# Fluid dynamics and heat transfer An introduction to the fundamentals by Brian D Storey.pdf

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Fluid dynamics and heat transfer An introduction to the fundamentals
Fluid dynamics and heat transfer An introduction to the fundamentals Brian D. Storey Olin College 2015 Brian D. Storey All rights reserved
Contents 1 Introduction page 1 1.1 Scope of the text 3 1.2 What is a fluid? 4 1.3 What is a continuum? 6 1.4 Prerequisites 7 2 Dimensional analysis 9 2.1 Units 9 2.2 Buckingham Pi Theorem 10 2.3 Making equations dimensionless 22 2.4 Summary 26 3 Conduction heat transfer 27 3.1 Heat flow 27 3.2 One-dimensional heat equation and conservation of energy 32 3.3 Dimensional analysis 39 3.4 General derivation of the heat equation 43 4 Analysis with the heat equation 51 4.1 1D transient behavior 52 4.2 1D Steady state 59 4.3 Steady state, 2D 64 4.4 Effective 1D heat flow 65 4.5 Simulations 69 5 Diffusive and convective mass transfer 73 5.1 Diffusive mass transfer 74
iv Contents 5.2 Physical picture of mass transfer 76 5.3 Convective mass transfer 79 5.4 Liebniz and Reynold’s transport theorem 83 5.5 Conservation of mass: the fluid 84 5.6 Dimensionless formulation 88 6 Conservation of momentum in a fluid 91 6.1 Transport theorem revisited 92 6.2 Linear momentum 92 6.3 F = m a 96 6.4 So what’s a tensor? 103 7 The Navier Stokes equations 105 7.1 Euler’s equation 106 7.2 Newtonian fluid & incompressible flow 108 7.3 Boundary conditions 111 7.4 Computing stress from flows 112 7.5 Comments on kinematics 113 7.6 Non-dimensionalization 119 7.7 The Reynolds number 120 7.8 Summary 122 8 Solutions to the Navier-Stokes equations 125 8.1 Flow between parallel plates - Poiseuille flow 126 8.2 Flow driven by a wall - Couette flow 131 8.3 Combined Poiseuille and Couette flow 133 8.4 Flow down a ramp 134 8.5 Impulsively started Couette flow 135 8.6 Slider bearing 137 8.7 Two layers of different viscosity 140 8.8 Cylindrical Couette flow 143 8.9 Poiseuille flow in a pipe 146 8.10 Flows around a spinning cylinder 149 8.11 Core annular flow of two immiscible fluids 151 8.12 Comments on the stability of solutions 155 8.13 Computational Fluid Dynamics (CFD) 157 9 Inviscid flow, Euler’s equation and Bernoulli 159 9.1 Flow along a streamline: Bernoulli 160 9.2 Euler equations across a streamline 163 9.3 Vorticity 167
Contents v 9.4 Irrotational flow 174 9.5 Lift on an airfoil 175 10 High Reynolds number flows 179 10.1 Impulsively started plate 180 10.2 Boundary layer equations and laminar solution 182 10.3 Turbulent boundary layers 187 10.4 Boundary layer separation 189 10.5 Drag on a sphere 190 10.6 Experimental observations of drag on a sphere 192 10.7 Turbulent pipe flow and modified Bernoulli 193 10.8 Turbulence theory 195 11 Control volume analysis 201 11.1 Control volume formulation 202 11.2 Examples 204 11.3 Some difficulties 214 12 Thermodynamics 217 12.1 Equations of state 218 12.2 Energy 219 12.3 The First Law of Thermodynamics 221 12.4 Specific heats 223 13 Energy conservation in fluid flows 227 13.1 Conservation law 228 13.2 Thermal energy equation 229 13.3 Viscous heating - example calculations 233 13.4 Coupled flow and heat transfer 240 14 Convective heat transfer: external flows 243 14.1 Forced convection 244 14.2 Flat plate thermal boundary layer 250 14.3 Natural convection 254 14.4 Vertical flat plate boundary layer 258 14.5 Convection calculations 259 14.6 Simulation 261 15 Energy balance in internal flows 263 15.1 Steady pipe flow 263 15.2 Pipe flow: Convection coefficients 267 15.3 General equation for pipe flow 270