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A heater coil is completely immersed in an oil bath that is insulated on all sides except for the top where the oil is in direct contact with the surrounding air that is maintained at a constant temperature, air. At t=0s, the coil is switched on and provides in watts of electrical power to the oil which has a thermal mass of moll and an initial temperature of Oinit-oill. The temperature of the oil is denoted by oil and the thermal resistance between the oil and air is Roil-air- a) Draw a schematic of the system clearly labeling the (assumed) directions of the heat transfer rates and the temperature at every node. b) Derive the governing differential equation for the temperature of the oil, oil- c) Where does init-oil appear in the system schematic and how does it affect the governing equations? d) Derive an expression for the steady-state temperature of the oil as a function of the various system parameters.

A heater coil is completely immersed in an oil bath that is insulated on all sides except for the top where the oil is in direct contact with the surrounding air that is maintained at a constant temperature, air. At t=0s, the coil is switched on and provides in watts of electrical power to the oil which has a thermal mass of moll and an initial temperature of Oinit-oill. The temperature of the oil is denoted by oil and the thermal resistance between the oil and air is Roil-air- a) Draw a schematic of the system clearly labeling the (assumed) directions of the heat transfer rates and the temperature at every node. b) Derive the governing differential equation for the temperature of the oil, oil- c) Where does init-oil appear in the system schematic and how does it affect the governing equations? d) Derive an expression for the steady-state temperature of the oil as a function of the various system parameters.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A heater coil is completely immersed in an oil bath that is insulated on all sides except for the top where the oil is in direct contact with the surrounding air that is maintained at a constant temperature, Oair. At t=0s, the coil is switched on and provides in watts of electrical power to the oil which has a thermal mass of moil and an initial temperature of Oinit-oil. The temperature of the oil is denoted by oil and the thermal resistance between the oil and air is Roil-air- a) Draw a schematic of the system clearly labeling the (assumed) directions of the heat transfer rates and the temperature at every node. b) Derive the governing differential equation for the temperature of the oil, oil- c) Where does Oinit-oil appear in the system schematic and how does it affect the governing equations? d) Derive an expression for the steady-state temperature of the oil as a function of the various system parameters.
Transcribed Image Text:A heater coil is completely immersed in an oil bath that is insulated on all sides except for the top where the oil is in direct contact with the surrounding air that is maintained at a constant temperature, Oair. At t=0s, the coil is switched on and provides in watts of electrical power to the oil which has a thermal mass of moil and an initial temperature of Oinit-oil. The temperature of the oil is denoted by oil and the thermal resistance between the oil and air is Roil-air- a) Draw a schematic of the system clearly labeling the (assumed) directions of the heat transfer rates and the temperature at every node. b) Derive the governing differential equation for the temperature of the oil, oil- c) Where does Oinit-oil appear in the system schematic and how does it affect the governing equations? d) Derive an expression for the steady-state temperature of the oil as a function of the various system parameters.
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