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To warm up some milk in a thin-walled glass cylindrical container whose diameter is 6 cm. The height of the milk in the glass is 7 cm. The milk container is placed into a large pan filled with hot water at 60°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is 120 W/m2.°C, determine how long it will take for the milk to warm up from 3°C to 38°C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Use the lumped system analysis to solve the problem. The properties of water and milk at 20°C are, k = 0.607 W/m.°C, p = 998 kg/m', and C, = 4.182 kJ/kg.°C. Answer: 5.8 min. ملاحظه: تكون هنا قيمة (0.1 < Bi) ويفترض لايطبق التحليل الكتلي , ولكن استخدم نفس التحليل والمعادلات في المحاضرة وكذلك في المثال لان الحليب يخلط باستمرار ولذلك تكون درجة حرارته منتظمه و متغيره مع الزمن لانه يكتسب حراره من الماء ويسخن وترتفع درجة حرارته مع الزمن ولذلك م مكن تطبيق طريقة الحل في التحليل الكتلي. Milk Water 7 cm 6 cm

To warm up some milk in a thin-walled glass cylindrical container whose diameter is 6 cm. The height of the milk in the glass is 7 cm. The milk container is placed into a large pan filled with hot water at 60°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is 120 W/m2.°C, determine how long it will take for the milk to warm up from 3°C to 38°C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Use the lumped system analysis to solve the problem. The properties of water and milk at 20°C are, k = 0.607 W/m.°C, p = 998 kg/m', and C, = 4.182 kJ/kg.°C. Answer: 5.8 min. ملاحظه: تكون هنا قيمة (0.1 < Bi) ويفترض لايطبق التحليل الكتلي , ولكن استخدم نفس التحليل والمعادلات في المحاضرة وكذلك في المثال لان الحليب يخلط باستمرار ولذلك تكون درجة حرارته منتظمه و متغيره مع الزمن لانه يكتسب حراره من الماء ويسخن وترتفع درجة حرارته مع الزمن ولذلك م مكن تطبيق طريقة الحل في التحليل الكتلي. Milk Water 7 cm 6 cm

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter3: Transient Heat Conduction
Section: Chapter Questions
Problem 3.12P
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To warm up some milk in a thin-walled glass cylindrical container whose diameter is 6 cm. The height of the milk in the glass is 7 cm. The milk container is placed into a large pan filled with hot water at 60°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is 120 W/m2.°C, determine how long it will take for the milk to warm up from 3°C to 38°C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Use the lumped system analysis to solve the problem. The properties of water and milk at 20°C are, k = 0.607 W/m.°C,p=998 kg/m', and C, = 4.182 kJ/kg.°C. Answer: 5.8 min. ملاحظه: تكون هنا قيمة (0.1 < Bi( ويفترض لايطبق التحليل الكتلي , ولكن استخدم نفس التحليل والمعادلات في المحاضرة وكذلك في المثال لان الحليب يخلط باستمرار ولذلك تكون درجة حرارته منتظمه و متغيره مع الزمن لانه يكتسب حراره من الماء ويسخن وترتفع درجة حرارته مع الزمن ولذلك م مكن تطبيق طريقة الحل في التحليل الكتلي. Water Milk 7 cm 6 cm
Transcribed Image Text:To warm up some milk in a thin-walled glass cylindrical container whose diameter is 6 cm. The height of the milk in the glass is 7 cm. The milk container is placed into a large pan filled with hot water at 60°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is 120 W/m2.°C, determine how long it will take for the milk to warm up from 3°C to 38°C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Use the lumped system analysis to solve the problem. The properties of water and milk at 20°C are, k = 0.607 W/m.°C,p=998 kg/m', and C, = 4.182 kJ/kg.°C. Answer: 5.8 min. ملاحظه: تكون هنا قيمة (0.1 < Bi( ويفترض لايطبق التحليل الكتلي , ولكن استخدم نفس التحليل والمعادلات في المحاضرة وكذلك في المثال لان الحليب يخلط باستمرار ولذلك تكون درجة حرارته منتظمه و متغيره مع الزمن لانه يكتسب حراره من الماء ويسخن وترتفع درجة حرارته مع الزمن ولذلك م مكن تطبيق طريقة الحل في التحليل الكتلي. Water Milk 7 cm 6 cm
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