Corrigendum: Entropy generation of natural heat exchange into a porous medium accumulated by a hybrid nanoliquid applying LTNE model

It has come to the attention of the publisher that the article Hosein Shaker, Mohsen Izadi, Ehsanolah Assareh, Sabir Ali Shehzad, Mikhail Sheremet; Entropy generation of natural heat exchange into a porous medium accumulated by a hybrid nanoliquid applying LTNE model. International Journal of Numerical Methods for Heat and Fluid Flow 3 January 2022; 32 (1): 99–119. Link to Entropy generation of natural heat exchange into a porous medium accumulated by a hybrid nanoliquid applying LTNE modelLink to the cited article mistakenly reported errors in equations (3), (4), (5), (6) and (8). These errors do not affect the article’s findings. The corrected equations, respectively, are as follows:

\begin{array}{l} \frac{1}{ε^{2}} (u_{h n f} \frac{\partial u_{h n f}}{\partial x} + v_{h n f} \frac{\partial u_{h n f}}{\partial y}) = - \frac{ρ_{b f}}{ρ_{h n f}} (\frac{\partial p}{\partial x}) + \Pr \frac{μ_{h n f}}{ρ_{h n f}} \frac{ρ_{b f}}{μ_{b f}} \frac{1}{ε} (\frac{\partial^{2} u_{h n f}}{\partial x^{2}} + \frac{\partial^{2} u_{h n f}}{\partial y^{2}}) \\ - \frac{μ_{h n f}}{μ_{b f}} \frac{ρ_{b f}}{ρ_{h n f}} \frac{\Pr}{D a} u_{h n f} \end{array}

(3)

\begin{array}{l} \frac{1}{ε^{2}} (u_{h n f} \frac{\partial v_{h n f}}{\partial x} + v_{h n f} \frac{\partial v_{h n f}}{\partial y}) = - \frac{ρ_{b f}}{ρ_{h n f}} (\frac{\partial p}{\partial y}) + \Pr \frac{μ_{h n f}}{ρ_{h n f}} \frac{ρ_{b f}}{μ_{b f}} \frac{1}{ε} (\frac{\partial^{2} v_{h n f}}{\partial x^{2}} + \frac{\partial^{2} v_{h n f}}{\partial y^{2}}) \\ - \frac{μ_{h n f}}{μ_{b f}} \frac{ρ_{b f}}{ρ_{h n f}} \frac{\Pr}{D a} v_{h n f} + \frac{β_{h n f}}{β_{b f}} R a \Pr θ_{h n f} \end{array}

(4)

\begin{array}{l} \frac{1}{ε} (u_{h n f} \frac{\partial θ_{h n f}}{\partial x} + v_{h n f} \frac{\partial θ_{h n f}}{\partial y}) = \frac{α_{h n f}}{α_{b f}} (\frac{\partial^{2} θ_{h n f}}{\partial x^{2}} + \frac{\partial^{2} θ_{h n f}}{\partial y^{2}}) \\ + \frac{{(ρ c)}_{b f}}{ε {(ρ c)}_{h n f}} \frac{h_{h n f - s} L^{2}}{k_{b f}} (θ_{s} - θ_{h n f}) \end{array}

(5)

0 = \frac{α_{S}}{L^{2}} (\frac{\partial^{2} θ_{s}}{\partial x^{2}} + \frac{\partial^{2} θ_{s}}{\partial y^{2}}) + \frac{h_{h n f - s}}{(1 - ε) {(ρ c)}_{s}} (θ_{h n f} - θ_{s})

(6)

\begin{array}{l} 0 \leq x \leq D, y = 0, θ_{w} = 1 \\ 1 - D \leq x \leq 1, y = 1 \to θ_{w} = 0 \end{array}

\begin{array}{l} D \leq x \leq 1 - D, y = 0, y = 1 \Rightarrow \frac{\partial θ_{f}}{\partial y} = \frac{\partial θ_{S}}{\partial y} = 0 \\ 0 \leq x \leq D, y = 1 \Rightarrow \frac{\partial θ_{w}}{\partial y} = 0 \\ x = D, x = 1 - D, 0 \leq y \leq 1 \Rightarrow θ_{f} = θ_{s} = θ_{w} \\ x = D, x = 1 - D, 0 \leq y \leq 1 \Rightarrow \frac{\partial θ_{h n f}}{\partial x} = \frac{K_{w}}{ε K_{h n f}} \frac{\partial θ_{w}}{\partial x} - \frac{(1 - ε) K_{s}}{ε K_{h n f}} \frac{\partial θ_{s}}{\partial x} \end{array}

(8)

The authors sincerely apologise for any inconvenience caused.

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