eqn1=f[η]'''+(1+ξcotξ)f[η]f[η]''-
2
(f[η]')
+
9
8
sin2ξ
ξ
+Λ
sinξ
ξ
(θ[η]+Nϕ[η])+
k
1
3
2
sinξ
ξ
-f[η]'+
k
2
2
3
2
sinξ
ξ
-
2
(f[η]')
ξf[η]'
∂(f[η]')
∂ξ
-f[η]''
∂(f[η])
∂ξ
;​​eqn2=
1
PR
θ[η]''+(1+ξcotξ)f[η]θ[η]'ξf[η]'
∂(θ[η])
∂ξ
-θ[η]'
∂(f[η])
∂ξ
;​​eqn3=
1
SC
θ[η]''+(1+ξcotξ)f[η]θ[η]'-γϕ[η]ξf[η]'
∂(θ[η])
∂ξ
-θ[η]'
∂(f[η])
∂ξ
;​​​​Replace[eqn1,eqn2,eqn3,ξ0]​​​​
Derivative
:∂(f[η]') cannot be interpreted. A partial derivative requires a subscript differentiation variable.