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This paper examines the time independent and incompressible flow of magnetohydrodynamic (MHD) nanofluid through a porous rotating disc with velocity slip conditions. The mass and heat transmission with viscous dissipation is scrutinized. The proposed partial differential equations (PDEs) are converted to ordinary differential equation (ODEs) by mean of similarity variables. Analytical and numerical approaches are applied to examine the modeled problem and compared each other, which verify the validation of both approaches. The variation in the nanofluid flow due to physical parameters is revealed through graphs. It is witnessed that the fluid velocities decrease with the escalation in magnetic, velocity slip, and porosity parameters. The fluid temperature escalates with heightening in the Prandtl number, while other parameters have opposite impacts. The fluid concentration augments with the intensification in the thermophoresis parameter. The validity of the proposed model is presented through Tables.

This article investigates the influence of ramped wall velocity and ramped wall temperature on time dependent, magnetohydrodynamic (MHD) natural convection flow of some nanofluids close to an infinitely long vertical plate nested in porous medium. Combination of water as base fluid and three types of nanoparticles named as copper, titanium dioxide and aluminum oxide is taken into account. Impacts of non linear thermal radiation flux and heat injection/consumption are also evaluated. The solutions of principal equations of mass and heat transfer are computed in close form by applying Laplace transform. The physical features of connected parameters are discussed and elucidated with the assistance of graphs. The expressions for Nusselt number and skin friction are also calculated and control of pertinent parameters on both phenomenons is presented in tables. A comparative study is performed for ramped wall and isothermal wall to evaluate the application extent of both boundary conditions.

The present study is related to the analytical investigation of the magnetohydrodynamic flow of Ag − MgO/ water hybrid nanoliquid with slip conditions via an extending surface. The thermal radiation and Joule heating effects are incorporated within the existing hybrid nanofluid model. The system of higher-order partial differential equations is converted to the nonlinear system of ordinary differential equations by interpreting the similarity transformations. With the implementation of a strong analytical method called HAM, the solution of resulting higher-order ordinary differential equations is obtained. The results of the skin friction coefficient, Nusselt number, velocity profile, and temperature profile of the hybrid nanofluid for varying different flow parameters are attained in the form of graphs and tables. Some important outcomes showed that the Nusselt number and skin friction are increased with the enhancement in Eckert number, stretching parameter, heat generation parameter and radiation parameter for both slip and no-slip conditions. The thermal profile of the hybrid nanofluid is higher for suction effect but lower for Eckert number, stretching parameter, magnetic field, heat generation and radiation parameter. For both slip and no-slip conditions, the hybrid nanofluid velocity shows an upward trend for both the stretching and mixed convection parameters.

Unsteady magnetohydrodynamic flow of Casson fluid over an infinite vertical plate is examined under ramped temperature and velocity conditions at the wall. Thermal radiation flux and heat injection/suction terms are also incorporated in the energy equation. The electrically conducting fluid is flowing through a porous material and these phenomena are governed by partial differential equations. After employing some adequate dimensionless variables, the solutions are evaluated by dint of Laplace transform. In addition, the physical contribution of substantial parameters such as Grashof number, radiation parameter, heat injection/suction parameter, porosity parameter, Prandtl number, and magnetic parameter is appropriately elucidated with the aid of graphical and tabular illustrations. The expressions for skin friction and Nusselt number are also derived to observe wall shear stress and rate of heat transfer. A graphical comparison between solutions corresponding to ramped and constant conditions at the wall is also provided. It is observed that graphs of the solutions computed under constant conditions are always superior with respect to graphs of ramped conditions. The magnetic field decelerates the flow, whereas the radiative flux leads to an upsurge in the flow. Furthermore, the shear stress is a decreasing function of the magnetic parameter.

This article provides a comprehensive analysis regarding effects of ramped wall temperature and ramped wall velocity on incompressible time-dependent magnetohydrodynamic flow of Maxwell fluid. The flow is due to free convection and bounded to an infinite vertical plate embedded in porous medium. Solutions of mass, shear stress, and energy fields are computed symmetrically by introducing some suitable non-dimensional parameters along with the Laplace transformation technique. The expression for the Nusselt number is also calculated. A comparison between solutions incorporating isothermal temperature and ramped wall temperature conditions is also executed to examine the profile differences. A graphical study is performed to highlight the influence of parameters on mass flow and energy transfer.

In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO 2 ) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and TiO 2 -based nanofluids is graphed.

Vacuum pump oil (VPO) is used as a lubricant in pumps of different machines. The rate of heat transport is a fundamental requirement of all phenomena. To enhance the rate of heat transmission and reduce the amount of energy consumed as a result of high temperatures. For this reason, the vacuum pump oil (VPO) is taken as a base fluid and Fe3O4 is the nanoparticles suspended in VPO. That’s why, the present study inspected the consequence of Hall current, Joule heating effect and variable thickness on these three-dimensional magnetohydrodynamics bidirectional flow of nanoliquid past on a stretchable sheet. Further, the Cattaneo-Christove heat flux and radiation impacts are also considered. The VPO−Fe3O4 nanofluid model is composed of momentum equations in x−direction, y−direction and temperature equations. The leading higher-order non-linear PDEs of the current study have been changed into non-linear ODEs with the implementation of appropriate similarity transformations. The procedure of the homotopy analysis method is hired on the resulting higher-order non-linear ODEs along with boundary conditions for the analytical solution. The significance of distinct flow parameters on the velocities in x−direction, y−direction and temperature profiles of the nanofluid have been encountered and briefly explained in a graphical form. Some important findings of the present modelling are that with the increment of nanoparticles volume fraction the nanofluid velocities in x−direction and y−direction are increased. It is also detected that higher estimations of magnetic field parameter, Prandtl number and thermal relaxation time parameter declined the nanofluid temperature. During this examination of the model, it is found that the Fe3O4-Vacuum pump oil (VPO) nanofluid enhanced the rate of heat transfer. Also, the vacuum pump oil (VPO) has many industrial and engineering applications. The current study will help to improve the rate of heat transmission by taking this into account due to which working machines will do better performance and the loss of useful energy will be decayed. Lastly, the skin friction coefficient and Nusselt number are also illustrated in a tabular form. Some major findings according to the numerical computation of the problem are that the enhancing estimations of magnetic parameter, nanoparticles volume fraction and wall thickness parameter augmented the skin friction coefficient in x−direction and Nusselt number. The reduction in skin friction coefficient of the nanofluid in y−direction is examined for Hall current and shape parameter.