Radiation Effect on MHD Convective Flow of Nanofluids over an Exponentially Accelerated Moving Ramped Temperature Plate

Abstract

The effect of thermal radiation on magnetohydrodynamic free convective flow of incompressible and viscous nanofluids, which is electrically conducting, over an exponentially accelerated moving ramped temperature plate is studied. The water-based nanofluids which contain the nanoparticles of copper, alumina, and titanium oxide are taken into consideration. The mathematical model of the problem is formulated by applying the nanoparticle volume fraction model. The governing equations for the flow, subjected to the associated conditions, have been solved analytically by Laplace transform method. Expressions of nanofluid velocity, temperature, shear stress, and Nusselt number have been obtained in compact form. Effects of controlling physical parameters on nanofluid velocity and temperature have been displayed using various graphs, whereas, for the engineering perspective, numerical values of shear stress are presented in table.

Appendix

$$\begin{aligned} f_{1} \left( {c_{1} ,c_{2} ,c_{3} ,c_{4} ,c_{5} } \right) & = \left\{ {\frac{1}{{c_{4} }} + \left( {c_{5} + \frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{3} }}} } \right)} \right\}{\text{e}}^{{c_{1} \sqrt {c_{2} c_{3} } }} {\text{erfc}}\left( {\frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{5} }}} + \sqrt {c_{3} c_{5} } } \right) \\ & \quad + \left\{ {\frac{1}{{c_{4} }} + \left( {c_{5} - \frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{3} }}} } \right)} \right\}{\text{e}}^{{ - c_{1} \sqrt {c_{2} c_{3} } }} {\text{erfc}}\left( {\frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{5} }}} - \sqrt {c_{3} c_{5} } } \right), \\ \end{aligned}$$

$$\begin{aligned} f_{2} \left( {c_{1} ,c_{2} ,c_{3} ,c_{4} ,c_{5} } \right) & = {\text{e}}^{{c_{1} \sqrt {c_{2} \left( {c_{3} + c_{4} } \right)} }} {\text{erfc}}\left( {\frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{5} }}} + \sqrt {\left( {c_{3} + c_{4} } \right)c_{5} } } \right) \\ & \quad + {\text{e}}^{{ - c_{1} \sqrt {c_{2} \left( {c_{3} + c_{4} } \right)} }} {\text{erfc}}\left( {\frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{5} }}} - \sqrt {\left( {c_{3} + c_{4} } \right)c_{5} } } \right), \\ \end{aligned}$$

$$\begin{aligned} f_{3} \left( {c_{1} ,c_{2} ,c_{3} ,c_{4} } \right) & = \left\{ {\frac{1}{{c_{3} }} + \left( {c_{4} + \frac{{c_{2} c_{1}^{2} }}{2}} \right)} \right\}{\text{erfc}}\left( {\frac{{c_{1} }}{2}\sqrt {\frac{{c_{2} }}{{c_{4} }}} } \right) \\ & \quad - c_{1} \sqrt {\frac{{c_{2} c_{4} }}{\pi }} {\text{e}}^{{ - (c_{2} c_{1}^{2} )/(4c_{4} )}} , \\ \end{aligned}$$

$$f_{4} \left( {c_{1} ,c_{2} ,c_{3} } \right) = \left( {\sqrt {\frac{{c_{1} }}{{c_{2} }}} + 2c_{3} \sqrt {c_{1} c_{2} } } \right)\left\{ {{\text{erfc}}\left( {\sqrt {c_{2} c_{3} } } \right) - 1} \right\} - 2\sqrt {\frac{{c_{1} c_{3} }}{\pi }} {\text{e}}^{{ - c_{2} c_{3} }} ,$$

$$\begin{aligned} f_{5} \left( {c_{1} ,c_{2} ,c_{3} ,c_{4} } \right) & = \sqrt {c_{1} \left( {c_{2} + c_{3} } \right)} \left\{ {{\text{erfc}}\left( {\sqrt {\left( {c_{2} + c_{3} } \right)c_{4} } } \right) - 1} \right\} \\ & \quad - \sqrt {\frac{{c_{1} }}{{\pi c_{4} }}} {\text{e}}^{{ - \left( {c_{2} + c_{3} } \right)c_{4} }} . \\ \end{aligned}$$