A small metal cube with a thermal mass mc and an initial temperature 0, is dropped into a container of water that is actively maintained at a constant temperature 0w. The cube quickly comes to rest on the bottom surface of the container. The bottom surface is maintained at a constant temperature 0 (note that this is different from 0w). The thermal resistance between the cube and the water is Rcw while the thermal resistance between the bottom surface of the container and the cube is RCB. The temperature of the cube is denoted by Oc. a) Draw the system schematic indicating the assumed directions of the heat transfer rates. Label all the nodes and system parameters. b) Derive the governing equation for the temperature of the cube, 0c. c) Where does to appear in the system schematic and how does it affect the governing equations?

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A small metal cube with a thermal mass mc and an initial temperature 0 is dropped into a
container of water that is actively maintained at a constant temperature 0w. The cube
quickly comes to rest on the bottom surface of the container. The bottom surface is
maintained at a constant temperature 0 (note that this is different from 0w). The
thermal resistance between the cube and the water is Rcw while the thermal resistance
between the bottom surface of the container and the cube is RCB. The temperature of the
cube is denoted by 0c.
a) Draw the system schematic indicating the assumed directions of the heat transfer
rates. Label all the nodes and system parameters.
b) Derive the governing equation for the temperature of the cube, 0c.
c) Where does to appear in the system schematic and how does it affect the governing
equations?
d) Calculate the steady-state temperature of the cube, css, assuming the following
system parameters:
0o = 21°C, 0B = 6°C, 0w = 0°C, Rcw = 2°C/W, and RCB = 4°C/W
Transcribed Image Text:A small metal cube with a thermal mass mc and an initial temperature 0 is dropped into a container of water that is actively maintained at a constant temperature 0w. The cube quickly comes to rest on the bottom surface of the container. The bottom surface is maintained at a constant temperature 0 (note that this is different from 0w). The thermal resistance between the cube and the water is Rcw while the thermal resistance between the bottom surface of the container and the cube is RCB. The temperature of the cube is denoted by 0c. a) Draw the system schematic indicating the assumed directions of the heat transfer rates. Label all the nodes and system parameters. b) Derive the governing equation for the temperature of the cube, 0c. c) Where does to appear in the system schematic and how does it affect the governing equations? d) Calculate the steady-state temperature of the cube, css, assuming the following system parameters: 0o = 21°C, 0B = 6°C, 0w = 0°C, Rcw = 2°C/W, and RCB = 4°C/W
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