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The study of squeezing fluids is considered to be one of the most important areas of scientific research due to its various engineering and bioapplications such as the squeezing processes that occur in the brake mechanisms in trucks and Piston’s systems, liquid metal lubrication systems, polymer processing and compression/injection molding as well as the contraction processes in the arteries and veins. This work deals with the study of one of these applications through modeling using the basic equations governing the squeezing fluids and their boundary conditions, and the presence of some external thermal influences such as the magnetic field and linear/nonlinear thermal radiation in its basic form as a nonlinear partial differential equations system, then converting this system into nonlinear ordinary differential equations that were solved numerically and analytically for special cases. The results focused on showing the thermal and flow behavior of the fluid at different concentrations of nanoparticles, which induce the effect of thermal forces represented by the magnetic field and thermal radiation. These results were demonstrated through a set of graphs and tables and discussed in detail, and in summary, some important results were found from the physical analysis. For some of these results, the use of different types and concentrations of particles increases the viscosity of the fluid, which causes an increase in temperature ranging between 17% and 45%.

Computational studies have been widely applied for the thermal evaluation of the nanomaterial thermal feature in different industrial and scientific issues. The squeezed flow and heat transfer features for Al₂O₃-water nanofluid among analogous plates are investigated using the GOHAM and its validity is verified by comparison with existing numerical results. Novel aspects of Brownian motion and thermal force were accounted in the simulation of nanomaterial flow within parallel plate. Analytical investigation has been done for diverse governing factors namely: the squeeze, chemical reaction factors and Eckert number. The obtained outcomes show that $|C_f|$ has direct relationship with absolute values of squeeze factor. Nu increases for large Eckert number and absolute values of squeeze number.

An attempt is made to analyze the effects of micropolar fluid squeezing film implementation between porous elliptical plates under the application of an external magnetic field. The appropriate improved hydromagnetic Reynolds equation governing the pressure distribution is acquired. The Reynolds equation is solved for lubrication features such as pressure distribution, load-carrying capacity and time-height relationships. It is noticed that a micropolar lubricant with a magnetic field may considerably impart a much-appreciated increase in load-carrying capacity, pressure distribution and response time compared to the classical case. Nevertheless, it is found that, as with the magnetic field, the larger values of the fluid gap number and the coupling number increase lubrication characteristics. Also, it is found that such a bearing cannot support a large number of lubrication characteristics because of the pores on the main path of fluid flow.

Squeezing flow of Casson liquid between two disks is a practical application in compression, polymer processing and injection molding. In this paper, the Casson liquid flow between two convectively heated disks is analyzed using Buongiorno model. Further, the heat and mass transport analysis is done by considering the impact of heat source/sink and activation energy. The continuity and momentum equations governing the unsteady two-dimensional flow are derived using conservative laws. The equations are reformulated using the similarity transformations and the reformulated equations are solved numerically with MATLAB routine bvp4c. The effect of embedding different physical parameters on the flow is analyzed through the graphs for both suction and blowing cases along with comprehensive solutions and equal Biot numbers. Results are validated with the existing literature. For both suction and blowing cases, squeezing number decreases the velocity near the lower disk but increases the velocity near the upper disk. Increasing magnetic field strength slightly increases velocity near the lower disk for equal Biot numbers.

There are several industrial and biological applications for the study of squeezing flow, including cell squeeze technology, blood flow and food production. In particular, the load and thrust bearing qualities of human body joints and the compression molding processes of metals and polymers might be explained by this solution, which could also illustrate the classical lubrication problems. So, this work investigated the effects of cross-diffusion, an induced magnetic field and joule heating on an unsteady squeezing Casson fluid on a spinning disc. Using the proper similarity transformations, the systems of partial differential equations are drained into a system of ordinary differential equations, which are solved numerically using the finite difference method. This analysis accounts for the effects of biophysical parameters on velocity components, magnetic fields, heat and mass transfer profiles. Additionally, graphic representations are provided for the skin friction coefficient, Nusselt number and Sherwood number for various values of the governing parameters. The current investigation has been matched with published results in order to validate validity, and good agreements have been seen. The impacts of the problem parameters under consideration are also explained numerically and graphically. The top disc’s rate of rotation is found to enhance the tangential fluid flow and temperature distribution, while it reduces velocity in the other directions and the induced magnetic field.

