a. What form does this equation reduce to for the case of steady-state, radial heat transfer?
b. Given the boundary conditions...
c. Generate an expression for the heat flow rate, qr, using the result from part (b).
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15.2 Starting with the Fourier field equation in cylindrical coordinates,
a. Reduce this equation to the applicable form for steady-state heat transfer in the θ direction.
b. For the conditions depicted in the figure—that is, T = To at θ = 0, T = Tz at θ = π, the radial surfaces insulated—solve for the temperature profile.
c. Generate an expression for the heat flow rate, qq, using the result of part (b).
d. What is the shape factor for this configuration?...
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15.3 Solve equation (16-19) for the temperature distribution in a plane wall if the internal heat generation per unit volume varies according to ... The boundary conditions that apply are T = T0 at x = 0 and T = TL at x = L.... (16-19)
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15.4 Use the relation T ds = dh dP/ρ to show that the effect of the dissipation function, Φ, is to increase the entropy, S. Is the effect of heat transfer the same as the dissipation function?
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15.5 In a boundary layer where the velocity profile is given by...where δ is the velocity boundary-layer thickness, plot the dimensionless dissipation function, Φδ2/μv2∞, vs. y/δ.
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15.6 A spherical shell with inner and outer dimensions of ri and ro, respectively, has surface temperatures Ti (ri) and To (ro). Assuming constant properties and one-dimensional (radial) con- duction, sketch the temperature distribution, T(r). Give reasons for the shape you have sketched.
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15.7 Heat is generated in a radioactive plane wall according to the relationship...where ... is the volumetric heat generation rate, kW/m3, L is the half thickness of the plate, and x is measured from the plate center line....Develop the equation that expresses the temperature difference between the plate center line and its surface.
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15.8 Heat is generated in a spherical fuel element according to the relationship...where ... is the volumetric heat generation rate, kW/m3, and ro is the outside cylinder radius. Develop the equation that expresses the temperature difference between the rod center line and its surface.
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