matlab When a metal sphere at constant initialtemperature is immersed in a large reservoir filled with cooler fluid,thesphere will eventually come into thermal equilibrium with the surrounding fluidat a temperature very close to the liquid bath.The t

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matlab When a metal sphere at constant initialtemperature is immersed in a large reservoir filled with cooler fluid,thesphere will eventually come into thermal equilibrium with the surrounding fluidat a temperature very close to the liquid bath.The t
matlab
When a metal sphere at constant initialtemperature is immersed in a large reservoir filled with cooler fluid,thesphere will eventually come into thermal equilibrium with the surrounding fluidat a temperature very close to the liquid bath.The temperature is usuallywritten in non-dimensional form:
θ =exp(0.2t)*(1/3t)*sin(3r)
where θ is the non-dimensionaltemperature,t is time in seconds and r is the non-dimensional radius.
1.If the value of time is fixed (for example:t=0),then a plot of θ vs.r is the temperature distribution in the sphere at this value of time.Compute the plot the 3 temperature distributions corresponding to 0,4,and 8 seconds on a
single plot and label the curves appropriately.
2.If the location in the sphere is fixed (for example:r=0.1),then a plot of θ vs.t is the so-called temperature history in the sphere at this spatial location.Compute and plot 3 temperature histories corresponding to r = 0.1,0.5 and 1 on a single plot and label the curves appropriately.

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这个题本身并不困难,其实就是绘制二维曲线然后再加上标注.

1、对于固定的时间t=0, 4, 8,在同一张图上绘制温度沿金属球径向的分布.由于r是无因次量,所以取值在0-1之间,代码如下：

r=0:0.1:1;
t=[0 4 8];
[T,R]=meshgrid(t,r);
Q=exp(0.2*T).*(1/3*T).*sin(3*R);
plot(r,Q)
legend('t=0','t=4','t=8')

2、对于固定的位置（半径）r = 0.1, 0.5, 1,在同一张图上绘制温度随时间变化的曲线.代码如下：

r=[0.1 0.5 1];
t=0:0.1:10;
[T,R]=meshgrid(t,r);
Q=exp(0.2*T).*(1/3*T).*sin(3*R);
plot(t,Q)
legend('r=0.1','r=0.5','r=1',0)

不过,我觉得题中所给公式可能存在问题,请再仔细核实一下.

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