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January 31, 2015

January 31, 2015

Posted by **Edwin** on Sunday, March 14, 2010 at 5:29am.

- Physics -
**drwls**, Sunday, March 14, 2010 at 7:39amFor the Newton's Law case,

the heat loss rate rate is h*A(T - 20). and this equals M C dT/dt. M is the mass, C the specific heat and

A is the area of the sphere(s). The differential equation can be solved for T(t) in terms of A, h, M and C. It results in an exponential approach to T = 20 C.

You have not been told the value of the "film heat transfer coefficient", h, although one could calculate it for natural of forced convection using heat transfer engineering formulas that are known. You may have to answer this question using equations rather than graphs with real numbers. Try to use dimensionless groups wherever you can.

In the "Stefan", more propertly called the Stefan-Boltzmann case,

e*sigma*A*(T^4 - 473^4) = M C dT/dt,

where T must be expressed in Kelvin.

e is the emissivity, which they may want you to assume is 1, and sigma is the Stefan Boltzmann constant.

I am going to have to leave the solving of the differential equations, and the "comparing" up to you. They are not difficult.

In a real situation, both types of heat transfer will usually be present, with the radiative "Stefan" type dominating at higher tempertures.

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