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The melting phenomenon plays a critical role in optimizing the performance of power storage, electronic cooling, and semiconductor devices. The present study aims to analyze the melting effect on the flow of Carreau fluid over a stretchable cylinder, with special consideration given to the impact of quadratic thermal radiation. Similarity variables and the homotopy analysis method are used to simplify and determine the semi-analytical homotopic solutions of the governing equations. The present findings reveal that the melting parameter increases the heat transfer rate by more than 10% for both fluids, water (Pr = 0.71), and polymer (Pr = 10). However, as the temperature ratio due to quadratic radiation increases, the local Nusselt number for water has been reduced by 25%, and an even more substantial reduction is observed for the polymer. The present study offers valuable insights into achieving optimal efficiency in electronic devices.

Nanofluid is an innovative technology that is essential in biomedical applications. A nanofluid study of human blood flow mathematically is more favorable since it provides a hypothesis for complex systems faster and is cost-saving. Academic researchers have expressed interest in investigating the characteristics of Casson nanofluid flow within a cylindrical structure, which serves as a representative model for the flow of blood in constricted human arteries. However, slip velocity boundary conditions were considered by only a certain number of researchers. The goal of this study is to develop mathematical modelling of Casson fluid flow with gold nanoparticles in the slip cylinder. The impacts of convective heat transfer, magnetohydrodynamics (MHD), and porous medium are also investigated. The Tiwari-Das nanofluid model is utilized in the governing equations. Then, the governing equations with the related boundary conditions are transformed into dimensionless form. The analytical solutions were obtained through the use of the Laplace transform and the finite Hankel transform in combination. The results of nanofluid velocity, temperature, skin friction, and Nusselt number are analyzed through the use of graphs and tables containing relevant parameters. Slip velocity causes an increment in blood velocity and a decrement in skin friction. Blood velocity and temperature are enhanced as the nanoparticles' volume fraction is increased. It is significant in cancer treatment to increase the heat transfer rate at targeted cancerous cells.

Abstract Nano-cryosurgery is one of the effective ways to treat cancerous cells with minimum harm to healthy adjacent cells. Clinical experimental research consumes time and cost. Thus, developing a mathematical simulation model is useful for time and cost-saving, especially in designing the experiment. Investigating the Casson nanofluid's unsteady flow in an artery with the convective effect is the goal of the current investigation. The nanofluid is considered to flow in the blood arteries. Therefore, the slip velocity effect is concerned. Blood is a base fluid with gold (Au) nanoparticles dispersed in the base fluid. The resultant governing equations are solved by utilising the Laplace transform regarding the time and the finite Hankel transform regarding the radial coordinate. The resulting analytical answers for velocity and temperature are then displayed and visually described. It is found that the temperature enhancement occurred by arising nanoparticles volume fraction and time parameter. The blood velocity increases as the slip velocity, time parameter, thermal Grashof number, and nanoparticles volume fraction increase. Whereas the velocity decreases with the Casson parameter. Thus, by adding Au nanoparticles, the tissue thermal conductivity enhanced which has the consequence of freezing the tissue in nano-cryosurgery treatment significantly.

Understanding fluid flow, heat, and mass transfer over a stretching cylinder is essential in ascertaining the quality of wire coating and coper thinning. This study looks at the influence of the heat source, thermal radiation, chemical reaction, and natural convection of Carreau fluid flows over a vertical stretching cylinder immersed in a porous medium. Suitable similarity variables are applied to convert the partial governing equations arising in fluid flows, heat, and mass transfer into ordinary differential equations. The optimal homotopy analysis method is then utilized to solve the transformed highly nonlinear governing equations. The impacts of the relevant parameters such as the Weissenberg number, porosity, heat source parameter, radiative number, chemical reaction parameter, mixed convection parameter, and curvature parameter on the dimensionless velocity, temperature, and concentration distribution as well as for the skin friction, Nusselt number, and Sherwood number are discussed through graphs and tables. It is observed that the velocity shows an opposite behavior as compared to temperature, and concentration in shear-thinning, n

In this article, the fluid flow and heat transfer on MHD Casson nanofluid influenced by the non-coaxial rotation of moving disk passing through a porous medium is analyzed. A mixture of single-wall and multi-wall carbon nanotubes in the human Casson blood is used as the nanoparticles. Make use of the Laplace transform technique, the analytical solutions of the temperature and velocity profiles are obtained. The results show that the temperature and velocity profiles increase with the incorporation of CNTs. The nanofluid velocity reduces with a higher magnetic strength, but it is improved with the porosity. The imposition of CNTs has descended both primary and secondary skin friction and amplified the Nusselt number. SWCNTs have provided a greater heat transfer rate and skin friction as compared to MWCNTs. The obtained solution is verified when the present results show an excellent agreement with the published results and numerical values by Gaver-Stehfest algorithm.

Nanofluid is one of the significant developments for having an efficient heat transport process. Its implementation in a non-coaxial rotating system has benefited from designing a mixer machine with two stirrer blades, a cooling fan, and jet engines. This study analytically investigates the free convection of unsteady non-coaxial rotating nanofluid flow through a moving disk. The suspension of single-wall or multi-wall carbon nanotubes in water is known as the nanofluid in this study. The fluid motion is affected by the effects of rotation and buoyancy forces. Using suitable dimensionless variables, the dimensional coupled partial differential of momentum and energy equations along with their initial and moving boundary conditions are converted into dimensionless form. The expressions for temperature and velocity profiles are obtained by solving governing equations using Laplace transform method. The validity of obtained solution is confirmed by having a good agreement when comparing present results with the published result. The results show that the insertion of CNTs particles into the rotating water causes the temperature and velocity profiles to increase. The amount of heat transferred by SWCNTs is greater than MWCNTs. Increasing CNTs particles have descended both primary and secondary skin friction but increased Nusselt number. Further analysis with the help of pictorial discussion for the fluid flows and heat transfer under the influences of nanoparticle volume fraction, Grashof number, the amplitude of disk, and time is carried out.