The usage of nanoparticles is effectively enhanced in industries and technologies because of their intensified thermal performance. Nanomaterials innovatively play a significant role in technological applications such as biosensors, the petroleum related industry and biofuels. Due to such exceptional performance of nanomaterials, the magneto-hydrodynamics squeezed nanofluid flow is examined through the parallel walls. The transportation phenomenon of heat and mass with viscous dissipation and double stratification is also investigated under Cattaneo–Christov phenomenon. The constitutive equations (PDEs) are transmuted with precise similarity variable into dimensionless equations (ODEs). The acquired ODEs are evaluated through the assistance of Homotopic technique. The impacts of the emerging parameters are described graphically on the concerned profiles. The graphical discussion clarifies that both stratification parameters diminish both profiles (thermal & solutal). Concentration field is decreased by the thermophoresis parameter. The relaxation time parameters decrease the heat and mass transport. Moreover, both Brownian and thermophoresis parameters raise the temperature.

Due to the numerous practices of non-Newtonian fluids in technological and industrial fields, the attention towards such fluids increases incredibly. The highly nonlinear equations emerge in the modeling of the non-Newtonian fluids. The differential transform method is one of the analytical methods which is used to acquire the solution to these complicated nonlinear equations in the series form. The current analysis comprises the squeeze flow of non-Newtonian fluid in two dimensions. Two infinite parallel plates are considered in which the time-dependent fluid is squeezed. The heat transfer mechanism is deliberated with the significance of heat absorption/generation. The nonlinear setup of ordinary differential equations is acquired by practicing the appropriate similarity variables on the governing equations of the concerned flow mechanism. The nonlinear setup is analytically resolved with the help of an analytical differential transform method. For the authenticity of the differential transform method, the analytical outcomes are compared with the numerical results. Graphical illustrations of fluid temperature and velocity profiles relative to the pertinent parameters are briefly explicated numerically and analytically. The fluid velocity demonstrates the descending behavior and the temperature field exhibits the expanding nature relative to the squeezing parameter.

Squeezing or squeeze flows have tremendous applications in applied fields, like engineering, biomedical sciences and rheological studies. This paper demonstrates the squeezing flow of kerosene-based nanoliquids between parallelly aligned plates, with a Riga-type fixed lower boundary. The effects of dispersing two types of copper-functionalized carbon nanotubes (CNTs), single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) are examined. Using appropriate transformations, a self-similar ordinary differential system is derived from the governing model of partial differential equations and substantial boundary conditions. Using the homotopy analysis method (HAM) and the $bvp4c$ package, analytical and numerical estimates are obtained, respectively. For higher values of the squeezing parameter, dimensionless temperature increases, while velocity patterns are upside-down. Moreover, increments in dimensionless parameters representing Riga constituent width, modified Hartmann number, nanoparticle concentration and radiation parameter improve heat transfer rates and thermal boundary layer thickness, however, adversely affect velocity. Despite enhanced friction effects, numerical results show that the Nusselt number increases as nanoparticle loads and radiation parameters increase. This suggests that convection rates are improved over conduction rates. Excellent agreement is found between analytical and numerical evaluations. Apparently, it is noticed that MWCNTs perform better than SWCNTs.

The transport phenomena of Casson nanofluid flow between two parallel disks subject to convective boundary conditions are analyzed in this paper. The mathematical model incorporates the impact of thermophoresis and Brownian motion since the Buongiorno’s nanoliquid model is adopted to characterize the nanoliquid’s transport features. The appropriate similarity transformations are applied to obtain the resulting nondimensional ordinary differential equations from the basic governing equations. The resulting ordinary differential equations and the associated boundary conditions are solved analytically by adopting the homotopy perturbation technique. Further, a statistical experiment is conducted to identify notable flow parameters which cause significant impact on the heat transfer rate. The characteristics of critical pertinent parameters on the flow field are graphically manifested. It is worth noting that the Casson nanofluid velocity escalates by augmenting the magnetic field parameter in the case of injection near the disks. Nanoparticle concentration is considerably diminished with an increment in thermophoresis parameter. In the cases of equal and unequal Biot numbers, the heat transfer rate is promoted with higher values of the Brownian motion parameter. Among the Casson fluid parameter, squeezing parameter and magnetic field parameter, the heat transfer rate discloses the highest positive sensitivity with the lowest value of the Casson fluid parameter.

