Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is described by the differential equation du = -a(u' – T*) (1. dt where u(t) is the absolute temperature of the body at time t, T is th absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is nuch larger than T, then solutions of equation (1) are well pproximated by solutions of the simpler equation du = -qu". -au". (2 dt Suppose that a body with initial temperature 2450 K is surrounded medium with temperature 280 K and that a = 6 × 10-1²K-³/s. ) Determine the temperature of the body at any time by solving equation (2). u(t) K p) Use a graphing utility to plot the graph of u versus t. :) Find the time r at which u(7) = 560 –that is, twice the ambient temperature. Up to this time the error in using equation (2) to approximate the solutions of equation (1) is no more than 1%.

Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is described by the differential equation du = -a(u' – T*) (1. dt where u(t) is the absolute temperature of the body at time t, T is th absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is nuch larger than T, then solutions of equation (1) are well pproximated by solutions of the simpler equation du = -qu". -au". (2 dt Suppose that a body with initial temperature 2450 K is surrounded medium with temperature 280 K and that a = 6 × 10-1²K-³/s. ) Determine the temperature of the body at any time by solving equation (2). u(t) K p) Use a graphing utility to plot the graph of u versus t. :) Find the time r at which u(7) = 560 –that is, twice the ambient temperature. Up to this time the error in using equation (2) to approximate the solutions of equation (1) is no more than 1%.

Name: Please solve & show steps... Heat transfer from a body to its surround
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Description: Please solve & show steps... Heat transfer from a body to its surroundings by radiation, based onthe Stefan-Boltzmann law, is described by the differential equationdu= -a(u' – T*)(1)dtwhere u(t) is the absolute temperature of the body at time t, T is

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

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