I= SIMILAR AND NON-SIMILAR ANALYTIC SOLUTIONS FOR STEADY FLOWS OF DIFFERENTIAL TYPE FLUIDS
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Title of Thesis
SIMILAR AND NON-SIMILAR ANALYTIC SOLUTIONS FOR STEADY FLOWS OF DIFFERENTIAL TYPE FLUIDS

Author(s)
Muhammad sajid
Institute/University/Department Details
Department of Mathematics/ Quaid-i-Azam University, Islamabad
Session
2006
Subject
Mathematics
Number of Pages
170
Keywords (Extracted from title, table of contents and abstract of thesis)
differential type fluids, analytic solutions, steady flows, newtonian fluids, non-newtonian fluids, optimal flow, homotopy analysis method, flat porous plate, pipe flow, planar, axisymmetric flow, stretching sheet, boundary layer flow, magnetohydrodynamic pipe flow

Abstract
It has been known that Newtonian fluids are inadequate to describe non-Newtonian fluids. Non-Newtonian flows arise in disparate process in engineering, science and biology for example, in polymer processing, coating, ink-jet printing, microfluidics, geological flows in the earth mantle, homodynamic and many others. Modeling non-Newtonian flows is important for understanding and predicting the behaviour of processes and thus for designing optimal flow configurations and for selecting operating conditions. Several models, mainly based on empirical observations, have been suggested for non-Newtonian fluids. The rheologists have been able to provide a theoretical Foundation in the form of a constitutive equations which can in principle, have any order. For applied mathematics and computer scientists the challenge comes from a different quarter. A constitutive equation of even the simplest non-Newtonian fluids are such that the differential equation describing the motion have, in general, their order higher than those describing the motion of the Newtonian fluids, but apparently there is no corresponding increase in the number of boundary conditions. Applied mathematicians and computer scientists are thus forced with the so-called ill-posed boundary value problems which, in theory have a family of infinitely many solutions. The task them becomes of selecting one of them under some plausible assumption. The main objective of this thesis is to consider the problems in one class of non-Newtonian fluids namely the fluids of differential type and to develop analytic solutions for them. The explicit, totally analytic solutions for the considered problems are obtained using the homotopy analysis method (HAM). The explicit form of the series is given for the analytical solutions. The dependence of the convergence of the obtained series is discussed. The flow problems regarding the flow of second. third and fourth grade fluids are investigated for both Cartesian and Cylindrical coordinates. The considered problems involve flat porous plate, pipe flow, planar and axisymmetric flow over a linear stretching sheet. The heat transfer analysis is carried out for the stretching problems. Two heating processes namely (i) prescribed surface temperature (PST case) and (ii) prescribed heat flux (PHF case) are taken into account. The effects of the emerging non-Newtonian parameters of interest are seen and discussed. Finally, the comparison of the obtained results with the existing results in the literature is also presented.

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14407.29 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents 0
1206.79 KB
2 1 Introduction 4
764.27 KB
3 2 Preliminaries 9
1504.36 KB
  2.1 Non-Newtonian Fluids 9
  2.2 Differential Type Fluids 11
  2.3 Flow Equations 13
  2.4 Energy Equation 13
  2.5 Boundary Layer Flow 14
  2.6 Flow Induced by a Stretching Sheet 18
  2.7 Homotopy Analysis Method 20
4 3 Boundary Layer Flow of a Third Order Fluid over a Stretching Sheet 22
1911.13 KB
  3.1 Mathematical Formulation 22
  3.2 Exact Analytic Solution 26
  3.3 Convergence of the Exact Analytic Solution 38
  3.4 Results and Discussion 41
5 4 Axisymmetric Flow of a Third Grade Fluid over a Radially Stretching Sheet 45
1115.24 KB
  4.1 Governing Equations 45
  4.2 Homotopy Analytic Solution 48
  4.3 Skin Friction 53
  4.4 Convergence of the Homotopy Analytic Solution 53
  4.5 Results and Discussion 54
6 5 On Flow of a Fourth Order Fluid Past a Porous Plate 59
1173.66 KB
  5.1 Formulation of the Flow Problem 59
  5.2 HAM Solution 62
  5.3 Convergence of the HAM Solution 66
  5.4 Results and Discussion 68
7 6 Magnetohydrodynamic Pipe Flow of a Fourth Order Fluid 75
807.08 KB
  6.1 Description of the Problem 75
  6.2 Analytical Solution 77
  6.3 Convergence of the Analytic Solution 81
  6.4 Results and Discussion 82
8 7 Magnetohydrodynamic Flow and Heat 'Transfer in a Third Order Fluid over a Stretching Sheet 84
2171.88 KB
  7.1 Flow Equations 85
  7.2 Heat transfer Analysis 92
  7.3 Convergence of the HAM Solution 99
  7.4 Results and Discussion 101
9 8 Axisymmetric Flow and Heat 'Transfer of a Second Grade Fluid over a Ra dially Stretching Sheet 113
1641.54 KB
  8.1 Flow Analysis 114
  8.2 Heat transfer Analysis 118
  8.3 Convergence of the Exact Analytic Solution 123
  8.4 Results and Discussion 127
10 9 Heat Transfer Analysis of Axisymmetric Flow of a Third Grade Fluid over a Radially Stretching Sheet 135
1099.2 KB
  9.1 Heat Transfer Analysis 136
  9.2 Convergence of the Analytic Solution 143
  9.3 Results and Discussion 144
11 10 Conclusions 150
1219.84 KB