Basic Flow Equations Research Articles

Local non-similar solutions for EMHD nanofluid flow with radiation and variable heat flux along slandering stretching sheet

Nanofluids are the next-generation energy-transfer substrate due to their exceptional thermodynamic properties. The study of heat transfer on stretched surfaces is important due to its applications in industry, manufacturing, and medicine. The flow across a nonlinear stretched surface with different thicknesses is examined in this study to analyze the impacts of magnetic and electrical field, joule heating, viscous dissipation, and thermal radiation by considering Cu/water as nanofluid. To explore the physical characteristics, initially the mathematical model of the problem is evaluated and cataloged all of its features. Basic flow equations and fundamental rules were used to formulate the considered problem. The flow-controlling “partial differential equations” (PDEs) are transformed into a set of non-dimensional ordinary differential equations” (ODEs) via appropriate non-similar transformations. By utilizing the local non-similarity procedure operating bvp4c, the mathematical model is reconstructed. Physical representations of temperature as well as velocity profiles show how various emerging parameters interact with the flow. It is perceived that when the strength of the magnetic field grows, the velocity of nanoparticles decreases. However, as the electric field’s strength progresses and the velocity distribution does as well, the temperature profile for the nanomaterials rises. The radiation factor enhances the temperature field. The presence of time- and space-dependent characteristics for radiation, heat production increases as the fluid temperature rises. The authors investigate the procedure for replicating the dimensionless non-similar framework adopting the local non-similarity procedure. As per the author’s observations, there is currently no comparable study available in the literature for the flow model under consideration. This research holds significant potential for researchers engaged in the exploration of industrial applications of nanofluids, particularly within geophysical and geothermic domains, solar water heating technologies, biomedical applications, and other interdisciplinary fields.

Stability of non-Newtonian nanofluid movement with heat/mass transportation passed through a hydro magnetic elongating/contracting sheet: multiple branches solutions

Nanomaterials have found wide applications in many fields, leading to significant interest in the scientific world, in particular automobile thermal control, heat reservoirs, freezers, hybrid control machines, paper creation, cooling organisms, etc. The aim of the present study is to investigate the MHD non-Newtonian nanofluid and time-based stability analysis to verify the stable branch by computing the smallest eigenvalue across a slendering, extending, or shrinking sheet with thermal radiation and chemical reactions. The basic flow equations have been obtained in terms of PDEs, which are then converted to ODEs in dimensionless form via a suitable transformation. Based on the MATLAB software package bvp4c, the numerical solution has been obtained for the system of equations. A comparative study of the present and published work is impressive. The influence of evolving factors such as Prandtl number, Schmidt number, magnetic factor, heat generation/absorption, thermal, thermophoresis factor, chemical factor, second-grade fluid factor, and Brownian number on the velocities, energy, and concentration patterns is discussed through graphs. It is perceived that the temperature distribution enriches owing to the greater magnitude of the heat source. Furthermore, it is observed that a greater magnitude of radiation improves the temperature curves. It is also investigated from the present analysis that concentration and temperature profiles increase due to the growing values of the thermophoresis factor.

Analytical investigation of graphene oxide blood base nanofluid with the impact of dynamic viscosity and viscous dissipation

The aim of this research paper is to analytically investigate graphene oxide blood base nanofluid with the impact of dynamic viscosity and viscous dissipation. The increased thermal conductivity of nanofluids over regular fluids motivates this research. The basic flow equations are used to model the flow problem in nonlinear partial differential equations (NLPDEs). The dimensionless parameters, classical lie group, and thermo-physical properties are applied to transform the developed NLPDEs into dimensionless ordinary differential equations (ODEs). The resultant ODEs are resolved using the homotopy analysis method (HAM), and graphical and tabular interpretations are used to note the effects of contributing parameters including magnetic parameter, dynamic viscosity, nanoparticle volume friction, Eckert number, and Prandtl number on the velocity profile and temperature distribution. From the obtained results, we see that the velocity profile is decreasing by increasing magnetic parameter, dynamic viscosity, nanoparticle volume friction, and the temperature profile is increasing by increasing dynamic viscosity and Eckert number. The tabular descriptions of convergence of the presented fluid flow are also provided.

