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Many researchers study the Casson fluid flow in the cylinder since it imitates human blood flow in the small arteries. However, only a few researchers considered slip velocity at the boundary. The slip velocity is crucial in blood flow study due to naturally occurs during stretchable movement of the arteries. Hence, the study aims to obtain analytical solutions and understand the fluid flow behaviour with the slip velocity effect for the unsteady free convection flow of Casson fluid in a cylinder. The analytical solutions are obtained by using the joint methods of the finite Hankel transform and the Laplace transform. All initial and boundary conditions are satisfied by the analytical solutions that were obtained. The behaviour of velocity and temperature profiles are plotted and discussed graphically. It is evident from the results that increasing the slip velocity, Grashof number and time will enhance blood velocity while increasing the Casson parameter causes a decrement of blood velocity. Besides, the Prandtl number increases resulting in blood velocity and the blood temperature falling. Lastly, the obtained analytical solution is validated by comparing it with the previous study and found to be in good mutual agreement. The obtained analytical solution is significant to check the accuracy of the numerical solutions

The Riga plate is a substantial alteration in the world of engineering. Mainly used in submarines to regulate water flow, studying the behaviour of fluid flowing over a Riga plate is very advantageous. Although there are ample studies on fluid flowing over a Riga plate, the introduction of fractional derivatives, coupled with a non-Newtonian fluid, has yet to be done. Within the field of fluid mechanics, specifically boundary layer flow, fractional derivatives do not have a proven geometrical representation. However, analytical solutions would be useful in aiding experimental researches in the future. Thus, this study aims to present an analytical function for a Caputo-Fabrizio fractional derivative on an unsteady Casson fluid flowing over an accelerating vertical Riga plate by using the Laplace transform method. The parametric effects considered in this study is elucidated. Through observation of obtained graphical results generated via the obtained analytical solutions, it is found that amplification of the fractional parameter and modified Hartmann number increases the fluid velocity with an average increment of 42.05% and 1.56%, respectively. While amplification of the Casson parameter and Prandtl number dampens the fluid velocity by an average of 45.09% and 43.56%, respectively

Recently, fluid with fractional-order derivative model attracted many researchers to further study compared with the classical fluid mode since it is more precise and realistic. To imitate the applications of blood flow in narrow arteries, researchers focused on the fractional Casson fluid flow in the cylinder. However, most researchers solved the problems numerically and without considering the slip effect at the boundary. Thus, obtaining solutions analytically to the unsteady fractional Casson fluid flow in the slip cylinder with free convection is the goal of this study. The Caputo-Fabrizio fractional derivative approach is utilized to model this problem. By joining the approach of the Laplace transform and finite Hankel transform, the fractional governing equations are solved, and analytical solutions to the velocity and temperature profiles are gained. The fluid velocity rises as the slip velocity and Grashof number increase and it declines with the increment of the Casson parameter and Prandtl number. Increasing the fractional parameter will result in an increase in fluid velocity and temperature for a large time interval. The slip velocity effect influenced fluid flow, especially at the cylinder’s wall. These findings are beneficial to explore the more fractional-order derivative model and for studying the problems in biomedical engineering.

One of non-Newtonian fluid, Casson fluid, has a diversify application in the manufacturing and engineering sector due to its elasticity behaviour. This study provides the analytical solution of unsteady Casson fluid with the presence of thermal radiation and chemical reaction in a porous medium. Formulation of this fluid model is initiated with the partial differential equation (PDE) of the momentum and energy equations as well as the concentration equation. By applying the proper non-dimensional variables, these equations are then converted into dimensionless form. Subsequently, the derivation of the exact solutions for the concentration, temperature and velocity profiles is conducted with the operation of the Laplace transform method that satisfies both initial and boundary equations. Graphical illustrations, which portray the various effects on this study are generated. It has been revealed that as the thermal radiation, chemical species and porosity increases, so does the velocity profile. However, MHD and Casson parameter shown opposite behaviour in the velocity profiles.

