The rapid development of nanotechnology in our emerging industries has drawn the interest of numerous researchers and scientists, especially in experimental and numerical studies. Therefore, the present analytical study will help reduce time and costs and validate the numerical study. However, the analytical research of carbon nanotubes with Casson fluid in a channel is still limited. Therefore, the current analytical study inspected the consequences of carbon nanotubes (CNTs) nanoparticles on the heat and mass transfer of magnetohydrodynamics (MHD) Casson nanofluid flow induced by a moving vertical plate with a porous region inside an asymmetrical channel. Dimensional governing equations are used for the modelling, which is then expressed in a dimensionless form by employing dimensionless variables. The analytical solutions for the velocity, temperature, and concentration are tackled using the Laplace transform technique. The temperature and velocity are significantly enhanced when increasing the nanoparticle volume fraction. This is due to the outstanding characteristic of nanofluid thermal conductivity, which results in an efficient heat transfer. This result has the potential to be applied to various nanofluid cooling technologies. Since the solutions are determined in an analytical form, this study could be used as a reference for other numerical and experimental works and a guide for several industries.

The feature of having a surface that can stretch has garnered attention in numerous industrial and engineering fields because of its advantages. Nevertheless, most fluid mechanics simulations for stretchable surfaces have predominantly relied on numerical solutions, with a notable lack of theoretical investigations into this matter. Consequently, the current research aims to contribute a theoretical exploration of heat transfer and boundary layer flow for Casson nanofluid on a linearly stretching sheet, considering the existence of porosity and magnetic field effects. Two distinct types of water-based nanofluids containing aluminium oxide and silicon dioxide are examined. By employing similarity transformations, the governing momentum and energy equations undergo transformation and subsequent analytical resolution using Laplace transformations. The resulting solutions are graphically presented to examine the influence of key parameters on temperature and velocity distribution. The analysis indicates that heat transfer is improved by the inclusion of nanoparticles, porosity, and a magnetic field. However, the velocity distribution slows down as a result of higher nanoparticle volume fraction, porosity, and magnetic field imposition.

In recent years, hybrid nanoparticles have gained significant attention for their ability to enhance thermal conductivity in various fluid systems, making them effective heat transport catalysts. Despite advancements in thermal fluid technology, a gap remains in understanding how hybrid nanoparticles interact within non-Newtonian Jeffrey fluid systems, particularly under complex boundary conditions like Newtonian heating. The present study aims to shed light on the effect of hybrid nanoparticles (alumina and copper) incorporated into a Jeffrey fluid model on flow and heat transport, considering them as heat transport catalyst and subject to Newtonian heating to optimize thermal efficiency. An exponentially accelerated plate is used to induce the fluid flow, taking into account the effects of porosity, MHD, and thermal radiation. The examined fluid exhibits an unsteady one-dimensional flow, formulated by deriving partial differential equations, which are subsequently transformed into ordinary differential equations using suitable non-dimensional variables and the Laplace transformation. This research distinguishes itself by presenting a novel mathematical model for MHD Jeffrey hybrid nanofluid, accounting for porosity and Newtonian heating effects. The inverse of Laplace is used to generate the exact solutions for velocity and temperature profiles, which is not explored in existing literature. Graphical representations are generated using Mathcad, depicting the velocity and temperature distributions. A comparison with prior study from the literature demonstrates strong agreement between our findings and theirs. The findings indicate that the velocity and temperature profiles of the hybrid nanofluid are higher with Newtonian heating than without it. Additionally, an increase in the Grashof number, radiation, acceleration, and porosity parameters also leads to an enhanced velocity profile.

Atherosclerosis is a condition where the arteries become narrowed and hardened due to the buildup of plaque, which is made up of cholesterol, fat and other substances. This narrowing restricts blood flow and can lead to severe complications such as heart attacks and strokes. The biofluid dynamics of blood is commonly studied numerically using various numerical methods, which can lead to the inaccuracies of results. Therefore, the analytical solution is important as it can provide a verification to the approximate solutions obtained by numerical methods. The present study interested to discover the realm of blood rheology in analytical field by investigating the blood flow under the influences of nanoparticles (drug-carriers), porosity (plaque) and magnetic field (external source of energy). The Navier Stokes equations incorporating the Casson fluid model govern the fluid flow subjected to suitable initial and boundary conditions. The conversion of dimensional governing equations into dimensionless is conducted using relevant dimensionless variables, which are then employed by the Laplace transform to attain the analytical solutions. The results report that the addition of carbon nanotube (CNTs) significantly enhances the heat transfer and velocity of the blood, which can be an advantage in the process of plaque fragmentation. Besides, this analytical study of blood flow provides valuable theoretical insights into the fundamental principles governing cardiovascular physiology, guiding the development of medical devices and treatments and informing clinical decision-making.

This research develops mathematical solutions for Casson fluid flow with free convective phenomena within channels with an accelerated plate. The study transforms the governing energy and momentum equations into the dimensionless form using appropriate variables. The Laplace transformation is used to acquire analytical solutions. Dimensionless parameters, such as the Prandtl number, Grashof number, accelerated parameter, and Casson fluid parameter, are determined, which are further investigated for their impacts on the flow and thermal behaviour. Visual representations of the mathematical results for velocity and temperature are presented using MATHCAD software through graphical plots. The study observes that fluid velocity increases with higher values of Gr but decreases with increased Pr. Additionally, temperature profiles exhibit a decrease with higher Prandtl numbers and an increase with time. The obtained results are validated by comparing them with published results in limiting cases, showing good agreement, and confirming the accuracy and reliability of the research outcomes.

Atherosclerosis is a condition where the arteries become narrowed and hardened due to the buildup of plaque, which is made up of cholesterol, fat and other substances. This narrowing restricts blood flow and can lead to severe complications such as heart attacks and strokes. The biofluid dynamics of blood is commonly studied numerically using various numerical methods, which can lead to the inaccuracies of results. Therefore, the analytical solution is important as it can provide a verification to the approximate solutions obtained by numerical methods. The present study interested to discover the realm of blood rheology in analytical field by investigating the blood flow under the influences of nanoparticles (drug-carriers), porosity (plaque) and magnetic field (external source of energy). The Navier Stokes equations incorporating the Casson fluid model govern the fluid flow subjected to suitable initial and boundary conditions. The conversion of dimensional governing equations into dimensionless is conducted using relevant dimensionless variables, which are then employed by the Laplace transform to attain the analytical solutions. The results report that the addition of carbon nanotube (CNTs) significantly enhances the heat transfer and velocity of the blood, which can be an advantage in the process of plaque fragmentation. Besides, this analytical study of blood flow provides valuable theoretical insights into the fundamental principles governing cardiovascular physiology, guiding the development of medical devices and treatments and informing clinical decision-making.