Joint Effects of Heat Source and Magnetic Field on Unsteady Chemically Reacting Fluid Flow Towards A Vertically Inclined Plate in Addition of Cu-Nanoparticles

The primary goal of this evaluation task is to research the mathematical analysis for unstable, free convective incompressible viscous heat also mass transfer fluid movement across an inclined a plate that is vertically positioned in the occurrence of copper nanoparticles, Magnetism, thermal generator & chemical reaction in porous media. For this investigation, we assumed the effects of Cu-nanoparticles and Angle of inclination effects in the governing equations. Additionally, the effects of fluctuating temperature & concentration are studied. We established a set of basic equations for this fluid flow and translated nonlinear partial difference equations into linear incomplete comparisons, which were then answered using the implicit limited alteration technique. The impacts of several engineering fluid variables on flow variables such as velocity, temperature, & concentration profiles were explored in this research study via the use of graphs to show the findings. Along with the other findings, the mathematical standards of skin friction, heat transmission rate, & mass transmission constants are calculated and reported in tabular form. Finally, and perhaps most importantly, the mathematical consequences of the code validation programme are related to previously publish analytical results. In the instance of pure and nanofluids, the velocity profiles are shown to increase with rising values of the Heat transfer using the Grashof number, the mass movement Grashof number, the parameter for permeability, and the passage of time Increases in magnetic field component, the Schmidt number and the Prandtl number, the parameter for the heat source, the component of the chemical reaction, and the degree of inclination all result in a drop in the velocity profiles. With respect to temperature profiles, they have been on the rise with passing time, in contrast to the Prandtl number and the heat source parameter, for which the opposite trend has been seen. We discovered that the temperature and velocity profiles are both steeper for nanofluids than for pure fluids when the parameters are increased. The concentration profiles rise with increasing times, but the opposite is true for the Schmidt number. Moreover, increasing Chemical reaction parameter values result in decreasing profiles of concentrations.

Theoretical investigation of the temperature characteristics and output parameters of an industrial crystalline silicon solar cell with a microfluidic cooling system

Operating temperature is a key factor affecting the output power of a crystalline silicon solar cell (c-Si SC). Based on solving basic semiconductor equations, Maxwell equations and heat flow equations by finite difference method, this work has theoretically investigated the influences of microfluidic cooling system on the temperature distributions and output parameters of an industrial c-Si SC packaged as a module form, where the cooling system is installed the interface between the aluminum electrode and back ethylene vinyl acetate layer and the cooling medium flowing through microchannel is selected as water. Under the influences of the cooling system, the back surface temperature of the c-Si SC is fixed at about water temperature and the front surface temperature will decrease with the water temperature decreasing. The temperature distributions of c-Si active layer and aluminum layer decrease approximately linearly along the two layer’s thickness directions. The cooling effects of the cooling system are mainly determined by water temperature and when the filling factor of microchannel is larger than 0.1, its influences on the temperature distribution of the c-Si SC are small. In the environmental temperature range from −15 °C to 60 °C, the increase rates of Voc, FF and η per degree Celsius with the water temperature decreasing are about 0.0014 V, 0.036% and 0.05%, respectively.

Analysis of Williamson nanofluid MHD over a nonlinear stretchable sheet by velocity slip and newtonian heating

In this paper, the influence of velocity slip and the Newtonian heating parameters on Williamson Nanofluid across a variable stretching sheet is studied. The basic fluid flow equations are turned into a system of coupled ordinary differential equations with appropriate conditions, which are solved numerically with the Keller-box approach. The outcomes show that, increasing Williamson parameter, due to the viscosity velocity of the fluid slowdown. As a result, it is noticed that the velocity slip parameter reduces Williamson Nanofluid velocity, while increasing shear stress, according to the results. Furthermore, it has been discovered that unlike velocity profiles, the slip influence is more pronounced on temperature and concentration profiles. Furthermore, the Newtonian heating parameter may be shown to have rising functions for velocity and dimensionless temperature. Newtonian heating has uses in the petroleum industry, heat exchangers, conjugate heat transfer around fins and solar radiation. It is discovered that the Joule heating parameter improves the thermal boundary layer thickness and slows down the velocity of the fluid, which aids in maintaining system temperature. Additionally, it has been found that the temperature profile exhibits a stronger slip effect compared with the velocity profile. To prepare toffee, chocolate and other delicacies as efficiently as possible, it is crucial to investigate the flow of Williamson fluids (such as drilling muds, clay coatings, various suspensions and some lubricating oils, thermoplastic melts, and a variety of colloids) in the incidence of heat transfer. The novelty of this paper is the effect of joule heating, Newtonian heating parameter and velocity slip on Williamson fluid velocity and temperature gradient. Furthermore, the heat and mass transfer rates are calculated for various parameters numerically and shown in tabular form.