Flow over a pipe or an elongated cylinder is widely applied in many engineering processes like wire coating and pipe coating. This encourages the present study to examine the fluid flow and heat transfer over a horizontal stretching cylinder with the impact of temperature-reliant thermal conductivity and thermal radiation. The influence of heat generation is also considered. The Carreau rheology model is applied to represent the liquid coating. The similarity technique is used to simplify the developed governing equations and then solved by the homotopy analysis method. The effects of the pertinent parameters such as the thermal conductivity parameter and Weissenberg number on the fluid field and heat transfer are studied by applying the calculated series of analytical solutions, which are scrutinized through graphs and tables. The Nusselt number has a negative function with the radiation and thermal conductivity parameters. Furthermore, the Weissenberg number affects the velocity and temperature profiles differently in conditions n < 1 and n ≥ 1, respectively. The present results are essential in optimizing the pipe coating process.

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 1 , and shear-thickening, n ≥ 1 , fluid for an increment of the Weissenberg number. Additionally, the thickness of the momentum, thermal, and concentration boundary layer is enhanced by the curvature of the cylinder.

Driven by technological advancement, the Riga plate can be seen as a key feature in developing the engineering world. As such, this study aims to investigate the effects of an accelerating semi-infinite Riga plate over a convective flow of MHD Casson fluid incorporated with the Caputo fractional derivative. The obtained governing PDEs are converted in dimensionless form and reduced to systems of ODEs via Laplace transform. Zakian's method of inverse Laplace transform is then utilised to generate graphical results in the time domain. Variations of parameter such as Casson, modified Hartmann number, Grashof number, magnetic parameter and fractional parameters are investigated for velocity profiles. Skin friction coefficient is also calculated and presented numerically. Study shows that Riga plate aids in fluid flow, hence increasing its velocity.

The melting phenomenon plays a vital role in power storage, electronic cooling, and semiconductor manufacturing. A better understanding of the phenomenon may produce an electronic device with optimal performance. In the present study, the melting effect on the flow of Carreau fluid over a stretchable cylinder is analyzed. Since the temperature difference is huge, quadratic thermal radiation is considered to simulate the real situation. To solve the governing equations, suitable similarity variables are applied to convert the complex nonlinear partial equations into ordinary equations. Semi-analytical homotopic solutions of the equation are then determined using the homotopy analysis method. The melting parameter has increased the heat transfer rate by more than 10% for both Prandhl fluids. As the temperature ratio due to the quadratic radiation increase, the local Nusselt number for the fluid with a Prandtl number, 0.71 has been reduced by 25%, and more reduction is observed for fluid with a Prandtl number, 10.

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.

Studies on Casson fluid are essential in the development of the manufacturing and engineering fields since it is widely used there. Meanwhile, fractional derivative has been known to be a constructive paradox that can be beneficial in the future. In this study, the development fractional derivative on Casson fluid flow is investigated. A fractional Casson fluid model with effect of thermal radiation is derived together with momentum and energy equations. The Caputo definition of fractional derivative is used in the mathematical formulation. Casson fluid with constant wall temperature over an oscillating plate in the presence of thermal radiation is considered. Solutions were obtained by using Laplace transform and are presented in the form of Wright function. Graphical analysis on velocity and temperature profiles was conducted with variations in parametric values such as fractional parameter, Grashof number, Prandtl number and radiation parameter. Numerical computations were carried out to investigate behaviours of skin friction and Nusselt number. It is found that when the fractional parameter is increased, the velocity and temperature profiles will also increase. Existence of fractional parameter in both velocity and temperature profiles shows the transitional phenomenon of both profiles from an unsteady state to steady state, providing a new perspective on Casson fluid flow. An increment in both profiles is also observed when the thermal radiation parameter is increased. The present results are also validated with published results, and it is found that they are in agreement with each other.

Carreau fluid flows past a stretching cylinder is elucidated in the present study. The transformed self-similarity and dimensionless boundary layer equations are solved by using the Homotopy analysis method. A convergence study of the method is illustrated explicitly. Series solutions of the highly nonlinear differential equations are computed and it is very efficient in demonstrating the characteristic of the Carreau fluid. Validation of the series solutions is achieved via comparing with earlier published results. Those results are obtained by using the Keller-Box method. The effects of the Weissenberg number and curvature parameter on the velocity profiles are discussed by graphs and tabular. The velocity curves have shown different behavior in and for an increase of the Weissenberg number. Further, the curvature parameter K does increase the velocity profiles.

