obtained through the formulated governing equations. The governing equations which are in the form of dimensional non-linear partial differential equations are reduced to dimensionless non-linear ordinary differential equations by using appropriate similarity transformation. Then, they are solved numerically by using the Keller-box method which is programmed in the Matlab software. It is found that the cold fluid moves towards the magnetic source that is close to the hot wall. Hence, leads to the better cooling rate and enhances the heat transfer rate. Meanwhile, an increase of the magnetite nanoparticles volume fraction, increases the ferrofluid capabilities in thermal conductivity and consequently enhances the heat transfer.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Matt Garrett
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Wavy Surface ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
The Mean

Abstract Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

Non-axisymmetric Homann stagnation point flow and heat transfer past a stretching/shrinking sheet using hybrid nanofluid

2020 ◽  
Vol 30 (10) ◽  
pp. 4583-4606 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Strain Rate ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Hybrid Nanofluid ◽  
Ambient Fluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat plate. Design/methodology/approach The similarity transformation which fulfils the continuity equation is opted to transform the coupled momentum and energy equations into the nonlinear ordinary differential equations. Numerical solutions which are elucidated in the tables and graphs are obtained using the bvp4c solver. Findings Non-unique solutions (first and second) are feasible for both stretching and shrinking cases within the specific values of the parameters. First solution is the physical/real solution based on the execution of stability analysis. An upsurge of the ratio of the ambient fluid strain rate to the plate strain rate can delay the boundary layer separation, whereas a boost of the ratio of the ambient fluid shear rate to the plate strain rate only accelerates the separation of boundary layer. The heat transfer rate of hybrid nanofluid is greater for the stretching case than the shrinking case. However, for the shrinking case, the heat transfer rate intensifies with the increment of the copper (Cu) nanoparticles volume fraction, whereas a contrary result is found for the stretching case. Originality/value The present numerical results are original and new. It can contribute to other researchers on electing the relevant parameters to optimize the heat transfer process in the modern industry, and the right parameters to generate non-unique solution so that no misjudgment on flow and heat transfer features.

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