Heat enhancement analysis of Maxwell fluid containing molybdenum disulfide and graphene nanoparticles in engine oil base fluid with isothermal wall temperature conditions

The goal of this paper is to examine the motion of a Maxwell nanofluid, including molybdenum disulfide and graphene nanoparticles, with ramped wall temperature (RWT) and isothermal wall temperature (IWT) at the barrier, by considering engine oil as the working fluids. The basic flow equation is converted to first-order ODEs by introducing the new variables. Using the numerical algorithm, the generated non-dimensional set of equations is computed using Runge–Kutta fourth-order method built-in function in MATLAB SOFTWARE with size . The iteration procedure was stopped until all of the nodes in the η-direction met the convergence condition 10−5. For confirmation of the results, the BVPh2 package is also applied. The physical parameters of interest such as local skin friction and Nusselt number are formulated and explained by tables. Lastly, the influence of molybdenum disulfide and graphene nanoscale on the convective heat and mass profiles of Maxwell ferrofluid is briefly explored. The novel part of this work is to examine the heat transfer analysis in engine oil base of Maxwell fluid with ramp and isothermal wall temperature conditions numerically, which has not been done in the published literature to date. Therefore, in the limiting sense, the present work is compared with published work.

Analytical study of fluid flow and thermal characteristics of flow in micro channel heat sinks with working fluid as water and alumina & water nanofluid

The electronic industry is looking at microchannel based MEMS technology to resolve the issue of increasing heat dissipation from electronic circuits. Micro-channels play an important role in development of small scale fluid flow devices. The internal flow configuration represents a convenient geometry for heat transfer between fluids used in chemical processing, environmental control, and energy conversion technologies. In order to fabricate such micro devices effectively, it is extremely important to understand the fundamental mechanisms involved in fluid flow and heat transfer characteristics in microchannels. This paper presents an analytical study of flow mechanism in microchannels, with a focus on effect of geometric dimensions and flow rate on the various flow parameters of a Rectangular microchannel. An attempt is also made to determine optimum microchannel dimensions based on the analysis. Basic flow equations are used for modelling the flow and determining various parameters. Further, the study analyses the effect of using Alumina & Water nanofluid on flow and thermal characteristics as compared to using water alone. The results observed show a deeper and wider microchannel would keep the pressure drop across the microchannel lower. Also using nanofluid as working fluid would result in lower pressure drop.

Extending the Validity of Basic Equations for One-dimensional Flow in Tubes with Distributed Mass Sources and Varying Cross Sections

Flow problems are solved using so-called fundamental equations and the corresponding initial and boundary conditions. The fundamental equations are the motion equation, the continuity equation, the energy conservation equation, and the state equations. In our paper, we extend the validity of the equation of motion used to describe one-dimensional, steady-state tubular flow to a case in which the mass flow of the medium changes along the tubular axis during the flow. Such flows occur in perforated and/or porous pipes and air ducts. The research in this direction was motivated by the fact that the extension and formulation of the equation of motion in this direction has not been carried out with completely general validity. In the equation of motion used to solve the problems, the isochoric and isotherm nature were assumed. In our paper, we present fundamental equations that formulate differential equations to describe polytrophic and expanding flows.

Three issues on nozzle thrust performance in cold-to-hot correlation considering variable specific heat effect