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.

Abstract The colloidal suspension of nanometer-sized particles of Fe3O4 in traditional base fluids is referred to as Ferro-nanofluids. These fluids have many technological applications such as cell separation, drug delivery, magnetic resonance imaging, heat dissipation, damping, and dynamic sealing. Due to the massive applications of Ferro-nanofluids, the main objective of this study is to consider the MHD flow of water-based Ferro-nanofluid in the presence of thermal radiation, heat generation, and nanoparticle shape effect. The Caputo-Fabrizio time-fractional Brinkman type fluid model is utilized to demonstrate the proposed flow phenomenon with oscillating and ramped heating boundary conditions. The Laplace transform method is used to solve the model for both ramped and isothermal heating for exact solutions. The ramped and isothermal solutions are simultaneously plotted in the various figures to study the influence of pertinent flow parameters. The results revealed that the fractional parameter has a great impact on both temperature and velocity fields. In the case of ramped heating, both temperature and velocity fields decreasing with increasing fractional parameter. However, in the isothermal case, this trend reverses near the plate and gradually, ramped, and isothermal heating became alike away from the plate for the fractional parameter. Finally, the solutions for temperature and velocity fields are reduced to classical form and validated with already published results.

In the current article, the Von Kármán swirling flow problem is extended for Navier’s slip condition on the stretching rotating disk surface with the Cattaneo-Christov heat flux. A semi-analytical study of magnetohydrodynamic Casson fluid flows over the rotating disk is carried out. The impact of the Joule heating and convective heating condition is considered. The nonlinear partial governing equations are transformed into the ordinary governing equations by using the similarity transformation technique and then solved by the optimal homotopy analysis method. The consequence of the pertinent parameters such as the Biot number, magnetic field, stretching parameter, Eckert number, and slip velocity parameter on the velocity and temperature distribution are graphically displayed and discussed. The study reveals that the thickness of the momentum boundary layer is decreased by the slip velocity parameter and the stretching rate of the disk. The thermal relaxation time has enhanced the rate of heat transfer and reduced the temperature profile in the fluid.

Fractional derivatives have been proven to showcase a spectrum of solutions that is useful in the fields of engineering, medical, and manufacturing sciences. Studies on the application of fractional derivatives on fluid flow are relatively new, especially in analytical studies. Thus, geometrical representations for fractional derivatives in the mechanics of fluid flows are yet to be discovered. Nonetheless, theoretical studies will be useful in facilitating future experimental studies. Therefore, the aim of this study is to showcase an analytical solution on the impact of the Caputo-Fabrizio fractional derivative for a magnethohydrodynamic (MHD) Casson fluid flow with thermal radiation and chemical reaction. Analytical solutions are obtained via Laplace transform through compound functions. The obtained solutions are first verified, then analysed. It is observed from the study that variations in the fractional derivative parameter, α, exhibits a transitional behaviour of fluid between unsteady state and steady state. Numerical analyses on skin friction, Nusselt number, and Sherwood number were also analysed. Behaviour of these three properties were in agreement of that from past literature.

The influence of free convection flow on unsteady Casson fluid over a vertical channel is studied in this paper. The governing equation consists of partial differential momentum and energy equations have been transformed into non-dimensional equations by using the appropriate nondimensional variables. The expression of exact solutions for nondimensional velocity and temperature profiles are obtained by using the Laplace transform method. The obtained exact solutions are found satisfied all the initial and boundary conditions. The behaviour of velocity and temperature profiles influenced by Casson fluid parameter, Grashof number, Prandtl number and time are plotted graphically and presented in tables. It can be observed that, the velocity profile and boundary layer thickness decrease when the values of Casson fluid parameter and Prandtl number increase. This is due to the increase of viscous force and retard the movement of the velocity. The present result is validated when the obtained exact solution of velocity is compared with published result and found in a good agreement.

Carbon nanotubes (CNTs) nanofluids are gaining increased popularity among researchers due to their outstanding thermal properties, leading to numerous promising industrial applications. Analytical solutions discovered in the study of CNTs nanofluids, combined with a Casson-type fluid model, are extremely limited. Therefore, a study on the heat transfer analysis of an unsteady and incompressible Casson carbon nanofluid flow is conducted. Human blood-based single-walled carbon nanotubes (SWCNTs) and human blood-based multi-walled carbon nanotubes (MWCNTs) are considered as nanofluids that move beyond an exponentially accelerated vertical plate. A set of dimensional momentum and energy equations, along with their initial and exponentially accelerated boundary conditions, is employed to represent the problem. The transformation of these equations to the dimensionless expression is achieved by using suitable dimensionless variables. The resulting equations are then tackled using Laplace transformation to acquire the analytical solution for temperature and velocity. Figures and tables are produced for a further analysis of temperature and velocity characteristics. The study shows that an increase in nanoparticle volume fraction enhances nanofluid flow and heat transmission, proving highly beneficial for cancer treatment. However, the flow is retarded due to the increment of Casson parameter values, while an enhancement is observed with a superior accelerating parameter. [ABSTRACT FROM AUTHOR]