Casson fluid is a non-Newtonian fluid with its unique fluid behaviour because it behaves like an elastic solid or liquid at a certain condition. Recently, there are several studies on unsteady Casson fluid flow through a cylindrical tube have been done by some researchers because it is related with the real-life applications such as blood flow in vessel tube, chemical and oil flow in pipelines and others. Therefore, the main purpose of the present study is to obtain analytical solutions for unsteady flow of Casson fluid pass through a cylinder with slip velocity effect at the boundary condition. Dimensional governing equations are converted into dimensionless forms by using the appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid parameters. Then, the dimensionless equations of velocity with the associated initial and boundary conditions are solved by using Laplace transform with respect to time variable and finite Hankel transform of zero order with respect to the radial coordinate. Analytical solutions of velocity profile are obtained. The obtained analytical result for velocity is plotted graphically by using Maple software. Based on the obtained result, it can be observed that increasing in Casson parameter, time and slip velocity will lead to increment in fluid velocity. Lastly, Newtonian fluid velocity is uniform from the boundary to the center of cylinder while Casson fluid velocity is decreased when approaching to the center of cylinder. The present result is validated when the obtained analytical solution of velocity is compared with published result and found in a good agreement.

An analytical solution to analyze the effects of radiation, magnetic, and permeability in an accelerating non-coaxial rotation phenomenon is not yet reported in the previous studies. Therefore, a radiative mixed convection flow for non-coaxial rotating MHD viscous fluid in a porous medium past an accelerated disk is studied. The fluid motion in this problem is induced by two sources which are rotating and buoyancy force. The dimensional coupled differential equations subjected to initial and accelerated boundary conditions are transformed to the dimensionless equations by utilizing appropriate dimensionless variables. The Laplace transform technique is applied to generate the closed form analytical solution for this problem. The impacts of Prandtl number, Grashof number, radiation, magnetic, porosity, and accelerated parameters on the temperature and velocity fields are illustrated graphically. The velocity and temperature profiles satisfy both the initial and boundary conditions, and the present results are found in accordance to the published work. The velocity is improved with the assistance of acceleration, radiation and porosity, while the implementation of magnetic field causes the opposite effect. Increasing radiation leads to the growth of the thermal boundary layer as well as reducing the heat transmission rate. This result can significantly contribute to the designing of heating systems because the imposition of radiation able to sustain an environment for a specific temperature. The obtained analytical solution can be used to check the correctness of the solution obtained from the numerical and experimental studies.

Unsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection flows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article [18] with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid, time, Prandtl number, Grashof number and magnetic field. Laplace transform method is used to solve the dimensionless equations with associated initial and boundary conditions. Solutions for velocity and temperature profiles are obtained. Skin friction and Nusselt number are also calculated. The obtained analytical results for velocity and temperature are plotted graphically to discuss the influence of dimensionless parameters on profiles. It is observed that fluid velocity increases with increases of Grashof number, Gr and time, t whereas it decreases with increases of Casson parameter, γ, magnetic field parameter, M and Prandtl number, Pr. Besides that, it is found that temperature profiles decrease with high value of Prandtl number, Pr while increases with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and it is found to be in a mutual agreement.

One major kind of arterial disease in blood flow that attracted many researchers is arterial stenosis. Arterial stenosis occurs when a lumen of artery is narrowed by the accumulation of fats, cholesterols and lipids plaques at the inner layer of the wall of an artery. To treat this arterial disease, the drug (solute) is injected into the blood vessels. Injection of the drug into the blood vessel cause the occurrence of chemical reaction between the drug and blood proteins and it affects the effectiveness of the solute transportation in blood flow. Hence, this study examines the unsteady dispersion of solute with the influence of chemical reaction and stenosis height through a very narrow artery with a cosine-curved stenosis. The blood is treating as Herschel-Bulkley (H-B) fluid. The momentum and constitutive equations are solved analytically to gain velocity of H-B blood flow. The convective-diffusion equation is solved by applying the generalized dispersion model to gain the dispersion function of solute. The influence of chemical reaction, power-law index, plug flow radius and stenosis height on the solute dispersion process is investigated. The results are validated with the previous solution without the effect of chemical reaction and stenosis. The results showed a good conformity between the two solutions. An increase in the chemical reaction coefficient, stenosis height, power-law index and plug flow radius reduces the dispersion function. It is observed that the solute dispersion in blood flow is affected by chemical reaction and stenosis height. H-B fluid is an appropriate fluid to investigate the blood velocity and transportation of the drug in blood flow to the targeted stenosed region through a very narrow artery for the treatment of arterial diseases. The results of the present study can potentially be used to predict the changes of blood flow behavior and dispersion process in blood flow.

