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Considering putting in diverse nanoparticles to the base fluid is the latest technique to increase the thermal accomplishment of ordinary fluids. for the present investigation, the flow and heat transfer of nanofluids over a spinning disk with an invariable stretching pace is observed. The non-Fourier flux, magnetic field, and radian heat have all been paid regard to. The nanoparticle used here is Graphene with water as a base fluid. The governing equations are reshaped by utilizing Von Karman transformation and worked it out numerically via boundary value problem solver (bvp5c). We also provided some of the results with magnetic field and beside magnetic field cases and found disparity in both circumstances. Results pointed out that with little proliferation in stretching force constant, the skin friction and the local Nusselt number, the velocity in radial and axial paths improved, when the velocity in the tangential trend and the thermal boundary layer thickness reduce, significantly.

For the present research, an attempt was made to study the influence of magnetic field and thermophoresis on an existing mathematical model. The impacts made by both magnetic parameter and thermophoresis over the nanofluids flux as well as the characteristics of transfer of heat are studied and analyzed by using a suitable numerical method (RungeKutta- Fehlberg method together with shooting technique) in maple2020. Also the effects of some emerging physical parameters on the profiles of momentum and temperature have been studied and analyzed in tables and graphs. Two solutions are obtainable if the free stream and the plate moves conversely to each other. At the end it was found that the Nusselt number is mostly an increasing function, whereas, the momentum and the temperature fluctuates with different parameters.

A theoretical analysis is performed for investigating the flow and heat transfer characteristics of Maxwell fluid over a stretching cylinder with Cattaneo–Christov, heat source or sink, and suction/injection. The solution to the transformed similarity equations is derived using Runge–Kutta fourth-order method along shooting technique. The present result for both the surface shear stress and the local Nusselt number is validated with the previously published results, while a very sound agreement is attained. The impacts of the distinct parameters related to this study are presented in graph and tabular form, respectively. Moreover, the local Nusselt number and surface shear stress have been computed for both the suction and injection cases. It is found that strengthening the thermal relaxation parameter value increases the heat transfer rate. The dimensional heat transfer rate is observed being rising in the injection case when compared with the suction case.

In this paper, a study of squeezing unsteady nanofluid flow between two parallel plates was conducted. While the thermal radiation effect along the temperature profile was considered. The homotopy perturbation method (HPM) was used to solve the twodimensional nonlinear momentum and energy equations. The results obtained in the current study were compared with the one obtained using Duan-Rach Approach (DRA) and Least Square Method (LSM). The results are found in understandable agreement with the aforementioned methods.

The present study investigated the variable viscosity and multiple slips on two-dimensional magnetohydrodynamic Carreau fluids due to slendering sheet filled with microorganisms. The Carreau model is used to characterize the behavior of the fluids with shearing thickening properties using the various values of exponent of power law. The diffusion-thermo and thermos diffusion effects are taken into account. The nonlinear sets of ordinary differential equations are treated numerically by shooting technique with Runge–Kutta Fehlberg method. Different parameters like magnetic interaction parameter $$ M $$ , Weissenberg number $$ We $$ , the index of power law $$ m $$ , various multiple slip parameters like the velocity slip parameter $$ \tau_{1} $$ , the temperature jump parameter $$ \tau_{2} $$ , the concentration $$ \tau_{3} $$ , and the concentration jump parameter $$ \tau_{4} $$ are analyzed. The velocity, the skin friction, the rate of heat transport namely Nusselt number and rate of mass transport as Sherwood number are elaborated graphically and computed in tabular benchmark. The analysis found that the density of motile organism grows with the growing magnetic field parameter, diffusion-thermo number, thermo-diffusion number and Weissenberg number.

In this paper, an analytical study of squeezing unsteady nanofluid flow between two parallel plates is carried out. The effects of thermal radiation and heat generation/absorption along the temperature profile were observed. The homotopy perturbation method (HPM) was used to solve the two-dimensional nonlinear momentum and energy equations. The results found in this study are being compared with the result obtained using the RK4 technique with shooting scheme. The results obtained fascinatingly agree with the numerical solutions. Keywords: Nanofluid, Squeezing flow, Nonlinear equations, Homotopy perturbation method (HPM), Runge-Kutta scheme (RK4)

In this paper, the effects of Brownian motion, thermophoresis, chemical reaction, heat generation, magnetohydrodynamic and thermal radiation has been included in the model of nanofluid flow and heat transfer over a moving surface with variable thickness. The similarity transformation is used to transform the governing boundary layer equations into ordinary differential equations (ODE). Both optimal homotopy asymptotic method (OHAM) and Runge-Kutta fourth order method with shooting technique are employed to solve the resulting ODEs. For different values of the pertinent parameters on the velocity, temperature and concentration profiles have been studied and details are given in tables and graphs respectively. A comparison with the previous study is made, where an excellent agreement is achieved. The results demonstrate that the radiation parameter N increases, with the increase in both the temperature and the thermal boundary layer thickness respectively. While the nanoparticles concentration profiles increase with the influence of generative chemical reaction γ 0.

In this paper, a revised optimal homotopy asymptotic method (OHAM) is applied to derive an explicit analytical solution of the Falkner-Skan wedge flow problem. The comparisons between the present study with the numerical solutions using (fourth order Runge-Kutta) scheme and with analytical solution using HPM-Padé of order [4/4] and order [13/13] show that the revised form of OHAM is an extremely effective analytical technique.

The two-dimensional steady boundary layer flow, of a nanofluid past a stretching sheet with a convective boundary condition in the presence of chemical reaction has been studied. The equation of volume fraction concentration consists of the Brownian motion and the thermophoresis effects. The governing equations are simplified via boundary value approximation and some similarity variables and solved using the Runge-Kutta fourth order method with shooting technique and homotopy perturbation method (HPM) with Pad� approximation (HPM-Pad�). All the salient parameters on the temperature and concentration profiles have been studied and details are given graphically. Thus the results found in this study are being compared with the previously published study, where an excellent agreement is achieved. As presented on tables. It is found that the reduced Nusselt number is a decreasing function of both generative and destructive chemical reaction γ. While the reduced Sherwood number is a decreasing function when chemical reaction parameter, γ0.