1 Introduction 1.1 Literature review 1.2 Preliminaries 1.2.1 Governing laws 1.3 Boundary-layer equations in cylindrical coordinates 1.4 Basic definitions 1.4.1 Boundary-layer thickness 1.4.2 Displacement thickness 1.4.3 Momentum thickness 1.4.4 Skin friction 1.4.5 Nusselt number 1.4.6 Reynolds number 1.4.7 Hartmann number 1.4.8 Strouhal number 1.4.9 Prandtl number 1.4.10 Eckert number 1.4.11 Squared residual error 2 Boundary-layer flow inside and over long thin moving pipe 2.1 Introduction 2.2 Magnetohydrodynamic flow inside permeable moving pipe 2.2.1 Mathematical formulation 2.2.2 Solution of the problem 2.2.3 Convergence of the series solution 2.2.4 Flow characteristics 2.2.5 Conclusion 2.3 Local non-similarity flow past impulsively started cylinder 2.3.1 Mathematical Formulation 2.3.2 Solution of the problem 2.3.3 Convergence of the series solution 2.3.4 Flow characteristics 2.3.5 Conclusion 3 Flow and heat transfer near rotating pipe 3.1 Introduction 3.2 Magnetohydrodynamic flow in permeable rotating pipe at slowlyexpanding and contracting wall 3.2.1 Mathematical formulation 3.2.2 Solution of the problem 3.2.3 Convergence of the series solution 3.2.4 Flow characteristics 3.2.5 Conclusion 3.3 Magnetohydrodynamic flow and heat transfer over stretchable rotating cylinder 3.3.1 Formulation of the problem 3.3.2 Solution of the problem 3.3.3 Results and discussion 3.3.4 Conclusion 4 Unsteady boundary-layer flow and heat transfer over stretching cylinder 4.1 Introduction 4.2 Flow analysis 4.2.1 Mathematical formulation 4.3 Heat transfer analysis 4.4 Solution of the problem