Export variable to another script running in background

i have a script inside which i have generated a background job which will run another script.
How do i export the variables from parent script to the child script which wil run in the background .

a.sh:-

 
export tmpdir="/usr/tmp"

nohup b.sh&

b.sh:-

 
echo $tmpdir

But i am not able to print the value of tmpdir in b.sh

Could this help you ?

$> cat a.sh
#!/bin/ksh
export tmpdir="/usr/tmp"
$> cat b.sh
#!/bin/ksh
. a.sh
echo $tmpdir

Invocation

$>chmod +x a.sh b.sh
$>b.sh &