Correction

This article refers to:

Unsteady Al2O3-Cu/H2O hybrid nanofluid flow over a rotatable stretching disk with heat generation and deceleration: Stable dual solutions

Article title: Unsteady Al₂O₃-Cu/H₂O hybrid nanofluid flow over a rotatable stretching disk with heat generation and deceleration: Stable dual solutions

Authors: Nur Syahirah Wahid, Norihan Md Arifin, Najiyah Safwa Khashi’ie, and Ioan Pop

Journal: Numerical Heat Transfer, Part A: Applications

DOI: https://doi.org/10.1080/10407782.2023.2285346

When this article was originally published online, equation 6(6) $$\begin{array}{c}t<0:\hspace{0.17em}u=v=w=0,T=T_{\infty }\text{for any}(r,\vartheta ,z);\hfill \\ t\ge 0:\left\{\begin{array}{c}u=U_w(r,t)=u_w(r,t)\lambda ,v=V_w(r,t)=v_w(r,t)\omega \hfill \\ w=w_w=0,T=T_w.\hfill \end{array}\right\}\text{\hspace{0.17em}at}z=0;\hfill \\ u\to 0,v\to 0,w\to 0,T\to T_{\infty }\text{as}z\to \infty .\hfill \end{array}\}$$(6) , 9(9) $$\left(\frac{{\mu }_{\mathit{\text{hnf}}}/{\mu }_f}{{\rho }_{\mathit{\text{hnf}}}/{\rho }_f}\right)f‴+2\mathit{\text{ff}}″-f{\prime }^2+g^2-\beta \left(f\prime +\frac{1}{2}\eta f″\right)=0,$$(9) , 21(21) $$\left(\frac{{\mu }_{\mathit{\text{hnf}}}/{\mu }_f}{{\rho }_{\mathit{\text{hnf}}}/{\rho }_f}\right)F‴+2\left(f_{0}F″+F{f}_0″\right)-2F\prime f_0\prime +2G{g}_0-\beta \left(F\prime +\frac{1}{2}\eta F″\right)+\gamma F\prime =0,$$(21) , 23(23) $$\frac{1}{\mathit{\text{Pr}}}\frac{k_{\mathit{\text{hnf}}}/k_f}{{\left(\rho C_p\right)}_{\mathit{\text{hnf}}}/{\left(\rho C_p\right)}_f}Q″+2(F{\theta }_0\prime +f_{0}Q\prime )-\frac{1}{2}\beta \eta Q\prime +\frac{\chi }{{\left(\rho C_p\right)}_{\mathit{\text{hnf}}}/{\left(\rho C_p\right)}_f}Q+\gamma Q=0,$$(23) were not correctly included. The appropriate equation 6(6) $$\begin{array}{c}t<0:\hspace{0.17em}u=v=w=0,T=T_{\infty }\text{for any}(r,\vartheta ,z);\hfill \\ t\ge 0:\left\{\begin{array}{c}u=U_w(r,t)=u_w(r,t)\lambda ,v=V_w(r,t)=v_w(r,t)\omega \hfill \\ w=w_w=0,T=T_w.\hfill \end{array}\right\}\text{\hspace{0.17em}at}z=0;\hfill \\ u\to 0,v\to 0,w\to 0,T\to T_{\infty }\text{as}z\to \infty .\hfill \end{array}\}$$(6) , 9(9) $$\left(\frac{{\mu }_{\mathit{\text{hnf}}}/{\mu }_f}{{\rho }_{\mathit{\text{hnf}}}/{\rho }_f}\right)f‴+2\mathit{\text{ff}}″-f{\prime }^2+g^2-\beta \left(f\prime +\frac{1}{2}\eta f″\right)=0,$$(9) , 21(21) $$\left(\frac{{\mu }_{\mathit{\text{hnf}}}/{\mu }_f}{{\rho }_{\mathit{\text{hnf}}}/{\rho }_f}\right)F‴+2\left(f_{0}F″+F{f}_0″\right)-2F\prime f_0\prime +2G{g}_0-\beta \left(F\prime +\frac{1}{2}\eta F″\right)+\gamma F\prime =0,$$(21) , 23(23) $$\frac{1}{\mathit{\text{Pr}}}\frac{k_{\mathit{\text{hnf}}}/k_f}{{\left(\rho C_p\right)}_{\mathit{\text{hnf}}}/{\left(\rho C_p\right)}_f}Q″+2(F{\theta }_0\prime +f_{0}Q\prime )-\frac{1}{2}\beta \eta Q\prime +\frac{\chi }{{\left(\rho C_p\right)}_{\mathit{\text{hnf}}}/{\left(\rho C_p\right)}_f}Q+\gamma Q=0,$$(23) are provided below. (6) $$\begin{array}{c}t<0:\hspace{0.17em}u=v=w=0,T=T_{\infty }\text{for any}(r,\vartheta ,z);\hfill \\ t\ge 0:\left\{\begin{array}{c}u=U_w(r,t)=u_w(r,t)\lambda ,v=V_w(r,t)=v_w(r,t)\omega \hfill \\ w=w_w=0,T=T_w.\hfill \end{array}\right\}\text{\hspace{0.17em}at}z=0;\hfill \\ u\to 0,v\to 0,w\to 0,T\to T_{\infty }\text{as}z\to \infty .\hfill \end{array}\}$$(6) (9) $$\left(\frac{{\mu }_{\mathit{\text{hnf}}}/{\mu }_f}{{\rho }_{\mathit{\text{hnf}}}/{\rho }_f}\right)f‴+2\mathit{\text{ff}}″-f{\prime }^2+g^2-\beta \left(f\prime +\frac{1}{2}\eta f″\right)=0,$$(9) (21) $$\left(\frac{{\mu }_{\mathit{\text{hnf}}}/{\mu }_f}{{\rho }_{\mathit{\text{hnf}}}/{\rho }_f}\right)F‴+2\left(f_{0}F″+F{f}_0″\right)-2F\prime f_0\prime +2G{g}_0-\beta \left(F\prime +\frac{1}{2}\eta F″\right)+\gamma F\prime =0,$$(21) (23) $$\frac{1}{\mathit{\text{Pr}}}\frac{k_{\mathit{\text{hnf}}}/k_f}{{\left(\rho C_p\right)}_{\mathit{\text{hnf}}}/{\left(\rho C_p\right)}_f}Q″+2(F{\theta }_0\prime +f_{0}Q\prime )-\frac{1}{2}\beta \eta Q\prime +\frac{\chi }{{\left(\rho C_p\right)}_{\mathit{\text{hnf}}}/{\left(\rho C_p\right)}_f}Q+\gamma Q=0,$$(23)