Heat Transfer Introduction and Conduction

Conduction  If a temperature gradient exits in a continuous substance, heat can flow unaccompanied by any observable motion of matter  Metallic solids – conduction occurs from the motion of unbound electrons  Other solids and liquids – conduction results from the transport of momentum of individual molecules along the temperature gradient  Gases – conduction occurs by random motion of molecules; heat is “diffused” from hotter regions to colder ones  Examples – heat flow in opaque solids, ie., brick wall of furnace or metal wall of a tube

Convection  When a current or macroscopic particle of fluid crosses a specific surface, such as the boundary of a control volume, it carries with it a definite quantity of enthalpy  Occurs only when forces act on the particle or stream of fluid and maintain motion against forces of friction  Thermodynamically, convection is not heat flow, but flux  Closely associated with fluid mechanics  Examples – transfer of enthalpy by eddies of turbulent flow, current of warm air from a furnace flowing across a room

Natural and Forced Convection  Natural convection – currents are the result of buoyancy forces generated by differences in density and differences in density are in caused by temperature gradients in fluid mass  Flow of air across a heated radiator  Forced convection – currents are set in motion by action of a mechanical device such a pump or agitator, flow is independent of density gradients  Heat flow to a fluid pumped through a heated pipe

Radiation  Transfer of energy through space by electromagnetic waves  If matter appears in the path, radiation will be transmitted, reflected, or absorbed  Only absorbed energy appears as heat  Examples – loss of heat from a radiator or uninsulated stream pipe; heat transfer in furnaces

Heat Transfer by Conduction  Fourier’s law  Temperature can vary with both location and time  Heat flow occurs from hot to cold Where A = area of isothermal surface n = distance measured normally to surface q = rate of heat flow across surface in direction normal to surface T = temperature k = proportionality constant

One-Dimensional Heat Flow Hot Gas B Water Temperature 700  C 25  C c III II I I – at instant of exposure of wall to high temperature II – during heating at time t III – at steady state

For Steady One-Dimensional Flow  Thermal conductivity, k  Proportionality factor that represents a physical property of a substance  q/A – rate of heat flow per unit area  dT/dn – temperature gradient  q – watts or Btu/h  dt/dn -  C/m or  F/ft  k – W/m-  C or Btu-ft-h-  F

 For small temperature ranges, k is constant  For larger temperature ranges, k = a + bT Where a and b are empirical constants  k for metals  Stainless – 17 W/m-  C  Silver – 415 W/m-  C  k for liquids  Water – 0.7 W/m-  C  k for gases  Air – W/m-  C  Solids with low k values are often used as insulators

Steady State Conduction  For a flat slab of thickness, B  R is the thermal resistance of the solid between two points

Resistances in Series TT TCTC TBTB TATA RARA RBRB RCRC BABAB BCBC TT TCTC TBTB TATA

Heat Flow through a Cylinder ToTo TiTi dr riri r roro

Heat Flow in Fluids  Typical equipment consists of a bundle of parallel tube encased in a cylindrical shell