A high-temperature effect is crucial in cold-to-hot correlation for thrust nozzles to employ experimental data of cold flow to predict the real flight performance of hot gas. The high-temperature nozzle flow behaves beyond the classical gas dynamics and restricts the feasibility of cold-flow experiments, and it becomes more severe due to the species transformation from cold air to hot gas when safety and cost are considered. For an in-depth awareness, this work refines three fundamental issues regarding the high-temperature variable specific heat effect on nozzle flow characteristics. A comprehensive analysis is performed from theory to applications. First, the flow properties of calorically perfect gas (CPG) and thermally perfect gas (TPG) are distinguished and connected via the basic flow equations. One-dimensional flow theory is extended by the generalized stagnation–static gas functions for TPG. The unanticipated intersections within pressure are discovered, which could produce substantial perplexities in nozzle performance determinations. Second, the pros and cons of two homologous nozzle thrust coefficients are clarified on application objects, definition methods, and solution manners. It is proved that temperature has no influence on thrust coefficients for CPG, while the variable specific heat effect might induce three types of false-positive thrust coefficients, to make flow state unidentified, and further shake the baseline of nozzle performance. Third, for the aggravated variable specific heat effect in cold-to-hot correlation from air to hot gas, two methods are proposed with reliable verifications to solve this issue through introducing a novel concept of relative nozzle operating conditions.

Impact of Varying Viscosity with Hall Current on Peristaltic Flow of Viscoelastic Fluid Through Porous Medium in Irregular Microchannel

In this article the peristaltic transport of viscoelastic fluid through irregular microchannel under the effect of Hall current, varying viscosity and porous medium is investigated. The mathematical expressions for the basic flow equations of motion are formulated and transformed into a system of ordinary differential equations by utilizing appropriate non dimensional quantities. The exact solution for the temperature distribution is obtained, while perturbation series solution for the stream function in terms of tiny viscosity parameter is used. Graphical illustrations are presented to capture the physical impact of embedded parameters in the fluid flow i.e. the fluid velocity field, temperature distribution, pressure rise, and trapped bolus. The study shows the opposite effect for Hall current parameter with the magnetic parameter on the flow characteristics.

Linear stability perspective on mixed convection flow of nanofluids in a differentially heated vertical channel

We report instability properties of mixed convection flow of different nanofluids in a differentially heated vertical channel through a linear stability analysis. A single-phase nanofluid model is used to report the instability mechanism of nanofluids, which fairly works for the low concentration of the nanoparticles. The stability results are examined for five different types of water-based nanofluids. The basic flow and linear disturbance equations are solved with the Chebyshev spectral collocation method. The influence of nanoparticles volume fraction (φ) in different water-based nanofluids is analyzed in terms of growth rate analysis, instability boundaries and kinetic energy analysis. The results reveal that increasing the concentration of nanoparticles in the water improves the stability of the basic flow. However, increasing the Reynolds number (Re) value destabilizes the basic flow of nanofluid due to the dominant nature of the shear force. Compared to conventional pure water fluid, the inclusion of nanoparticles in pure water delays the onset of instabilities by reducing the growth of the disturbance. The order of stability for different nanofluids in (φ,Gr/Re)-plane is observed as: Al2O3/water >TiO2/water >CuO/water >Cu/water >Ag/water nanofluid, where Gr is Grashof number. By increasing the volume percentage of nanoparticles, the friction coefficient at the heated wall of the channel decreases. The kinetic energy balance at the critical level shows that shear instability is the most dominant instability for considered nanofluids.

Prevalence of secondary flow due to hall currents on radiative squeezing flow of a CuO-water nanofluid in a rotating channel: numerical prediction

The current study describes three-dimensional incompressible mixed convection flow with convective heat and mass transport on squeezing nanofluid from a rotating channel under impact of Hall current, heat source and Soret number. The current flow model is formulated to consider water based nanofluids with nanoparticle CuO (Copper Oxide). Effectively a nanoscale formulation with the Tiwari-Das model deployed to study material properties. The basic flow equations rendered to non-dimensional form via similarity transformation for which numerical simulations utilizing the fourth-fifth order Runge-Kutta-Fehlberg scheme with the help of Maple, it is a simple iteration scheme that does not require any evaluation of perturbation and linearization for solving non-linear system of equations. Graphical results for primary velocity, secondary velocity, temperature and nanoparticle concentration distributions are presented for different controlled parameters. Furthermore, computed numerical results for skin friction, Nusselt number and Sherwood number for different emerging parameters are tabulated and discussed in detail. The results are verified for limiting cases by comparing with various investigators and found to be in excellent agreement. Outcomes reveal that decrease in secondary flow to a rising channel rotating term and Hall current term. Squeezing term improved the flow rate motion, but reduces nanoparticle conductivity and species diffusion. Thermo-diffusion term stimulated the CuO nanofluid reaction. The authors have hope that the results obtained in the present study not only provide useful information for applications, it also serves as a complement to the previous studies.

