| (3.33) |
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Equation (3.33) is second order and linear in T*. To remove the inhomogeneity, let
| (3.34) |
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| (3.35) |
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| The general solution is (See Boyce and Di Prima) | |||
| (3.36) |
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Using the first BC |
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| (3.37) |
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| Using BC 2 |
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| (3.38) |
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| so that |
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| (3.39) |
since
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| This is the temperature distribution: | |||
| (3.40) |
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| The parameters are | |||
| Now |
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| (3.41) |
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| (3.42) |
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units: m-1 | |
| where | D = 2R | ||
| kf = thermal conductivity of the fluid | |||
| k = thermal conductivity of the rod | |||
| (3.43) |
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dimensionless | |