Heat Transfer Introduction and Conduction Conduction If a

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 Where A = area of isothermal surface n = distance measured normally to surface = rate of heat flow across surface in direction normal to surface T = temperature k = proportionality constant q § Temperature can vary with both location and time § Heat flow occurs from hot to cold

Temperature One-Dimensional Heat Flow 700 C III II Hot Gas c Water 25 C I B 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 § d. T/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 + b. T 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. 5 – 0. 7 W/m- C § k for gases § Air – 0. 024 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 thermal resistance of the solid between two points

Resistances in Series TA T TB TC TA RA RB RC TB T BA BB BC TC

Heat Flow through a Cylinder dr ri To Ti r ro

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