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Heat Transfer Introduction and Conduction
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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
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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
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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
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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
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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
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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
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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
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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 - 0.5 – 0.7 W/m- C k for gases Air – 0.024 W/m- C Solids with low k values are often used as insulators
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Steady State Conduction For a flat slab of thickness, B R is the thermal resistance of the solid between two points
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Resistances in Series TT TCTC TBTB TATA RARA RBRB RCRC BABAB BCBC TT TCTC TBTB TATA
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Heat Flow through a Cylinder ToTo TiTi dr riri r roro
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Heat Flow in Fluids Typical equipment consists of a bundle of parallel tube encased in a cylindrical shell
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