Similarity solution for induced magnetic field boundary layer flow of metallic nanofluids via convectively inclined stationary/moving flat plate: Spectral relaxation computation

AbstractThe present article describes a mathematical model for incompressible free convection flow with convective heat transport from an inclined stationary/moving flat plate under impact of induced magnetic field (IMF). The current flow model is formulated to consider different water‐based nanofluids with metallic nanoparticles (Copper and Silver). Effectively a nanoscale formulation with the Tiwari‐Das model deployed to study material properties for specific nanoparticles and base fluid. A similarity solution is obtained for non‐dimensional form via similarity transformation rendered from basic flow equations for which numerical simulations utilizing the Spectral Relaxation Method (SRM). SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation and linearization for solving non‐linear system of equations. Graphical results for linear velocity, IMF, temperature, skin friction and Nusselt number distributions are presented for the different metallic‐aqueous nanofluid cases as well as stationary/moving flat plate. The results are verified for limiting cases by comparing with various investigators for the case of stationary as well as moving flat plate and found to be in excellent agreement. Furthermore, computed numerical results for skin friction and Nusselt number for different emerging parameters in case Cu and Ag nanofluids for moving plate which are tabulated and discussed in detail.

Entropy Generation Analysis for MHD Flow of Hybrid Nanofluids over a Curved Stretching Surface with Shape Effects

The characteristic of magnetohydrodynamic flow of viscous fluids is explained here. The energy equation behavior is studied in the presence of heat, viscous dissipation, and joule heating. The major emphasis of this study is the physical behavior of the entropy optimization rate. Based on the implementation of curvilinear coordinates, the basic flow equations are established. Nonlinear partial differential expressions are reduced by appropriate transformation to the ordinary differential system. In the engineering and industrial processes, nanoparticles and their shape have practical consequences. For this reason, we give a detailed investigation of the shape impacts on the flow through the curved stretching surface of nanoparticles. The flow equations are reduced into a number of nonlinear differential equations which are solved numerically using a useful numerical approach called Runge‐Kutta‐4 (RK‐4). The shooting method is first used to reduce the equations to a number of problems of first order, and then the RK‐4 approach is used for solution. Impacts for entropy optimization, Bejan number, velocity, concentration, and temperature of several physical parameters are graphically studied.

Radiative heat energy exploration on Casson-type nanoliquid induced by a convectively heated porous plate in conjunction with thermophoresis and Brownian movements

The interest of this study is to establish a mathematical model and rheological aspects of chemically reacting Casson-type nanofluid flow considering ethylene glycol-based nanoparticles with thermophoretic diffusion and Brownian motion. The basic flow equations are transmuted into non-dimensional form, these dimensionless leading equations are determined to the most excellent potential systematic using some influential similarity transformations with the employment of the Chebyshev Spectral Collocation method. The outcomes for flow rate, temperature, concentration and engineering quantities distribution are shown in terms of graphical presentation. Findings revealed that larger values of Casson fluid parameter lead to suppress velocity as well as fluid temperature. The nanofluid temperature reduces for Brownian motion parameter and enchances for thermophoresis parameter. An increase in Lewis number means a decrease in mass diffusivity resulted in to suppression in fluid concentration. The model results confirmation is tabulated, and the data assessment of the present study with formerly communicated is found excellently accurate.

Numerically framing the impact of magnetic field on nanofluid flow over a curved stretching surface with convective heating

