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.

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.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.8P

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The air-conditioning system in a Chevrolet van for use in desert climates is to be sized. The system is to maintain an interior temperature of 20C when the van travels at 100 km/h through dry air at 30C at night. If the top of the van is idealized as a flat plate 6 m long and 2 m wide and the sides as flat plates 3 m tall and 6 m long, estimate the rate at which heat must be removed from the interior to maintain the specified
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2.43 A turbine blade 6.3 cm long, with cross-sectional area and perimeter , is made of stainless steel . The temperature of the root, , is . The blade is exposed to a hot gas at , and the heat transfer coefficient is K. Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.
1.43 A simple solar heater consists of a flat plate of glass below which is located a shallow pan filled with water, so that the water is in contact with the glass plate above it. Solar radiation passes through the glass at the rate of . The water is at and the surrounding air is at . If the heat transfer coefficients between the water and the glass, and between the glass and the air are respectively, determine the time required to transfer of surface to the water in the pan. The lower surface of the pan is assumed to be insulated.
2.7 A very thin silicon chip is bonded to a 6-mm thick aluminum substrate by a 0.02-mm thick epoxy glue. Both surfaces of this chip-aluminum system are cooled by air at , where the convective heat transfer coefficient of air flow is . If the heat dissipation per unit area from the chip is under steady-state conditions, draw the thermal circuit for the system and determine the operating temperature of the chip.
1.67 In beauty salons and in homes, a ubiquitous device is the hairdryer. The front end of a typical hairdryer is idealized as a thin-walled cylindrical duct with a 6-cm diameter with a fan at the inlet that blows air over an electric heating coil as schematically shown in the figure. The design of this appliance requires two power settings, with which the air blown over the electric heating coil is heated from the ambient temperature of to an outlet temperature of and with exit air velocities of 1.0 m/s and 1.5 m/s. Estimate the electric power required for the heating coil to meet these conditions, assuming that heat loss from the outside of the dryer duct is neglected.
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A 0.6-cm diameter mild steel rod at 38C is suddenly immersed in a liquid at 93C with hc=110W/m2K. Determine the time required for the rod to warm to 88C.
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The interior wall of a large, commercial walk-in type meat freezer is covered under normal operating conditions with a 2-cm thick layer of ice. One day, a power outage cuts electricity to the refrigeration system of the freezer. Estimate the time required to melt this layer of ice if it has a mass density of 700kg/m3 and a latent heat of fusion of 334 kJ/kg. Consider the air temperature inside the freezer to be 20C with a heat transfer coefficient of 2W/m2K for convection from the freezer surface to air, and clearly state the assumptions made in your calculations.