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The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.

The fluid momentum problem is mathematically formulated by using the Prandtl–Eyring constitutive law. Also, the non-Fourier heat flux model is considered to disclose the heat transfer characteristics. The governing problem contains the nonlinear partial differential equations with appropriate boundary conditions. To facilitate the computation process, the governing problem is transmuted into dimensionless form via appropriate group of scaling transforms. The numerical technique shooting method is used to solve dimensionless boundary value problem.

The expressions for dimensionless velocity and temperature are found and investigated under different parametric conditions. The important features of fluid flow near the wall, i.e. wall friction factor and wall heat flux, are deliberated by altering the pertinent parameters. The impacts of governing parameters are highlighted in graphical as well as tabular manner against focused physical quantities (velocity, temperature, wall friction factor and wall heat flux). A comparison is presented to justify the computed results, it can be noticed that present results have quite resemblance with previous literature which led to confidence on the present computations.

The computed results are quite useful for researchers working in theoretical physics. Additionally, computed results are very useful in industry and daily-use processes.

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low‐Prandtl‐number fluids. The flow is driven by the horizontal temperature gradient between the vertical walls maintained at different temperatures. Two‐dimensional equations of conservation and energy are solved using a finite element method and a fractional step time. The discrete equations systems are solved in the lap of each element‐mesh with the aim of verifying the Boussinesq hypothesis locally. To compare our results with the earlier predictions, we have chosen the fluids for Prandtl‐numbers 0.001, 0.005 and 0.01 and with Grashof numbers up to 1 × 10⁷. To predict the steady state solutions with an oscillary transient period, the results are reduced in terms of the time series average Nusselt‐number at the vertical walls, the velocity at the center of the cavity and near right boundary. In addition, the isotherms and the velocity field are produced with the aim of showing the main circulation and particularly the weak circulations at the corners of the cavity.

The purpose of this paper is to test an efficiency algorithm based on lattice Boltzmann method (LBM) and using it to analyze two-dimensional natural convection with low Prandtl number.

Steady state or oscillatory results are obtained using double multiple-relaxation-time thermal LBM. The velocity and temperature fields are solved using D2Q9 and D2Q5 models, respectively.

With different Rayleigh number, the tested natural convection can either achieve to steady state or oscillatory. With fixed Rayleigh number, lower Prandtl number leads to a weaker convection effect, longer oscillation period and higher oscillation amplitude for the cases reaching oscillatory solutions. At fixed Prandtl number, higher Rayleigh number leads to a more notable convection effect and longer oscillation period.

Double multiple-relaxation-time thermal LBM is applied to simulate the low Prandtl number (0.001-0.01) fluid natural convection. Rayleigh number and Prandtl number effects are also investigated when the natural convection results oscillate.

The aim of the present paper is to investigate the homogeneous and heterogeneous reactions on Prandtl fluid flow at a stretching sheet with an induced magnetic field and slip boundary conditions.

The governing equations include the continuity, induced magnetic field, momentum, energy and homogeneous–heterogeneous equations. Initially, with suitable similarity variables, the governing partial differential equations and converted into a system of ordinary differential equations. Then, the nonlinear ordinary differential equations are solved by a shooting technique with the help of the BVC5C Matlab package.

The results of the present investigation are presented through graphs for different values of the various parameters. The authors observed that the large values of the stretching ratio and the induced magnetic parameters are moderate magnetic field, velocity and temperature primarily. Also, the authors found the more velocity and temperatures by boosting the slip parameters.

In addition, the values of the skin friction and the rate of heat transfer for various values of physical parameters are tabulated and deliberated in detail.

The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.

The boundary layer approach is employed to simplify the governing equations. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. In order to solve this system of ordinary differential equations numerically, shooting method in conjunction with Runge-Kutta-Fehlberg method is used.

The effects of physical parameters involved in velocity and temperature profiles are shown through graphs. It is observed that Sisko fluid parameter and curvature parameter enhances fluid velocity while motion of fluid is retarded by increasing magnetic field strength. Additionally temperature of fluid raise with curvature parameter while it fall down for larger values of Prandtl number. Skin friction coefficient and Nusselt number are computed and presented in graphs and tables for further analysis. It can be seen that curvature parameter increases both skin friction and Nusselt number while magnetic field and Prandtl number decayed skin friction and Nusselt number, respectively. Also Sisko parameter enlarges skin friction coefficient. The accuracy of solution is verified by comparing it with existing literature.

The computed results are interested for industrial and engineering processes, especially in cooling of nuclear reactors.