The effect of the thermal radiation on the MHD Casson fluid along with the fractional derivative in an oscillating vertical plate is elucidated. More exactly, the Caputo fractional model is utilized in developing the governing equations. Besides, the influence of the buoyancy force due to the temperature gradient has also been considered. The derived fractional partial differential equations are converted into ordinary differential equations by using the Laplace transform technique and then are solved for analytical solutions via the characteristic method. The inversion of the Laplace transformation is obtained through the numerical approach of Zakian. The effects of various physical parameters on the velocity and temperature profiles, Nusselt number, and skin friction have been analyzed and depicted in graphs and tables. The distribution of the velocity and temperature either in viscous or Casson fluid do enhance by the fractional parameter.

The effects of radiation and magnetohydrodynamic on unsteady Casson fluid through an accelerated plate is analysed. The problem is formulated in the form of Partial Differential Equations (PDE) with imposed initial and boundary conditions. The Partial Differential Equations are transformed into dimensionless form by introducing suitable non-dimensional variables. Laplace transform method is used to derive the exact solutions for temperature and velocity profiles, fulfilling all initial and boundary conditions. The effects of parameters are depicted and illustrated graphically for radiation, Casson fluid and time, as well as Magnetohydrodynamics (MHD). It is found that the thermal radiation rises due to an increase in temperature. Besides, the increasing of Casson fluid and MHD parameter has decreasing effect on velocity. Finally, the influence of time will increase the velocity of the fluid.

Fractional derivative has perfectly adopted to model few physical phenomena such as viscoelasticity of coiling polymers, traffic construction, fluid dynamics and electrical networks. However, the application of the fractional derivatives for describing the physical characteristics of non-Newtonian fluid over a moving plate is still rare. In the present study, the effect of the Caputo fractional derivative on the Casson fluid flow which is induced by an accelerated plate is analytically analysed. The governing equations are initially transformed into dimensionless expressions by using suitable dimensionless variables. Then the Laplace transform method is utilized to calculate the exact solutions for the fractional governing partial differential equations. The obtained solutions are validated by comparing the results for specific case with the existing solutions in the literature. The impact of fractional parameter, Prandtl number, and time on the velocity and temperature profiles are graphically showed and discussed. The results depict that the temperature and velocity increase with the increment of fractional parameter and time. Interestingly, the velocity decreases at region near the plate but is enhanced at the area far away from the plate when the Casson fluid parameter is increased. This study is essential in understanding the factional non-Newtonian fluid flows which is more realistic in nature.

This study investigates radiation effect on unsteady oscillatory free convection between two parallel plates with mass diffusion. Appropriate non-dimensional variables are used to reduce the dimensional governing equations to dimensionless equation along with imposed initial and boundary conditions. The solutions for velocity, temperature, and concentration profiles are obtained by using Laplace transform method. To illustrate the behavior of the fluid flow, graphical results are presented with influenced of Schmidt number, Prandtl number, radiation parameter, oscillating parameter, Grashof, and mass Grashof number. The corresponding expressions for skin friction, Nusselt number, and Sherwood number are also calculated. It is observed that increasing radiation parameter, Prandtl, and Schmidt number will increase the Nusselt number but the skin friction will be reduced.

Non-coaxial rotation system has encountered in various fields such as engineering field in designing advanced cooling and heating system, food processing and mixer machines. In the present study, the effect of the non-coaxial rotation of a vertical disk on the heat and mass transfer of Newtonian nanofluids in a porous medium is analytically discussed. The influence of the magnetic field and thermal radiation is also taken into the consideration. Two different types of nanofluids which are single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with water as the base fluid are analyzed and compared. Suitable dimensionless variables are utilized to convert the governing partial differential equations associated with the initial and boundary conditions into the dimensionless form. Then, the exact solutions of the dimensionless governing equations are calculated by using the Laplace transform method. A limiting case study of the obtained analytical solutions is constructed to compare with the previously published results to verify its validity. The distributions of the velocity, temperature, and concentration along with the Skin friction, Nusselt number, and Sherwood number due to the variation of the pertinent parameters are displayed and scrutinized through graphs and tables. In the frame of non-coaxial rotation, the nanofluid with the SWCNTs nanoparticles have illustrated a higher rate of heat transfer as compared to MWCNTs nanofluid. Moreover, the heat transmission in the nanofluid has been enhanced by increasing the volume fraction of the nanoparticle and also the intensity of the radiation. This suggests that heating or cooling in a system such as a nuclear reactor can be improved by properly selecting the type of the nanofluid and also the volume fraction of the nanoparticle.

