i. Explanation Given: Temperature of the nitrogen is T ∞ = 25 ° c Velocity of the nitrogen is V = 5 m / s Assumptions: Lumped capacitance method is valid. Constant properties. Radiation exchange with the large surroundings. Properties taken from the table are: μ = 177 × 10 − 7 N . s / m 2 υ = 15.7 × 10 − 6 m 2 / s k = 0.0257 W / m . k Pr = 0.716 Nitrogen- ( T s ¯ = 873 K ) μ s = 368 × 10 − 7 N . s / m 2 Calculation: Neglecting the radiation, the cooling time can be determined by, t = ρ ( π D 3 / 6 ) c h ¯ π D 2 ln θ c θ = ρ θ c 6 h ¯ ln T i − T ∞ T f − T ∞ The convection coefficient is obtained from the Whitaker correlation with , Re D = V D υ = 5 × 0.01 15.7 × 10 − 6 = 3185 Hence, N u D ¯ = ( h ¯ D / k ) = 2 + ( 0 ii. To determine Time required to cool down the sphere accounting effects of radiation and convection.

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ISBN: 9780470501979

Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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Chapter 7, Problem 7.76P

To determine

Time required to cool down the sphere neglecting radiation.

ii.

To determine

Time required to cool down the sphere accounting effects of radiation and convection.

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Chapter 7, Problem 7.75P

Chapter 7, Problem 7.77P

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Time required to cool down the sphere neglecting radiation.

Solution Summary: The author explains the time required to cool down the sphere neglecting radiation. The convection coefficient is obtained from the Whitaker correlation.

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Time required to cool down the sphere neglecting radiation.

Time required to cool down the sphere accounting effects of radiation and convection.

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Chapter 7 Solutions