Convection - CHAPTER 6: INTRODUCTION TO CONVECTION For...

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C HAPTER 6: I NTRODUCTION TO C ONVECTION For conduction through solids, we derived the general heat diffusion equation based on all the mechanisms by which heat can be transferred or generated in a solid control volume: = + + + q z T k z y T k y x T k x t T c p ρ ( E in – E out ) cond + E gen = E storage q x q x+dx q z q z+dz q y q y+dy
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What happens if instead we use a fluid (gas, liquid) control volume? All these terms remain BUT… heat transfer by bulk fluid flow also becomes possible: T u c t T c q T k p p + = + ρ 2 ( E in – E out ) cond + E gen = E storage + E fluid flow where z T w y T v x T u T u + + = u = velocity in x -direction; v = velocity in y- direction; w = velocity in z -direction During our studies of conduction, we treated convection as a boundary condition (i.e. if all the convective medium has T = T b dT/dx = dT/dy = dT/dz = 0 in the fluid itself) However, if dealing with heat transfer through fluids, the inertial (flow) term becomes important to the analysis.
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This is particularly true for convection analysis given that convection involves heat transfer via both conduction and advection , the physical movement of heated (or cooled) fluid from a solid interface or within a fluid. Advection may arise from different types of fluid flows: h External flows Forced , i.e. flowing at a significant velocity (pumps, fans) Free , i.e. stagnant flow where diffusion effects dominate h Internal flows (pipes & conduits) Thus, in order to develop a framework for convection analysis, we need to know something about how fluids flow under these different circumstances b FLUID MECHANICS
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F LUID M ECHANICS The flow properties of a fluid are defined by its density ( ρ ) and viscosity ( μ ) [ Note: both strong functions of T ] Density – mass per unit volume b Property of atoms/molecules High density (liquids) b larger inertial force required to move a given volume of fluid ( F = ma ) Viscosity - internal resistance of a fluid to flow (unit: Pa s = N/m 2 s) b Intermolecular interactions b Molecular tangling (polymers) High viscosity (oil, polymers) b large inertia/resistance to flow b Flow in highly viscous fluids may generate frictional heat (viscous dissipation)
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Velocity Boundary Layer When a velocity gradient exists in a flow field, the fluid experiences shear forces. A measure of the shear force per unit area is called shear stress , τ . u/ y = fluid velocity For a fluid traveling in the x -direction over a surface, the force diagram acting on the fluid is shown below: y u Area Force = = μ τ FLUID FLOW Friction Applied Force SURFACE
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Key Feature: No-Slip Surface where net force = 0 (applied flow force = surface frictional drag) b wall velocity u = dx/dt | x=0 = 0 Thus, the velocity profile of a flowing
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Convection - CHAPTER 6: INTRODUCTION TO CONVECTION For...

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