The problem of laminar natural convection from a vertical circular cone maintained at either a uniform surface temperature or a uniform surface heat flux, and placed in a thermally stratified medium is considered. The governing non‐similarity boundary layer equation for uniform surface temperature are analyzed by using two distinct solution methodologies; namely, (i) a finite difference method and (ii) a local non‐similarity method. For uniform surface heat flux case, the solutions of the governing non‐similarity boundary layer equations are obtained by using three distinct solution methodologies, namely, (i) a finite difference method, (ii) a series solution method and (iii) an asymptotic solution method. The solutions are presented in terms of local skin‐friction and local Nusselt number for different values of Prandtl number and are displayed graphically. Effects of variations in the Prandtl number and stratification parameter on the velocity and temperature profiles are also shown graphically. Solutions obtained by finite difference method are compared with the other methods and found to be in excellent agreement.

The purpose of this paper is to present the solution of a highly nonlinear fluid dynamics in a low Prandtl number regime, typical for metal‐like materials, as defined in the call for contributions to a numerical benchmark problem for 2D columnar solidification of binary alloys. The solution of such a numerical situation represents the first step towards understanding the instabilities in a more complex case of macrosegregation.

The involved temperature, velocity and pressure fields are represented through the local approximation functions which are used to evaluate the partial differential operators. The temporal discretization is performed through explicit time stepping.

The performance of the method is assessed on the natural convection in a closed rectangular cavity filled with a low Prandtl fluid. Two cases are considered, one with steady state and another with oscillatory solution. It is shown that the proposed solution procedure, despite its simplicity, provides stable and convergent results with excellent computational performance. The results show good agreement with the results of the classical finite volume method and spectral finite element method.

The solution procedure is formulated completely through local computational operations. Besides local numerical method, the pressure velocity is performed locally also, retaining the correct temporal transient.

The aim of this paper is to investigate the convective heat transfer in swirl tubes, which are obtained by roto‐translating a circular section eccentric with respect to the rotation axis. The geometry is numerically investigated with the aim of evaluating the convective heat transfer enhancement effect due to the secondary flow induced by the centrifugal force.

The governing equations, i.e. continuity, momentum and energy equations, are integrated numerically within Comsol Multiphysics^® environment, under the assumption of incompressible Newtonian and constant properties fluid and of periodically fully developed laminar flow for what concerns both the hydrodynamic and the thermal problem under the uniform wall heat flux thermal boundary condition.

The heat transfer performance of the geometry is discussed in relation to the flow pattern. In particular, the numerical results show that two different stable flow regimes may exist, according to the ratio of the Reynolds number to the dimensionless helix pitch. The Nusselt number augmentation becomes significant for high Prandtl number fluids when a critical Re/P* value, corresponding to the onset of the centrifugal forces induced secondary flow, is reached.

The geometry here investigated represents an interesting solution to enhance the convective heat transfer in situations in which the flow, although disturbed, persists in the laminar regime. This type of enhanced tubes shows then interesting heat transfer performances (which becomes particularly significant for high Prandtl number values) by thus suggesting convenient applications also for highly viscous fluids which are often treated under the laminar flow regime.

The purpose of this paper is to discuss a combined similarity-numerical approach that is used to study the unsteady two-dimensional flow of a non-Newtonian nanofluid over a contracting cylinder using Buongiorno’s model and the Casson fluid model that is used to characterize the non-Newtonian fluid behavior.

Similarity transformations are employed to transform the unsteady Navier-Stokes partial differential equations into a system of ordinary differential equations. The transformed equations are then solved numerically by means of the very robust symbolic computer algebra software MATLAB employing the routine bvpc45.

The effect of increasing values of the Casson parameter is to suppress the velocity field (in absolute sense), the temperature and concentration decrease as Casson parameter increase. The heat and mass transfer rates decrease with the increase of unsteadiness parameters and Brownian motion parameter. In addition, they increase as the Casson parameter and the thermophoresis parameter increase.

The problem is relatively original and represents a very important contribution to the field of non-Newtonian nanofluids.

The purpose of this paper is to study the steady mixed convection flow over a vertical cone in the presence of surface mass transfer when the axis of the cone is inline with the flow.

In this case, the numerical difficulties to obtain the non‐similar solution are overcome by applying an implicit finite difference scheme in combination with the quasilinearization technique.

Numerical results are reported here to display the effects of Prandtl number, buoyancy and mass transfer (injection and suction) parameters at different stream‐wise locations on velocity and temperature profiles, and on skin friction and heat transfer coefficients.

Thermo‐physical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate the density changes to temperature changes and to couple in this way the temperature field to the flow field.

Convective heat transfer over a stationary cone is important for the thermal design of various types of industrial equipments such as heat exchangers, conisters for nuclear waste disposal, nuclear reactor cooling systems and geothermal reservoirs, etc.

The combined effects of thermal diffusion and surface mass transfer on a vertical cone has been studied.