You can set inplace to True (default is False):

area.replace(0, np.nan, inplace=True)

See examples in docs.

DataFrame.fillna() or Series.fillna() will do this for you.

Example:

In [7]: df
Out[7]: 
          0         1
0       NaN       NaN
1 -0.494375  0.570994
2       NaN       NaN
3  1.876360 -0.229738
4       NaN       NaN

In [8]: df.fillna(0)
Out[8]: 
          0         1
0  0.000000  0.000000
1 -0.494375  0.570994
2  0.000000  0.000000
3  1.876360 -0.229738
4  0.000000  0.000000

To fill the NaNs in only one column, select just that column.

In [12]: df[1] = df[1].fillna(0)

In [13]: df
Out[13]: 
          0         1
0       NaN  0.000000
1 -0.494375  0.570994
2       NaN  0.000000
3  1.876360 -0.229738
4       NaN  0.000000

Or you can use the built in column-specific functionality:

df = df.fillna({1: 0})