(a). Explanation Given: Diameter of inserted tube walled tube is, d 1 = 30 mm Diameter of cylindrical bale hay is, d 2 = 2 m Thermal conductivity of baled hay is, k = W / m ⋅ K The temperature inside the inserted tube is T ∞ , i = 20 ° C Outside air temperature is T ∞ , o = 0 ° C Heat transfer coefficient inside the inserted tube is, h i = 200 W / m 2 . K Outside convection heat transfer coefficient, h o = 25 W / m 2 ⋅ K Internal heat generation for wet hay is, q ˙ = 100 W / m 3 Calculation: The steady-state temperature distribution equation for cylinder can be written as 1 r ∂ ∂ r ( k r ∂ T ∂ r ) + q ˙ = 0 ∵ Thermal conductivity is constant ⇒ k r ∂ ∂ r ( r ∂ T ∂ r ) = − q ˙ ⇒ ∂ ∂ r ( r ∂ T ∂ r ) = − q ˙ r k Integrating the above equation, ⇒ r ∂ T ∂ r = − q ˙ r 2 2 + C 1 ⇒ ∂ T ∂ r = − q ˙ r 2 k + C 1 r ........ ( 1 ) Again integrating the above equation, T ( r ) = − q ˙ 4 k r 2 + C 1 ln ( r ) + C 2 ......... ( 2 ) At r = r 1 the boundary condition can be given as, [ − k d T d r ] r = r 1 = h i ( T − T ∞ , i ) From equation ( 1 ) & ( 2 ) − k [ − q ˙ r 2 k + C 1 r ] = h i [ − q ˙ 4 k r 2 + C 1 ln ( r ) + C 2 − T ∞ , i ] For r = r 1 − k [ − q ˙ r 1 2 k + C 1 r 2 ] = h i [ − q ˙ 4 k r 1 2 + C 1 ln ( r 1 ) + C 2 − T ∞ , i ] 1 h i [ q ˙ r 1 2 − C 1 k r 1 ] = [ − q ˙ 4 k r 1 2 + C 1 ln ( r 1 ) + C 2 − T ∞ , i ] 1 200 [ 100 × 0.015 2 + 0.04 C 1 0.015 ] = [ − 100 4 × 0.04 × 0.015 2 + C 1 ln ( 0.015 ) + C 2 − 20 ] 1 200 = ( 0.75 − 2.67 C 1 ) = ( − 0.141 − 4.2 C 1 + C 2 − 20 ) 3 (b). To determine To plot: the radial temperature distribution in the hay. (c). To determine To plot: the radial temperature distribution in the hay.

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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 3, Problem 3.83P

(a).

To determine

The steady-state heat transfer per unit length of the tube.

(b).

To determine

To plot: the radial temperature distribution in the hay.

(c).

To determine

To plot: the radial temperature distribution in the hay.

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Chapter 3, Problem 3.82P

Chapter 3, Problem 3.84P

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The steady-state heat transfer per unit length of the tube.

Solution Summary: The author explains the steady-state heat transfer per unit length of the tube and the thermal conductivity of baled hay.

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The steady-state heat transfer per unit length of the tube.

To plot: the radial temperature distribution in the hay.

To plot: the radial temperature distribution in the hay.

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Chapter 3 Solutions