(a) Explanation Given: Fin length is L = 10 mm . Thermal conductivity is k = 180 W/ m ⋅ K . Thickness is t = 1 mm . Convection coefficient is h = 100W/ m 2 ⋅ K . Calculation: The fin heat transfer rate for Cases A, B and D are given by Eqs. (3.72), (3.76) and (3.80), where M = ( 2 h w 2 t k ) 1 / 2 ( t b − t ∞ ) = ( 2 × 100 W/m 2 ⋅ K × 0.001 m × 180 W/m ⋅ K ) 1 / 2 ( 75 ° C ) w = 450 w W , m ≈ ( 2 h / k t ) 1 / 2 = ( 200 W/m 2 ⋅ K / 180 W/m ⋅ K × 0.001 m ) 1 / 2 = 33.3 m -1 , mL ≈ 33.3 m -1 × 0.010 m = 0.333 , and, ( h / m k ) ≈ ( 100 W/m 2 ⋅ K 33.3 m -1 × 180 W/m ⋅ K ) = 0.0167. From Table B-1, it follows that s i n h m L ≈ 0.340 , c o s h m L ≈ 1.057 , a n d t a n h m L ≈ 0.321 . From knowledge of q f , equation (3.86), (3.81) and (3.83) yield, n f = q ′ f h ( 2 L + t ) θ b , ε f ≈ q ′ f h t θ b , R ′ t , f = θ b q ′ f Case A: from equation (3.72), (3.82), (3.83) and (3.70), Heat rate per unit width is calculated as follows: q ′ f = M w ( sinh m L + ( h / m k ) cosh m L cosh m L + ( h / m k ) cosh m L ) = ( 450 W/m ) ( 0 (b) To determine Effect of length on the heat rate.

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ISBN: 9780470501962

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

Publisher: Wiley, John & Sons, Incorporated

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When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a bur…

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Chapter 3, Problem 3.133P

(a)

To determine

Heat rate per unit width, thermal resistance, efficiency, effectiveness and tip temperature for different tip conditions.

(b)

To determine

Effect of length on the heat rate.

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Chapter 3, Problem 3.132P

Chapter 3, Problem 3.134P

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Heat rate per unit width, thermal resistance, efficiency, effectiveness and tip temperature for different tip conditions.

Solution Summary: The author explains the fin heat transfer rate for Cases A, B, and D.

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Heat rate per unit width, thermal resistance, efficiency, effectiveness and tip temperature for different tip conditions.

Effect of length on the heat rate.

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Chapter 3 Solutions