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Consider the net radiant heat flux between an object and its surroundings as given by qrad,net...

Consider the net radiant heat flux between an object and its surroundings as given by

qrad,net = ǫ σ ( T4 − T ∞4 ) ( 1 ) where ǫ is the emissivity, σ is the Stefan-Boltzmann constant (5.670374419×10−8 in

W ), T is the object’s temperature and T is the surrounding (ambient) temperature. m2K4 ∞

  1. 1-a) Linearize qrad,net in terms of ǫ, T, and T∞, use deviation variables and call this expression qL′ .

  2. 1-b) Compute the value for qrad,net with ǫ = 0.9, T = 700 K, and T ∞ = 300 K.

  3. 1-c) Using both the linearized and nonlinear equation, compute the numeric change

    in qrad,net (in watts) for each of the following cases:

    1. (a) ǫ increases by 0.01.

    2. (b) T increases by 1 K.

    3. (c) T∞ increases by 1 K.

    4. (d) T increases by 5 K.

    5. (e) T∞ increases by 5 K.

    6. (f) ǫ increases by 0.01 and T increases by 5 K and T∞ increases by 5 K.

    7. (g) Using the linearized model, find the range of T that causes a ± 5% change in qrad,net.

    8. (h) Using the nonlinear model, find the range of T that causes a ± 5% change in qrad,net.

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