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Heat Transfer Rates

Heat Transfer Rates. Conduction: Fourier’s Law. heat flux [W/m 2 ]. thermal conductivity [W/m-K]. temperature gradient [K/m]. Convection: Newton’s Law of Cooling. fluid temperature [K]. heat flux [W/m 2 ]. heat transfer coefficient [W/m 2 -K]. surface temperature [K].

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Heat Transfer Rates

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  1. Heat Transfer Rates Conduction: Fourier’s Law heat flux [W/m2] thermal conductivity [W/m-K] temperature gradient [K/m] Convection: Newton’s Law of Cooling fluid temperature [K] heat flux [W/m2] heat transfer coefficient [W/m2-K] surface temperature [K] Radiation: Stefan-Boltzmann Law (modified) surface temperature [K] emissive power [W/m2] surface emissivity [ ] Stefan-Boltzmann constant [5.67×10-8 W/m2-K4]

  2. Transient Conduction: Lumped Capacitance Define: thermal time constant We can plot the normalizedsolution to the general problem • Notes: • The change in thermal energy storagedue to the transient process is: • General Transient Problem: Special Case negligible radiation, heat flux & heat generation

  3. 1-D Steady Conduction: Plane Wall Governing Equation: Dirichlet Boundary Conditions: Solution: temperature is not a function of k Heat Flux: heat flux/flow are a function of k Heat Flow: • Notes: • A is the cross-sectional area of the wall perpendicular to the heat flow • both heat flux and heat flow are uniform  independent of position (x) • temperature distribution is governed by boundary conditions and length of domain  independent of thermal conductivity (k)

  4. 1-D Steady Conduction: Cylinder Wall Governing Equation: Dirichlet Boundary Conditions: Solution: heat flux is non-uniform Heat Flux: heat flow is uniform Heat Flow: heat flow per unit length • Notes: • heat flux is not uniform  function of position (r) • both heat flow and heat flow per unit length are uniform  independent of position (r)

  5. 1-D Steady Conduction: Spherical Shell Governing Equation: Dirichlet Boundary Conditions: Solution: Heat Flux: heat flux is non-uniform heat flow is uniform Heat Flow: • Notes: • heat flux is not uniform  function of position (r) • heat flow is uniform  independent of position (r)

  6. Thermal Resistance

  7. Thermal Circuits: Composite Plane Wall Circuits based on assumption of isothermal surfaces normal to x direction or adiabatic surfaces parallel tox direction Actual solution for the heat rate q is bracketed by these two approximations

  8. Thermal Circuits: Contact Resistance In the real world, two surfaces in contact do not transfer heat perfectly Contact Resistance: values depend on materials (A and B), surface roughness, interstitial conditions, and contact pressure typically calculated or looked up Equivalent total thermal resistance:

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