Transport in Porous Media

, Volume 101, Issue 3, pp 533–533 | Cite as

Erratum to: Thermodynamically Consistent Limiting Forced Convection Heat Transfer in a Asymmetrically Heated Porous Channel: An Analytical Study

  • P. K. Mondal

1 Erratum to: Transp Porous Med (2013) 100:17–37 DOI 10.1007/s11242-013-0203-5

In our recent paper (P. K. Mondal, 2013; Transp Porous Med (2013) 100:17–37), Section 2 contains the closed form expression of temperature profile (Eq. 16) and expressions of different terms like \(I_1 -I_{11}\) are incorrect in the form in which it appears. The expression of temperature profile along with each of the expression of \(I_1,I_6 \) and \(I_{11}\) contains typographical error. In this erratum we seek to rectify the errors, and present those in a corrected form as given below. However, rest of the formulations and results are correct.
$$\begin{aligned} \theta&= \frac{\left( {1-A} \right) }{\left( {1+A} \right) }\hat{{y}}+Q\left[ {\frac{1}{2}-\frac{\hat{{y}}^{2}}{2}} \right] +\frac{\text {Br}}{R_1 \cdot \text {Da}}\left[ {\begin{array}{l} \left\{ {\frac{1}{2}-\frac{\hat{{y}}^{2}}{2}} \right\} +\frac{1}{2\cosh ^{2}\beta }\left\{ {\frac{1}{2}-\frac{\hat{{y}}^{2}}{2}} \right\} \\ +\frac{1}{4\beta ^{2}\cosh ^{2}\beta }\left\{ {\frac{\cosh \left( {2\beta } \right) }{2}-\frac{\cosh \left( {2\beta } \right) \hat{{y}}}{2}} \right\} \\ -\frac{2}{\beta ^{2}}\left\{ {1-\frac{\cosh \beta \hat{{y}}}{\cosh \beta }} \right\} \\ \end{array}} \right] \nonumber \\&+\frac{R_2 }{2\varepsilon }\left[ {\left\{ {\frac{1}{2}-\frac{\hat{{y}}^{2}}{2}} \right\} -\frac{1}{2\beta ^{2}}\left\{ {\frac{\cosh \left( {2\beta } \right) }{2}-\frac{\cosh \left( {2\beta } \right) \hat{{y}}}{2}} \right\} } \right] \end{aligned}$$
$$\begin{aligned} I_1&= \frac{S}{R_1^{1/2} }[0]\end{aligned}$$
$$\begin{aligned} I_6&= \frac{\text {Br}}{8R_1^{3/2} \cdot \text {Da} \cdot \beta ^{2} \cdot \cosh ^{2}\beta }\left[ {\frac{\sinh ({2\beta })}{\beta }-\left( {\frac{3\sinh \beta +\sinh \left( {3\beta } \right) }{3\beta \cosh \beta }} \right) } \right] \end{aligned}$$
$$\begin{aligned} I_{11}&= \frac{R_2 }{8\varepsilon \cdot \beta ^{2} \cdot R_1^{1/2} }\left[ {\frac{\sinh \left( {2\beta } \right) }{\beta }-\left( {\frac{3\sinh \beta +\sinh \left( {3\beta } \right) }{3\beta \cosh \beta }} \right) } \right] \end{aligned}$$

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKalyani Government Engineering CollegeKalyani India

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