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

This preview shows pages 1–7. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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)
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online