Slide 1

AME 60634 Int. Heat Trans. D. B. Go 1 Heat Transfer Rates heat flux [W/m 2 ] thermal conductivity [W/m-K] temperature gradient [K/m] heat flux [W/m 2 ] heat transfer coefficient [W/m 2 -K] surface temperature [K] fluid temperature [K] emissive power [W/m 2 ] surface emissivity [ ] Stefan-Boltzmann constant [5.6710 -8 W/m 2 -K 4 ] surface temperature [K] Conduction: Fouriers Law Convection: Newtons Law of Cooling Radiation: Stefan-Boltzmann Law (modified)

Slide 2

AME 60634 Int. Heat Trans. D. B. Go 2 Transient Conduction: Lumped Capacitance General Transient Problem: Special Case negligible radiation, heat flux & heat generation Define: thermal time constant We can plot the normalized solution to the general problem Notes: The change in thermal energy storage due to the transient process is:

Slide 3

AME 60634 Int. Heat Trans. D. B. Go 3 1-D Steady Conduction: Plane Wall Governing Equation: Dirichlet Boundary Conditions: Solution: Heat Flux: Heat Flow: temperature is not a function of k 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 ) heat flux/flow are a function of k

Slide 4

AME 60634 Int. Heat Trans. D. B. Go 4 1-D Steady Conduction: Cylinder Wall Governing Equation: Dirichlet Boundary Conditions: 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 ) Solution: Heat Flux: Heat Flow: heat flow per unit length heat flux is non-uniform heat flow is uniform

Slide 5

AME 60634 Int. Heat Trans. D. B. Go 5 1-D Steady Conduction: Spherical Shell Governing Equation: Dirichlet Boundary Conditions: Solution: Heat Flux: Heat Flow: Notes: heat flux is not uniform function of position ( r ) heat flow is uniform independent of position ( r ) heat flux is non-uniform heat flow is uniform

Slide 6

AME 60634 Int. Heat Trans. D. B. Go 6 Thermal Resistance

Slide 7

AME 60634 Int. Heat Trans. D. B. Go 7 Thermal Circuits: Composite Plane Wall Circuits based on assumption of (a)isothermal surfaces normal to x direction or (b)adiabatic surfaces parallel to x direction Actual solution for the heat rate q is bracketed by these two approximations

Slide 8

AME 60634 Int. Heat Trans. D. B. Go 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: