Series solution for the upper-convected Maxwell fluid over a porous stretching plate

Hayat, Tasawar; Abbas, Zaheer; Sajid, Muhammad

doi:10.1016/j.physleta.2006.04.117

Cited by 219 publications

(143 citation statements)

References 43 publications

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“…Using the UCM model, MHD boundary layer flow of a UCM fluid in a rectangular porous channel was successfully investigated. The study on dynamics of upper-convected Maxwell fluid is extended in Hayat et al (2006) and reported that boundary layer thickness decreases by increasing the magnitude of MHD parameter, suction/injection velocity parameter and relaxation time parameter. In recent years, many researchers has investigated and reported the effect of some parameters on upper-convected Maxwell fluid flow (see Sadeghy et al (2006), Abbas et al (2008), Sadeghy et al (2009), Pop et al (2012, Motsa et al (2012), Mustafa et al (2012), Prasad et al (2013) and ).…”

Section: Introductionmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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An upper-convected Maxwell (UCM) fluid flow over a melting surface situated in hot environment is studied. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying the classical boundary condition of temperature to account for both. It is assumed that the ratio of inertia forces to viscous forces is high enough for boundary layer approximation to be valid. The corresponding influence of exponentially space dependent internal heat generation on viscosity and thermal conductivity of UCM is properly considered. The dynamic viscosity and thermal conductivity of UCM are temperature dependent. Classical temperature dependent viscosity and thermal conductivity models are modified to suit the case of both melting heat transfer and thermal stratification. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations and completed the solution numerically using the Runge-Kutta method along with shooting technique (RK4SM). The numerical procedure is validated by comparing the solutions of RK4SM with that of MATLAB based bvp4c. The results reveal that increase in stratification parameter corresponds to decrease in the heat energy entering into the fluid domain from freestream and this significantly reduces the overall temperature and temperature gradient of UCM fluid as it flows over a melting surface. The transverse velocity, longitudinal velocity and temperature of UCM are increasing function of temperature dependent viscous and thermal conductivity parameters. At a constant value of melting parameter, the local skin-friction coefficient and heat transfer rate increases with an increase in Deborah number.

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Section: Introductionmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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“…Further, the flow region is under the influence of a uniform transverse magnetic field B=(0,B 0 ,0): Imposition of such a magnetic field stabilizes the flow (see [16]). It is also assumed that the induced magnetic field is negligible: This is valid for small magnetic Reynolds number.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…in the momentum equation (2.2b) as in [16]. It is assumed that the normal stress is of the same order of magnitude as that of the shear stress.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Obviously for the theoretical results to be of any importance, more general visco-elastic fluid models such as upper convected Maxwell model or Oldroyd B model should be invoked in the analysis. Indeed these two fluid models are being used recently to study the visco-elastic fluid flow over a stretching or non-stretching sheet with or without heat transfer [14][15][16][17][18][19][20]. Recently, Prasad et al [20] studied the effects of the temperature-dependent thermo-physical properties on the MHD boundary layer flow and heat transfer of a UCM fluid over a stretching sheet in the presence of internal heat generation/absorption.…”

Section: Introductionmentioning

confidence: 99%

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Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

Vajravelu

Prasad

Santhi

2015

Adv. Appl. Math. Mech.

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Abstract. An analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.

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“…From the literature, there has been extensive research regarding non-Newtonian fluids with and without heat transfer analysis [13][14][15][16][17]. A few researchers, have been investigated the problem on the peristaltic motion of a Jeffery fluid under the effect of a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

The effects of heat generation or absorption on MHD stagnation point of Jeffrey fluid

Kasim

Jiann

Shafie³

et al. 2014

AIP Conference Proceedings

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Series solution for the upper-convected Maxwell fluid over a porous stretching plate

Cited by 219 publications

References 43 publications

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

The effects of heat generation or absorption on MHD stagnation point of Jeffrey fluid

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