Temperature Dynamics of a Heated Object Consider the heat transfer system in Example 7.7, in which a steel sphere is submerged in hot water and the temperature of the sphere is assumed to be uniform. Build a Simscape model of the physical system and find the sphere’s temperature output T(t).

Question

Temperature Dynamics of a Heated Object

Consider the heat transfer system in Example 7.7, in which a steel sphere is submerged in hot water and the temperature of the sphere is assumed to be uniform. Build a Simscape model of the physical system and find the sphere's temperature output [latex]T(t)[/latex]. Compare the result with that obtained in Example 7.7.

Accepted Answer

The Simscape block diagram corresponding to the physical system is shown in Figure 7.41. The temperature of the hot water is known as [latex]100^{\circ} \mathrm{C}[/latex] or [latex]373 \mathrm{~K}[/latex]. The Ideal Temperature Source block in the library of Simscape/Foundation Library/Thermal/Thermal Sources is used to represent the temperature input. A Simulink-PS Converter block converts the constant value of [latex]373 \mathrm{~K}[/latex] into a physical signal. Double-click on the block and define the Input signal unit as [latex]K[/latex].

Because the temperature of the sphere is assumed to be uniform, only the convective heat transfer between the water and the sphere is considered in modeling. The corresponding block can be found in the library of Simscape/Foundation Library/Thermal/Thermal Elements. Double-click on the block and define Area as [latex]0.0013 \mathrm{~m}^{2}[/latex], and Heat transfer coefficient as [latex]350 \mathrm{~W} /\left(\mathrm{m}^{2} \cdot \mathrm{K}\right)[/latex]. The block Thermal Mass in the same library is used to represent the steel sphere. The associated parameters are Mass, Specific heat, and Initial temperature, and their values are [latex]0.0329 \mathrm{~kg}, 440 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})[/latex], and [latex]25^{\circ} \mathrm{C}[/latex] or [latex]298 \mathrm{~K}[/latex]. All parameter values can be determined using the information given in Example 7.7.

To measure the sphere's temperature, drag the Ideal Temperature Sensor block in the library of Simscape/Foundation Library/Thermal/Thermal Sensors. The PSSimulink Converter block converts the physical signal to a Simulink signal. Double-click on the block and define the Output signal unit as [latex]\mathrm{K}[/latex]. Because the simulation result in Example 7.7 is given in units of [latex]{ }^{\circ} \mathrm{C}[/latex], we can also define the unit as [latex]\mathrm{C}[/latex] and check the box of Apply affine conversion.

Run the simulation and the same curve as shown in Figure 7.29 can be obtained, which is the resulting temperature output [latex]T(t)[/latex] of the heated sphere.

Question 7.11: Temperature Dynamics of a Heated Object Consider the heat tr...

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