Effect of heat source/sink and thermal radiation on an unsteady MHD Casson flow past over an exponentially accelerated vertical plate

Abstract

This study examines the behavior of an unsteady magnetohydrodynamic Casson fluid past over an exponentially accelerated vertical plate in a rotating system. The flow is driven by the combined effects of thermal radiation, heat source/sink, chemical reaction and Hall current taken into account. The non-dimensional equations governing the system are solved using the Laplace transform technique, yielding expressions that offer insights into velocity, temperature and concentration profiles. The axial velocity decreases with increasing thermal radiation and chemical reaction, while it increases with Casson and heat source/sink. The current findings are compared with previous studies, revealing substantial agreement. Additionally, the study examines skin friction, heat transfer and mass transfer rates. The insights gained from the heat transport processes have implications across various applications in cooling systems, aerospace engineering and energy storage technologies. The results of this study have direct relevance in engineering applications and are determined analytically.

Appendix A

$\bar{a} = \frac{2M^2}{m^2+1}+2i\left( \Omega -\frac{M^2m}{m^2+1}\right)$

$\alpha _0 = \textrm{Sc}$

$\alpha _1 = \frac{\textrm{Pr}}{1+R_\textrm{a}}$

$\alpha _2 = \frac{{\bar{a}}-\beta H_\textrm{T}\alpha _1}{\beta \alpha _1-1}$

$\alpha _3 = \frac{\beta }{\beta \alpha _1-1}$

$\alpha _4 = \frac{{\bar{a}}-\beta \alpha _0K_\textrm{c}}{\beta \alpha _0-1}$

$\alpha _5 = \frac{\beta }{\beta \alpha _0-1}$

$s_0 = \sqrt{\frac{{\bar{a}}}{\beta }}$

$s_1 = \sqrt{\frac{{\bar{a}}+a}{\beta }}$

$s_2 = \sqrt{\alpha _1(H_\textrm{T}+\alpha _2)}$

$s_3 = \sqrt{\alpha _0(K_\textrm{c}+\alpha _4)}$

$s_4 = \sqrt{\frac{{\bar{a}}+\alpha _2}{\beta }}$

$s_5 = \sqrt{\frac{{\bar{a}}+\alpha _4}{\beta }}$

$s_6 = \sqrt{H_\textrm{T}\alpha _1}$

$s_7 = \sqrt{K_\textrm{c}\alpha _0}$

$s_8 = \left( t\sqrt{\frac{{\bar{a}}}{\beta }}-\frac{1}{2\sqrt{\beta }}\right)$

$s_9 = \left( t\sqrt{H_\textrm{T}\alpha _1}-\frac{1}{2}\sqrt{\frac{\alpha _1}{H_\textrm{T}}}\right)$

$s_{10} = \left( t\sqrt{K_\textrm{c}\alpha _0}-\frac{1}{2}\sqrt{\frac{\alpha _0}{K_\textrm{c}}}\right)$

$r_0 = \left( 1-\textrm{erfc}(\sqrt{\bar{a} t})\right)$

$r_1 = \left( 1-\textrm{erfc}(\sqrt{({\bar{a}}+a)t})\right)$

$r_2 = (1-\textrm{erfc}(\sqrt{H_\textrm{T}t}))$

$r_3 = (1-\textrm{erfc}(\sqrt{K_\textrm{c}t}))$

$r_4 = (1-\textrm{erfc}(\sqrt{(H_\textrm{T}+\alpha _2)t}))$

$r_5 = (1-\textrm{erfc}(\sqrt{(K_\textrm{c}+\alpha _4)t}))$

$r_6 = (1-\textrm{erfc}(\sqrt{({\bar{a}}+\alpha _2)t}))$

$r_7 = (1-\textrm{erfc}(\sqrt{({\bar{a}}+\alpha _4)t}))$

$t_0 = \frac{1}{\sqrt{\pi t}}e^{-({\bar{a}}+a)t}$

$t_1 = \frac{1}{\sqrt{\pi t}}\left[ e^{-(H_\textrm{T}+\alpha _2)t}-e^{-({\bar{a}}+\alpha _2)t}\right]$

$t_2 = \frac{1}{\sqrt{\pi t}}\left[ e^{-(K_\textrm{c}+\alpha _4)t}-e^{-({\bar{a}}+\alpha _4)t}\right]$

$t_3 = \frac{1}{\sqrt{\pi t}}\left[ {\frac{e^{-{\bar{a}}t}}{\sqrt{\beta }}}-\sqrt{\alpha _1}e^{-H_\textrm{T}t}\right]$

$t_4 = \frac{1}{\sqrt{\pi t}}\left[ {\frac{e^{-{\bar{a}}t}}{\sqrt{\beta }}}-\sqrt{\alpha _0}e^{-K_\textrm{c}t}\right]$

$t_5 = \sqrt{\frac{t}{\pi }}\left[ {\frac{e^{-{\bar{a}}t}}{\sqrt{\beta }}}-\sqrt{\alpha _1}e^{-H_\textrm{T}t}\right]$

$t_6 = \sqrt{\frac{t}{\pi }}\left[ {\frac{e^{-{\bar{a}}t}}{\sqrt{\beta }}}-\sqrt{\alpha _0}e^{-K_\textrm{c}t}\right]$

$e_0 = e^{at}$

$e_1 = e^{\alpha _2 t}$

$e_2 = e^{\alpha _4 t}$