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The convection coefficient for flow over a solid sphere may be determined by submerging the sphere,...

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Mechanical Engineering

The convection coefficient for flow over a solid sphere may bedetermined by submerging the sphere, which is initially at 25 °C,into the flow, which is at 75 °C, and measuring its surfacetemperature at some time during the transient heating process. Ifthe sphere has a diameter of 0.1 m, a thermal conductivity of 20W/(m·K), and a thermal diffusivity of 4.0×10-5 m2/s, atwhat time will a surface temperature of 60 ºC be recorded if theconvection coefficient is 300 W/(m2·K)?

a) When deciding if the lumped capacitance method can be used,what is the value of the Biot number?

Bi c= 0.2505 ( correct)

b) When using the one-term approximation for transient 1-Dconduction, what is the value of the applicable Biot number? UseTable 5.1.

Bi=??

c) Using the one-term approximation, if Bi in Table 5.1 wereequal to 0.5, what would be the value of C1 for this problem?

C1=??

d) Use the one-term approximation method to solve for theFourier number.
F0=??

e) Solve for the time required for the surface of the sphere toreach 60 ºC, in sec.

t=?? sec

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