Purpose Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in engineering and industrial domains. The purpose of this study to simulate numerically the magneto-nanofluid flow and heat transfer over a curved stretching surface. Heat transport is explored in the presence of viscous dissipation. At the curved surface, the convective boundary condition is adopted. Three different nanoparticles, namely, copper, aluminium oxide and titanium dioxide are taken into consideration because of easily available in nature. Design/methodology/approach The basic flow equations are framed in terms of curvilinear coordinates. The modelled partial differential equations are transformed into a system of non-linear ordinary differential equations by means of appropriate similarity transformation. The subsequent non-linear system of equations is then solved numerically by using the Runge–Kutta–Felhberg method with the shooting scheme via bvp4c MATLAB built-in function. Impacts of various physical parameters on velocity, pressure and temperature distributions, local skin-friction coefficient, local Nusselt number and wall temperature are portrayed through graphs and tables followed by a comprehensive debate and physical interpretation. Findings Graphical results divulge that augmenting values of the magnetic parameter cause a decline in velocity profiles and stream function inside the boundary layer. The magnitude of the pressure function inside the boundary layer reduces for higher estimation of curvature parameter, and it is also zero when the curvature parameter goes to infinity. Furthermore, the temperature is observed in a rising trend with growing values of the magnetic parameter and Biot number. Practical implications This research study is very pertinent to the expulsion of polymer sheet and photographic films, metallurgical industry, electrically-conducting polymer dynamics, magnetic material processing, rubber and polymer sheet processing, continuous casting of metals, fibre spinning, glass blowing and fibre, wire and fibre covering and sustenance stuff preparing, etc. Originality/value Despite the huge amount of literature available, but still, very little attention is given to simulate the flow configuration due to the curved stretching surface with the convective boundary condition. Very few papers have been examined on this topic and found that its essence inside the boundary layer is not any more insignificant than on account of a stretching sheet. A numerical comparison with the published works is conducted to verify the accuracy of the present study.

Modeling of an isothermal flow of a magnetohydrodynamic, viscoplastic fluid during forward roll coating process

An isothermal and incompressible flow of a magnetohydrodynamici (MHD) viscoplastic fluid has been examined while passing through the area among two co-rotating rolls. Applying lubrication approximation theory (LAT), the basic flow equations of mass and momentum are derived and subsequently non-dimensionalized. Exact solutions of velocity and pressure gradient distributions are evaluated. To evaluate the complex integrals, Trapezoidal rule for numerical integration is used. The significant engineering parameters like, the roll separation force, maximum pressure and the power transferred to the fluid by the rolls, are also numerically computed. The results demonstrate that the velocity field and pressure gradient are significantly affected due to the presence of the viscoplastic parameter. Magnetic field is found to be the controlling parameter for power input, separating force, and distance among attachment and detachment points, being extremely beneficial for the roll coating process. It has been learnt through this study that MHD can be an effective tool in the coating industry to regulate the engineering quantities in which coating thickness is the most important.

Thermosolutal convective non‐Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink

AbstractIn the current study, a mathematical formulation is developed by combining the non‐Newtonian (Casson) fluid model to simulate the thermosolutal free convection radiative flow over a vertical surface. The current flow model is formulated with a heat sink/source and radiation driven by Arrhenius kinetics. The basic flow equations are transmuted into a nondimensional form via similarity transformations for which numerical simulations are performed utilizing the Runge‐Kutta‐Fehlberg method with shooting technique. The results obtained for velocity, energy, and species mass concerning various flow parameters are presented graphically. Computed results for skin friction, Nusselt number, and Sherwood number are tabulated. The results have been verified for limited cases by comparing with various investigations, revealing excellent accuracy. The detailed geometry reveals that an increase in the activation energy enhances the flow velocity and heat transport in the Casson fluid system due to exothermic heat reaction. With the increase of the Frank‐Kamenetskii term, there is a substantial rise in temperature distribution and a decrease in concentration profiles due to high Arrhenius exothermic process, which revealed that the presence of Arrhenius kinetics is more effective to improve heat transportation phenomenon. Enhancement of the heat source/sink term completely boosts heat distribution. Rise in Radiation parameter, temperature field increases by reducing heat dissipation to the ambient.

Calendering analysis of non-isothermal viscous nanofluid containing Cu-water nanoparticles using two counter-rotating rolls

This study is a non-isothermal analysis of the calendering process using a water based nanofluid with Cu-nanoparticles. The basic flow equations are simplified under the lubrication approximation theory (LAT) and non-dimensionalized. Theoretical velocity and pressure gradient solutions are achieved, and temperature distribution is numerically computed by finite difference method. The impact of nanoparticle volume fraction on pressure distribution, fluid velocity, temperature distribution, power input, and separating force are presented through graphs and discussed. Nanoparticle volume fraction enhances the magnitude of pressure, pressure gradient, and temperature distribution. Power input and roll-separating force also rise for higher nanoparticle volume fraction. Model II of dynamic viscosity of nanofluid has a greater impact on physical parameters as compared to the model I of dynamic viscosity.