Correction to: Swimming of Gyrotactic Microorganisms in Unsteady Flow of Eyring Powell Nanofluid with Variable Thermal Features: Some Bio-technology Applications

Correction to: International Journal of Thermophysics (2020) 41:159 https://doi.org/10.1007/s10765-020-02736-2

In study [1], the governing Eqs. 9, 11 for MHD flow of Eyring-Powell nanofluid due to oscillatory stretching surface in absence of buoyancy forces and activation energy are presented as [2,3,4,5,6,7,8]:

$$ \frac{\partial u}{{\partial t}} + u\left( {\frac{\partial u}{{\partial x}}} \right) + v\left( {\frac{\partial u}{{\partial y}}} \right) = \left( {\nu + \frac{1}{{\rho_{f} \beta_{1} \beta_{2} }}} \right)\left( {\frac{{\partial^{2} u}}{{\partial y^{2} }}} \right) - \frac{1}{{2\rho \beta_{1} \beta_{2}^{3} }}\left[ {\left( {\frac{\partial u}{{\partial y}}} \right)^{2} \frac{{\partial^{2} u}}{{\partial y^{2} }}} \right] - \left( {\frac{{\sigma B_{0}^{2} }}{{\rho_{f} }} + \frac{\nu \vartheta }{{k^{ * } }}} \right)u, $$

(9)

$$ \frac{\partial C}{{\partial t}} + u\frac{\partial C}{{\partial x}} + v\frac{\partial C}{{\partial y}} = D_{B} \frac{{\partial^{2} C}}{{\partial y^{2} }} + \frac{{D_{T} }}{{T_{\infty } }}\frac{{\partial^{2} T}}{{\partial y^{2} }}, $$

(11)

where $\beta_{1}$ and $\beta_{2}$ are the fluid parameters of the Eyring-Powell model [2,3,4,5,6,7,8] and $\vartheta$ is porous medium. It is emphasized that the modelling of Eq. 9 is based on theory of Powell and Eyring [9].

In view of transformations (15–16) in [1], formulated system is:

$$ \left( {1 + K} \right)F_{\eta \eta \eta } - SF_{\eta \tau } - F_{\eta }^{2} + FF_{\eta \eta } - HaF_{\eta } - \Gamma KF_{\eta \eta }^{2} F_{\eta \eta \eta } = 0, $$

(17)

$$ \varphi_{\eta \eta } + \frac{Nt}{{Nb}}\theta_{\eta \eta } - S(Sc)\varphi_{\tau } + ScF\varphi_{\eta } = 0, $$

(19)

Since in Eq. 9, the contributions of buoyancy forces are not considered, therefore, no effects of $\lambda$ have been entertained. Moreover, $Ha = \left( {\sigma B_{0}^{2} /\rho_{f} b + \nu \vartheta /bk^{ * } } \right)$ is the Hartmann number and $\delta = \Omega_{0} /b\left( {\rho c} \right)_{p}$ heat source parameter while $K = 1/\mu \beta_{1} \beta_{2}$ and $\Gamma = u_{w}^{2} b/2\nu \beta_{2}^{2}$ Eyring fluid parameters [2,3,4,5,6,7,8,9]. In absence of buoyancy forces, Figs. 3(c–d), 4(c), 6(b) and 7(b) have no effects on analysis.

Equation 24, is presented as:

$$ {\text{Re}}_{x}^{1/2} C_{f} = \left( {1 + K} \right)F_{\eta \eta } \left( {0,\tau } \right) - \frac{K}{3}\Gamma F_{\eta \eta }^{3} \left( {0,\tau } \right). $$

(24)

Moreover, in study [1], color illustration “Green Lines” in Fig. 4 and Fig. 5(c) should be read as “Blue Lines”.