*FIND: Ratio KNOWN: Expression for the local heat transfer coefficient of air at prescribed velocity and temperature flowing over electronic elements on a circuit board and heat dissipation rate for a 4 ⋅ 4 mm chip located 120mm from the leading edge. SCHEMATIC: COMMENTS: (1) Note that the estimated value for Tf used to evaluate the air properties was reasonable.(2) Alternatively, we could have evaluated chip h by performing the integration of the local value, h(x).KNOWN: A spherical shell with prescribed geometry and surface temperatures.*

FIND: Time required to cool to a prescribed temperature.

ASSUMPTIONS: (1) Negligible radiation effects, (2) Constant properties. 5.10 to a sphere (Lc = ro/3), Hence, the temperature of the steel remains approximately uniform during the cooling process, and the lumped capacitance method may be used. 5.4 and 5.5, COMMENTS: Due to the large value of Ti, radiation effects are likely to be significant during the early portion of the transient. Problem 19.2 (WWWR) Air Water Benzene Mercury Glycerin υ 1.7× 10 − 5 0.474× 10 − 5 0.473× 10 − 5 1.06× 10 − 6 0.138× 10 − 2 Cρ 1.008× 103 1.0 0.45 0.033 0. Re 2.3× 105 1.02× 107 1.02× 107 4.57× 107 37800 Pr 0.699 2.72 5.21 0.021 1305 Nu 348 15.4 77.3 1.17 35.

This is because more energy must be lost from the substance of greater heat capacity to drop the temperature. Heat capacities and heat transfer coefficients are themselves temperature dependent quantities, so my answers are only valid for modest $\Delta T$.

For example, the heat capacity of hydrogen gas changes in very interesting ways as you get to really low temperatures, due to the equilibrium ratio of ortho/para hydrogen (both hydrogen, but with different nuclear spin states).

St 2.1× 10 − 3 5.55× 10 − 7 1.45× 10 − 6 1.22× 10 − 6 7.21× 10 − 7 Problem 19.8 (WWWR) 2 sin 900 2500sin 1.

in / , in qx x ab AL q Wm x m A ⎛⎞ππ⎛ ⎞ = ⎜⎟= ⎜ ⎟ ⎝⎠ ⎝ ⎠ 77.4 83.5 1 cos 1.

SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional (radial) conduction, (3) No internal heat generation, (4) Insulation has uniform properties independent of temperature and position. 2.1, for this one-dimensional (cylindrical) radial system has the form This relation requires that the product of the radial temperature gradient, d T/dr, and the radius, r, remains constant throughout the insulation.

For our situation, the temperature distribution must appear as shown in the sketch.

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