The aim of this work is to present a natural convective and squeezing flow model of two-dimensional couple stress nanofluid which is flowing on the sensory surface with variable fluid viscosity. The fluid flowing on a microcantilever sensory surface and squeezing is happening at free stream. The sensor is also useful to detect the movement of fluid and the variations in thermal and solutal rates. The Cattaneo–Christov model is adopted along with nanoparticle and chemical reaction to explore the transmission of heat and mass rates. The analysis of heat transmission in non-Newtonian couple stress fluid flowing on squeezed sensory surface by using the Cattaneo–Christov heat conduction model has various industrial and scientific applications including the polymer processing, wastewater treatment, chemical reactors, biomedical flows, cooling and heating processes in industries, heat exchangers, microfluidics, oil and gas industries. All the assumptions are applied in the basic governing laws laws and then we get the model of the partial differential equations. The governing model of equations is transmuted into ordinary differential equations form via the transformations and then the numerical results of these ODE’s are examined with a well-defined numerical technique “Shooting Method”. For higher inputs of couple stress, squeezing index and permeability velocity, the fluid’s internal velocity decreases. Because of the Prandtl number and thermal relaxation coefficient, the heat transfer mechanism slows down. Mass transfer increases for greater inputs of the thermal diffusivity coefficient and decreases due to concentration relaxation. Further, the numerical dependency of emerging parameters on the skin friction is illustrated in tabular form. The parametric effects on the model (velocity, temperature and concentration) are introduced using numerical values shown in the table.

In this article, Magnetohydrodynamic (MHD) squeezing flow between two parallel disks is considered. The upper disk is taken to be solid and the lower one is permeable. Soret and Dufour effects are measured to explore the thermal-diffusion and diffusion-thermo effects. Governing PDEs are converted into system of ODEs with the support of suitable similarity transforms. Homotopy analysis method (HAM) has been employed to obtain the expressions for velocity, temperature and concentration profiles. Effects of different emerging parameters such as squeezing number $S$, Hartman number $M$, Prandtl number Pr, Eckert number Ec, dimensionless length $\delta$ and Schmidt number Sc on the flow are also discussed with the help of graphs for velocity, temperature and concentration. The local Nusselt and Sherwood numbers along with convergence of the series solutions are presented with the help of graphs. From the results obtained, we observed that the physical quantities like skin friction coefficient increases with increasing value of Hartmann number $M$ in the blowing case $(A<0)$ whereas a fall is observed in the suction case $(A>0)$. However, the rate of heat transfer at upper wall increases with increasing values of Dufour number Du and Soret number Sr for both the suction $(A>0)$ and blowing flow $(A<0)$, whereas, for the larger values of Dufour number Du and smaller values of Soret number Sr, a rapid fall is observed in Sherwood number Sh for both the suction $(A>0)$ and blowing $(A<0)$ cases. A numerical solution is obtained by employing Runge–Kutta method of order four (RK-4) to check the validity and reliability of the developed algorithm. A well agreement is found between both the solutions.

This paper addresses the squeezed flow of third grade fluid between two parallel disks. Heat transfer in present flow is characterized by Cattaneo–Christov theory. Thermal relaxation time effects on the boundary layer is examined. Suitable transformations are invoked for a system of ordinary differential equations. Convergent series solutions are thus obtained using homotopic approach. Influences of different parameters on the velocity and temperature profile are discussed.

This communication addresses unsteady squeezing flow of second grade liquid. NonFourier heat flux model is implemented to discuss heat transfer features subject to heat generation/absorption. Homogeneous–heterogeneous reactions are addressed. Firstly, the problems are nondimensionalized by suitable variables and then solutions for strong nonlinear systems are presented. Convergence region is particularly determined for obtained solutions. Statistical declaration and probable error for drag force are computed. Velocity is found to decay for larger estimation of fluid parameter while thermal and concentration fields are enhanced for higher heat generation and squeezing parameters.