Presentation on theme: "Internal Flow: Heat Transfer Correlations"— Presentation transcript:
1 Internal Flow: Heat Transfer Correlations Chapter 8Sections 8.4 through 8.8
2 Fully Developed Flow Laminar Flow in a Circular Tube: The local Nusselt number is a constant throughout the fully developedregion, but its value depends on the surface thermal condition.Uniform Surface Heat Flux :Uniform Surface Temperature :Turbulent Flow in a Circular Tube:For a smooth surface and fully turbulent conditions , theDittus – Boelter equation may be used as a first approximation:The effects of wall roughness and transitional flow conditionsmay be considered by using the Gnielinski correlation:
3 Fully Developed (cont.) Smooth surface:Surface of roughness :Noncircular Tubes:Use of hydraulic diameter as characteristic length:Since the local convection coefficient varies around the periphery of a tube,approaching zero at its corners, correlations for the fully developed regionare associated with convection coefficients averaged over the peripheryof the tube.Laminar Flow:The local Nusselt number is a constant whose value (Table 8.1) depends onthe surface thermal condition and the duct aspect ratio.Turbulent Flow:As a first approximation, the Dittus-Boelter or Gnielinski correlation may be usedwith the hydraulic diameter, irrespective of the surface thermal condition.
4 Effect of the Entry Region The manner in which the Nusselt decays from inlet to fully developed conditionsfor laminar flow depends on the nature of thermal and velocity boundary layerdevelopment in the entry region, as well as the surface thermal condition.Laminar flow in acircular tube.Combined Entry Length:Thermal and velocity boundary layers develop concurrently from uniformprofiles at the inlet.
5 in the entry region is restricted to thermal effects. Entry Region (cont)Thermal Entry Length:Velocity profile is fully developed at the inlet, and boundary layer developmentin the entry region is restricted to thermal effects.Such a condition may alsobe assumed to be a good approximation for a uniform inlet velocity profile ifWhy?Average Nusselt Number for Laminar Flow in a Circular Tube with UniformSurface Temperature:Combined Entry Length:Thermal Entry Length:
6 Average Nusselt Number for Turbulent Flow in a Circular Tube : Entry Region (cont)Average Nusselt Number for Turbulent Flow in a Circular Tube :Effects of entry and surface thermal conditions are less pronounced forturbulent flow and can be neglected.For long tubes :For short tubes :Noncircular Tubes:Laminar Flow:depends strongly on aspect ratio, as well as entry region and surfacethermal conditions. See references 11 and 12.
7 As a first approximation, correlations for a circular tube may be used Entry Region (cont)Turbulent Flow:As a first approximation, correlations for a circular tube may be usedwith D replaced by .When determining for any tube geometry or flow condition, allproperties are to be evaluated atWhy do solutions to internal flow problems often require iteration?
8 The Concentric Tube Annulus Fluid flow throughregion formed byconcentric tubes.Convection heat transfermay be from or to innersurface of outer tube andouter surface of inner tube.Surface thermal conditions may be characterized byuniform temperature or uniform heat fluxConvection coefficients are associated with each surface, where
9 Fully Developed Laminar Flow Annulus (cont)Fully Developed Laminar FlowNusselt numbers depend on and surface thermal conditions (Tables 8.2, 8.3)Fully Developed Turbulent FlowCorrelations for a circular tube may be used with replaced by
10 Problem: Solar Collector Problem 8.30: Determine the effect of flow rate on outlet temperatureand heat rate for water flow through the tube of aflat-plate solar collector.