1) Heat Transfer problem, The time-dependent temperature of an object changes at a rate proportional to the difference b

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1 Heat Transfer Problem The Time Dependent Temperature Of An Object Changes At A Rate Proportional To The Difference B 1 (42.29 KiB) Viewed 12 times

1) Heat Transfer problem, The time-dependent temperature of an object changes at a rate proportional to the difference between the temperature of its surroundings and the temperature of the object. This relation is expressed as the Newton's Law of cooling and is written as: dTt) ht pc Tt T(t)- T.(+) dt 1 Where p is the density of the object, c is its specific heat, h is the heat transfer coefficient between the object and its surroundings, A. is the surface area of the object, V is the volume of the object, and T. (1) is the temperature of the surroundings. For simplicity, the equation can be expressed as: dTt) dt + mT(+) = m1 (+ The solution of this equation can be found through the use of an integrating factor as: mt pot T(t) = me*** |(34+To bemidt where T, is the initial temperature of the surroundings and Bis the rate at which the temperature of the surroundings is changing. Show that: T(t+ + TT 1-(*+I. - - ) -(-..- ) :- n where T, = T(0)