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Effects of pressure gradient on convective heat transfer in a boundary layer flow of a Maxwell fluid past a stretching sheet

Kashif A. N., Salah F., Sankar D. S., Izyan M. D. N., Viswanathan K. K.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 3

104--118

EN

The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient [...], Deborah number [...], the ratio of the free stream velocity parameter to the stretching sheet parameter [...] and Prandtl number [...] on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m. It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles.

2

Unsteady flow of a Maxwell fluid induced by non-coaxial rotation of a disk and the fluid at infinity

Ersoy H. V.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 1

159-165

EN

In this note, the unsteady flow of a Maxwell fluid produced by non-coaxial rotation while a disk and the fluid at infinity are initially rotating with the same angular velocity about a common axis is considered. Even in the case of a non-Newtonian fluid, it is shown that there is an exact solution for this flow geometry. The velocity field is obtained with the help of the Laplace transform technique.

3

Radiation and thermal diffusion effects on MHD unsteady Maxwell fluid past a porous flat through porous medium

Eldabe N. T. M., Hassan A. A. A, Ghaly A. Y.

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 2

153-163

EN

Radiation and thermal diffusion effects of magnetohydrodynamic flow for non Newtonian fluid through a porous medium past an infinite porous flat plate arc presented. The flow under consideration obeys Maxwell rheological model. Solutions for velocity, temperature and concentration distributions arc obtained with the help of finite difference method. The effects of various parameters such as relaxation parameter λ of the Maxwell fluid, permeability of the fluid K, magnetic parameter M, Dufour number Df, Soret number Sr, Prandtl number Pr, radiation parameter N and Schmidt number Sc on the velocity, temperature and concentration profiles are studied and illustrated graphically. We obtained also the rate of heat transfer and concentration gradient during the course of discussion.

4

Blasius flow of viscoelastic fluids: a numerical approach

Sadeghy K., Sharifi M.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 2

399-411

EN

The effects of a fluid elasticity on the characteristics of a boundary layer in a Blasius flow are investigated for a second-grade fluid, and also for a Maxwell fluid. Boundary layer approximations are used to simplify the equations of motion which are finally reduced to a single ODE using the concept of similarity solution. For the second-grade fluid, it is found that the number of boundary conditions should be augmented to match the order of the governing equation. A combination of finite difference and shooting methods are used to solve the governing equations. Results are presented for velocity profiles, boundary layer thickness, and skin friction coefficient in terms of the local Deborah number. An overshoot in velocity profiles is predicted for a second-grade fluid but not for a Maxwell fluid. The boundary layer is predicted to become thinner for the second-grade fluid but thicker for the Maxwell fluid, the higher the Deborah number. By an increase in the level of fluid elasticity, a drop in wall skin friction is predicted for the second-order fluid but not for the Maxwell fluid.

5

Flow induced by a constantly accelerating edge in a Maxwell fluid

Fetecau C., Fetecau C.

Archives of Mechanics

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2004

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Vol. 56, nr 5

411-417

EN

The paper deals with the flow induced by a constantly accelerating edge in a Maxwell fluid. The solutions obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For ... › 0 they reduce to those corresponding to a Navier-Stokes fluid.

6

On the viscoelastic core of a line vortex embedded in a stagnation point flow

Erdogan M. E.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

577-588

EN

The viscoelastic core of a line vortex embedded in a radially inward axisymmetric stagnation point flow for a Maxwell fluid and an Oldroyd B fluid is considered. Velocity, vorticity and stress distributions are calculated and compared with those of the Newtonian fluid. It is found that there are pronounced effects of viscoelastic properties on these distributions with respect to those of the Newtonian fluid.

7

Komputerowe modelowanie procesu formowania włókien ze stopionego polimeru krystalizującego. Cz. I. Model matematyczny

Jarecki L.

Polimery

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2001

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T. 46, nr 5

335-343

PL

Podjęto próbę zbudowania pełnego komputerowego modelu formowania włókien ze stopionego polimeru zdolnego do krystalizacji, w którym to modelu uwzględniono najważniejsze efekty występujące w procesie. Sformułowano -więc podstawowe równania dynamiczne procesu formowania z uwzględnieniem efektów cieplnych objętościowego tarcia lepkiego rozciąganej cieczy polimerowej, efektów nieizochorycznych wynikających z zależności gęstości polimeru od temperatury oraz stopnia krystaliczności [równania (36a)-(36e)]. Krystalizacja orientowana prowadzi do wystąpienia dodatkowego równania różniczkowego pierwszego rzędu w modelu. Wydzielające się ciepło krystalizacji modyfikuje osiowy profil temperatury i wprowadza dodatkowy człon do równania bilansu energii. Postęp krystalizacji w sposób istotny wpływa na właściwości reologiczne formowanej strugi (lepkość), na równanie zachowania pędu oraz na dynamikę procesu. Efekty lepkosprężystości zostały uwzględnione z założeniem modelu cieczy Maxwella, a wyniki porównano z modelem zakładającym ciecz lepką Newtona. Model komputerowy uwzględnia też różne strefy chłodzenia i grzania, z różnymi wartościami temperatury i prędkości poprzecznego nadmuchu powietrza.

EN

The model tries to allow for the essential effects occurring in the melt spinning process. The basic dynamic equations were reformulated to include heat production resulting from viscous dissipation of energy in the bulk and nonisochoric effects associated with temperature- and crystalli-nity-dependent variations in polymer density (eqns. 36a-36e). An additional first-order differential equation is introduced to allow for stress-induced crystallization. Crystallization affects the temperature profile and contributes a heat term in the energy balance equation. This influences significantly the rheology (viscosity) of the polymer as also the momentum balance equation and spinning dynamics. Maxwell's upper-convected model is used to allow for viscoelasticity. The effects obtained are compared with the model that assumes the occurrence of a purely Newtonian viscous fluid. The model allows for the occurrence of heating/cooling zones having various temperatures and for various air cross-blow rates. The effects discussed are illustrated with axial profiles of local velocity, temperature, tensile stress and crystallinity, all computed for melt spinning from poly(ethylene terephthalate) (PET) (Figs. 2-4, 7-9, Part II). Melt spinning from PET involving zone heating allowed to disclose a limited range of spinning speeds and zone temperatures, and also multiple solutions of the model, consequent upon coupling of stress-induced crystallization and crystallinity-controlled solidification. The range of admissible spinning speeds is governed by the temperature of the heating zone. Model computations showed zone heating to increase considerably amorphous orientation at moderate take-up speeds and to reduce appreciably the take-up stress.