Analytical approach to unidirectional flow of non-Newtonian fluids of differential type
This thesis is regarding the development of mathematical models and analytical techniques for non-Newtonian fluids of differential types on a vertical plate, horizontal channel, vertical channel, capillary tube and horizontal cylinder. For a vertical plate, a mathematical model of the unsteady fl...
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| Format: | Thesis |
| Language: | English English |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/1574/1/24p%20MOHAMMED%20ABDULHAMEED.pdf http://eprints.uthm.edu.my/1574/2/MOHAMMED%20ABDULHAMEED%20WATERMARK.pdf |
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| Summary: | This thesis is regarding the development of mathematical models and analytical
techniques for non-Newtonian fluids of differential types on a vertical plate, horizontal
channel, vertical channel, capillary tube and horizontal cylinder. For a vertical
plate, a mathematical model of the unsteady flow of second-grade fluid generated
by an oscillating wall with transpiration, and the problem of magnetohydrodynamic
(MHD) flow of third-grade fluid in a porous medium, have been developed. General
solutions for the second-grade fluid are derived using Laplace transform, perturbation
and variable separation techniques, while for the third-grade fluid are derived using
symmetry reduction and new modified homotopy perturbation method (HPM). For a
horizontal channel, a new analytical algorithm to solve transient flow of third-grade
fluid generated by an oscillating upper wall has been proposed. A new approach of the
optimal homotopy asymptotic method (OHAM) have been proposed to solve steady
mixed convection flows of fourth-grade fluid in a vertical channel. The accuracy of
the approximate solution is achieved through the residual function. For a capillary
tube, two flow problems of the second-grade fluid were developed. Firstly, oscillating
flow and heat transfer driven by a sinusoidal pressure waveform, and secondly, free
convection flow driven due to the reactive nature of the viscoelastic fluid. The solutions
for the first problem were derived using Bessel transform technique while for the
second problem by using a new modified homotopy perturbation transform method.
For a horizontal cylinder, an unsteady third-grade fluid in a wire coating process
inside a cylindrical die is developed. A special case of the problem is obtained
for magnetohydrodynamic flow with heat transfer for second-grade fluid. Both of
these two problems are solved using a new modified homotopy perturbation transform
method. Data, graph and solutions obtained are shown and were found in good
agreement with previous studies. |
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