Heat Exchange. There are basically two mechanisms by which a physical body excha

Question

Heat Exchange. There are basically two mechanisms by which a physical body exchanges heat with its environment. The contact heat transfer across the body's surface is driven by the difference in the body's temperature and that of the environment; this is known as Newton's law of cooling. However, heat transfer also occurs due to thermal radiation, which according to Stefan's law of radiation is governed by the difference of the fourth powers of these temperatures. In most cases one of these modes dominates the other. Problems 15 and 16 invite you to simulate each mode numerically for a given set of initial conditions. Newton's Law of Cooling. Newton's law of cooling states that the rate of change in the temperature T( of a body is proportional to the difference between the temperature of the medium M( and the temperature of the body. That is, dt where K is a constant. Let K-0.04 (min)-1 and the temperature of the medium be constant, M( 293 kelvins. If the body is initially at 360 kelvins, use Euler's method with h 3.0 min to approximate the temperature of the body after (a) 30 minutes. (b) 60 minutes.

Explanation / Answer

I am going to give you one equation which can help you to solve the problem.

Let y(t) where the temperature at time t x dt where dt is the given time interval.

y(t+1) - y(t) = K [M(t) - y(t)] x dt

We can solve for now y(t+1)

y(t+1) = y(t) + K[M(t) - y(t)] x dt

y(t+1) = ( 1 - c dt) y(t) + c M(t) dt

Here dt = 3 min and y(t) = 360 Kelvin. Put all the values and solve for 30 and 60 minutes

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