In this paper, free convection of nanofluids flow with oscillating vertical parallel plates and mass diffusion were considered. Obtained equations were converted into ordinary differential equations with appropriate transformations. Method of Laplace transform was used to find the exact solutions of velocity, temperature and concentration profiles from the dimensionless governing equations. Discussion of graph pertaining to different embedded parameters such as Prandtl number, Schmidt number, Grashof and mass Grashof number, oscillating parameter and nanoparticles volume fraction parameter was also added. Skin friction, Nusselt and Sherwood number were also discussed and deliberated.

Mixed convection of unsteady non-coaxial rotation flow of viscous fluid over an accelerated vertical disk is investigated. The motion in the fluid is induced due to the rotating and buoyancy force effects. The problem is formulated and extended in terms of coupled partial differential equations with some physical boundary and initial conditions. The non-dimensional equations of the problem are obtained by using the suitable non-dimensional variables. The exact solutions of non-coaxial velocity and temperature profiles are obtained by using Laplace transform method which are satisfying all the initial and boundary conditions. Skin friction and Nusselt number are also calculated. The physical significance of the mathematical results is shown in various plots and is discussed for Grashof and Prandtl numbers as well as magnetic, porosity, time and accelerated parameters. It is found that, the velocity with the effect of acceleration is higher compared to constant velocity. In limiting sense, the present solutions are found identical with published results.

In the current article, the Von Karman 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.

The study analyzed the heat transfer of water-based carbon nanotubes in non-coaxial rotation flow affected by magnetohydrodynamics and porosity. Two types of CNTs have been considered; single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). Partial differential equations are used to model the problem subjected to the initial and moving boundary conditions. Employing dimensionless variables transformed the system of equations into ordinary differential equations form. The resulting dimensionless equations are analytically solved for the closed form of temperature and velocity distributions. The obtained solutions are expressed in terms of a complementary function error. The impacts of the embedded parameters are graphically plotted in different graphs and are discussed in detail. The Nusselt number and skin friction are also evaluated. The temperature and velocity profiles have been determined to meet the initial and boundary conditions. An augment in the CNTs’ volume fraction increases both temperature and velocity of the nanofluid as well as enhances the rate of heat transport. SWCNTs provides high values of Nusselt number compared to MWCNTs. For verification, a comparison between the present solutions and a past study is conducted and achieved excellent agreement.

In this paper, the unsteady of magnetohydrodynamics (MHD) second grade fluid in a porous medium due to non–coaxial rotation is investigated. The effects of heat and mass transfers (double diffusion) through an oscillating disk are considered. The non–dimensional governing momentum, energy and mass equations are obtained by using the suitable non–dimensional variables. The Laplace transform method is used to obtain the exact solutions of non–dimensional velocity, temperature and concentration profiles. The expressions of skin friction, Nusselt number and Sherwood number are also presented. The numerical result for all fluid flow profiles are plotted in graphs for the different parameters studied. The results also show that, velocity for present solution (with heat and mass transfers) has a significant impact on the velocity profiles in non-coaxial rotation due to exhibits high thermal diffusivity and thermal conductivity. The obtained exact solutions are found to be identical to the Guria [10]. It is worth mentioning that, the exact solutions are in excellent agreement with the numerical solutions of Inverse Laplace transform obtained by Gaver-Stehfest algorithm.

This paper studied unsteady free convection flow between two parallel plates with mass diffusion. One of the plates is considered oscillating. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions. The exact solution to velocity, temperature and concentration profiles are obtained using the Laplace Transform technique. The graphical results of the solutions are presented to illustrate the behavior of the fluid flow with the influence of Schmidt number, Prandtl number, oscillating parameter, Grashof and mass Grashof number. The corresponding expressions for skin friction, Nusselt number and Sherwood number are also calculated. It is observed that increasing Prandtl and Schmidt numbers will increased the Nusselt number but decreased the skin friction.

Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutionsfor velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.

