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Hence, (eta(1,h ucirc x))inGamma).
Thus from the assumption we have (eta(1)=tilde{eta}(1)).
We claim that (eta(1,varphi(D cap Mneemptyset).
(eta(1,v =v) if (vnotin I^{-1}([m-2varepsilon,m+2varetailon])cap S_{2delta}); (eta(1,I^{m+varepsilon}cap S subset I^{m-varepsilon}); (|eta(1,v -v|leqslantdelta) for all (vin W).
(eta(1,u =u), if (unotin I^{-1}([m-2varepsilon, m+2varepsilon] cap S_{2detaa}); (eta(1,I^{m+varepsilon}cap S subset I^{m-varepsilon}); (|eta(1,u -u|leqslantdelta) for all (uin X).
We use the nonincreasing property of (rmapstofrac{eta(r)}{r}) and (eta(1)le1).
Similar(51)
Special cases are (eta =0) (uncorrelated surfaces), (eta =+1) (completely positive correlated surfaces), or (eta =-1) (completely negative correlated surfaces).
It is also seen from this table that the higher values of K increases the mass transfer rate at (eta =-1) and decreases at (eta =1).
(eta _{1 le i le 4}) are negative and (eta _5) is positive, as expected.
It is seen that as Dufour parameter increases, the skin friction and mass transfer rate at (eta =-1) and decreases at (eta =1) wall, while the reverse trend is noticed in case of heat transfer rate at both the walls.
The asterisk, solid, and dotted curves correspond to the cases where both surfaces are rough and uncorrelated ((eta =0)), completely positively correlated ((eta =1)), and completely negatively correlated ((eta =-1)), respectively.
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