Explanation Calculation: Write the expression for the conservation of heat energy of capacitance C 1 . d d t ( C 1 T 1 ) = q i − q 1 .... (I) Here, the thermal capacitance of the heating element is C 1 , the temperature of the heating element is T 1 , the rate of heat input to the heating element is q i , the rate of heat input from the heating element to the air is q 1 . Write the expression for the conservation of heat energy of capacitance C 2 . d d t ( C 2 T 2 ) = q 1 − q o .... (II) Here, the thermal capacitance of the oven air is C 2 , the temperature of the oven air is T 2 , the rate of heat output from the oven wall is q o . Write the expression for the convective heat transfer rate from the heating element to the air. q 1 = h A ( T 1 − T 2 ) .... (III) Here, the convective heat transfer coefficient is h and the area of the heating element is A . Write the expression for the convective heat transfer rate from the oven wall to the surroundings. q o = h o A o ( T 2 − T 0 ) .... (IV) Here, the convective heat transfer coefficient is h o and the area of the boundary is A o . Write the expression for the thermal resistance of the heating element. R 1 = 1 h A h A = 1 R 1 Write the expression for the thermal resistance for the surrounding heat transfer. R 2 = 1 h A h o A o = 1 R 2 Substitute 1 R 1 for h A in Equation (III). q 1 = ( T 1 − T 2 ) R 1 Substitute 1 R 2 for h o A o in Equation (IV). q o = ( T 2 − T 0 ) R 2 Substitute ( T 1 − T 2 ) R 1 for q 1 in Equation (I)

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ISBN: 8220100254963

Author: Palm

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Chapter 7, Problem 7.54P

To determine

The model for the temperature T1 and T2.

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Chapter 7, Problem 7.53P

Chapter 7, Problem 7.55P

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Chapter 7 Solutions

EBK SYSTEM DYNAMICS

Ch. 7 - Prob. 7.1P Ch. 7 - Refer to the water storage and supply system shown...Ch. 7 - Prob. 7.3P Ch. 7 - In Figure P7.4 the piston of area A is connected...Ch. 7 - Refer to Figure 7.1.4a. and suppose that p\ — p2=...Ch. 7 - Pure water flows into a mixing tank of volume V =...Ch. 7 - Consider the mixing tank treated in Problem 7.6....Ch. 7 - Derive the expression for the fluid capacitance of...Ch. 7 - Prob. 7.9P Ch. 7 - Prob. 7.10P

Ch. 7 - 7.11 Derive the expression for the capacitance of...Ch. 7 - Air flows in a certain cylindrical pipe 1 m long...Ch. 7 - Derive the expression for the linearized...Ch. 7 - Consider the cylindrical container treated in...Ch. 7 - A certain tank has a bottom area A = 20 m2. The...Ch. 7 - A certain tank has a circular bottom area A = 20...Ch. 7 - The water inflow rate to a certain tank was kept...Ch. 7 - Prob. 7.18P Ch. 7 - Prob. 7.19P Ch. 7 - In the liquid level system shown in Figure P7.20,...Ch. 7 - The water height in a certain tank was measured at...Ch. 7 - Derive the model for the system shown in Figure...Ch. 7 - (a) Develop a model of the two liquid heights in...Ch. 7 - Prob. 7.24P Ch. 7 - Design a piston-type damper using an oil with a...Ch. 7 - Prob. 7.26P Ch. 7 - 7.27 An electric motor is sometimes used to move...Ch. 7 - Prob. 7.28P Ch. 7 - Prob. 7.29P Ch. 7 - Figure P7.3O shows an example of a hydraulic...Ch. 7 - Prob. 7.31P Ch. 7 - Prob. 7.32P Ch. 7 - Prob. 7.33P Ch. 7 - Prob. 7.34P Ch. 7 - Prob. 7.35P Ch. 7 - Prob. 7.36P Ch. 7 - Prob. 7.37P Ch. 7 - (a) Determine the capacitance of a spherical tank...Ch. 7 - Obtain the dynamic model of the liquid height It...Ch. 7 - Prob. 7.40P Ch. 7 - Prob. 7.41P Ch. 7 - Prob. 7.42P Ch. 7 - Prob. 7.43P Ch. 7 - Prob. 7.44P Ch. 7 - Prob. 7.45P Ch. 7 - The copper shaft shown in Figure P7.46 consists of...Ch. 7 - A certain radiator wall is made of copper with a...Ch. 7 - A particular house wall consists of three layers...Ch. 7 - A certain wall section is composed of a 12 in. by...Ch. 7 - Prob. 7.50P Ch. 7 - Prob. 7.51P Ch. 7 - A steel tank filled with water has a volume of...Ch. 7 - Prob. 7.53P Ch. 7 - Prob. 7.54P Ch. 7 - Prob. 7.55P

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