This paper investigated unsteady free convection flow between two parallel plates with mass diffusion. One of the plate are considered oscillating. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions. The exact solution for velocity, temperature and concentration profiles are obtained using the Laplace Transform technique. The graphical results of the solutions are presented to illustrate the behavior of the fluid flow with the influenced of Schmidt number, Prandtl number, oscillating parameter, Grashof and mass Grashof number. The corresponding expressions for skin friction, Nusselt number and Sherwood number are also calculated. It is observed that increasing Prandtl and Schmidt number will increased the Nusselt number but decreased the skin friction.

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 this paper, the effects of heat and mass transfer (double convection) on unsteady magnetohydrodynamic flow of incompressible viscous fluids in a porous medium under the influence of non-coaxial rotation are analyzed. The flow is induced due to buoyancy force and oscillating bounding disk. The dimensionless governing equations for the velocity field, temperature and concentration distributions are solved analytically by using the Laplace transform technique. The results for skin friction, Nusselt number and Sherwood number are also presented. The numerical results are computed for the effects of various indispensable flow parameters and displayed using several graphs. The numerical results showed the behavior of the physical parameters on the fluid flow in primary and secondary velocities as well as on heat and mass transfer. It is found that the velocity profiles for solution that considering heat and mass transfer are higher compared to solution without mass transfer. Physically, mass is a particle that transfers heat energy from one place to another place and enhances the velocity to increase. It is worth mentioning that the analytical solutions are in excellent agreement with the numerical solutions obtained by Gaver–Stehfest algorithm and present solutions are found identical with the published results.

The effects of ramped wall temperature, rotation and porosity on mixed convection flow of incompressible second grade fluid are studied. The momentum equation is modelled in a problem of rotating fluid with constant angular velocity subjected to initial and oscillating boundary conditions. The energy equation is also introduced. Some suitable non-dimensional variables are used to write equations into non-dimensional form. Laplace transform method is used to solve these equations in order to obtain the analytical solutions of velocity and temperature profiles. Computations are carried out and presented graphically to analyse the effect of second grade fluid parameter, rotation parameter, porosity parameter, Prandtl number and Grashof number on the profiles. It is found that, for larger values of porosity parameter, the fluid velocity will increase for both primary and secondary velocities. The results also show that, velocity for ramped wall temperature is lower compared to isothermal temperature. It is worth to mention that, the exact solutions obtained in this study can be used to check correctness of the results obtained through numerical schemes.

Heat and mass transfer in unsteady non-coaxial rotating flow of viscous fluid over an infinite vertical disk is investigated. The motion in the fluid is induced due to two sources. Firstly, due to the buoyancy force which is caused because of temperature and concentration gradients. Secondly, because of non-coaxial rotation of a disk such that the disk executes cosine or since oscillation in its plane and the fluid is at infinity. The problem is modeled in terms of coupled partial differential equations with some physical boundary and initial conditions. The dimensionless form of the problem is solved via Laplace transform method for exact solutions. Expressions for velocity field, temperature and concentration distributions are obtained, satisfying all the initial and boundary conditions. Skin friction, Nusselt number and Sherwood number are also evaluated. The physical significance of the mathematical results is shown in various plots and is discussed for several embedded parameters. It is found that magnitude of primary velocity is less than secondary velocity. In limiting sense, the present solutions are found identical with published results.

The influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Casson fluid over a vertical plate embedded in porous medium with arbitrary wall shear stress has studied. Casson fluid is a non-Newtonian fluid. The partial differential equations that govern the flow, heat and mass transfer are transformed to non-dimensional by using suitable non-dimensional variables, which are then solved analytically by using the Laplace transform technique. Analytical expressions for velocity, temperature and concentration fields are determined. Additionally, the exact expressions of the Nusselt number and Sherwood number are also obtained. Numerical results of velocity, temperature and concentration profiles with various values of embedded flow parameters are graphically shown and the influences to the characteristic of the fluid flow are discussed in detail. The variations in Nusselt number and Sherwood number are displayed in tabular form.

Rotating effects and magnetohydrodynamic (MHD) free convection flow of second grade fluids in a porous medium is considered in this paper. It is assumed that the bounding infinite inclined plate has ramped wall temperature with the presence of heat and mass diffusion. Based on Boussinesq approximation, the analytical expressions for dimensionless velocity, temperature and concentration are obtained by using the Laplace transform method. All the derived solutions satisfying the involved differential equations with imposed boundary and initial conditions. The influence of various parameters on the velocity has been analyzed in graphs and discussed.