Isothermal Wedge Research Articles

Electrically conducting micropolar nanofluid with heat source/sink over a wedge: Ion and hall currents

A theoretical exercise is conferred for the magneto-micropolar nanofluid layer flow past a wedge surface by virtue of its numerous fundamental problems which arise in nanotechnology, chemical engineering, polymers etc. The model exemplify an isothermal wedge surface. The fluid is incompressible, viscous, electrically conducting and carrying ion slip and Hall currents with source or sink. The Eringen micropolar model is set up for rheological properties of the nanofluid. A Tiwari-Das nanoscale formulation is utilized in order to study specific nanoparticles and base fluids. The dimensionless transformed, coupled momentum, angular momentum (micro-rotation) and thermal perimeter layer equations are solved with the efficient MATLAB bvp4c numerical scheme. Validation with earlier studies is conducted. The influence of Hartman number M, Hartree pressure gradient parameter m, Eringen vortex viscosity (micropolar) parameter K, nanoparticle volume fraction ϕ, heat absorption (sink) parameter Φ, Prandtl number Pr and nanoparticle type on velocity F′,G′, angular velocity H, temperature θ, skin friction function and Nusselt number function are visualized graphically and in tables. The magnetic effects supports the transverse, horizontal velocity and temperature but suspends the angular velocity. Optimum rate of heat transfer is procured with iron oxide nanoparticles dropped in water and copper nanoparticles hanging in engine-oil.

Mixed convection flows of tangent hyperbolic fluid past an isothermal wedge with entropy: A mathematical study

AbstractThe nonlinear, steady, and mixed convective boundary layer flow and heat transfer of an incompressible tangent hyperbolic non‐Newtonian fluid over an isothermal wedge in the presence of magnetic field are analyzed numerically using the implicit Keller‐Box finite‐difference technique. The entropy analysis due to MHD flow of a tangent hyperbolic fluid past an isothermal wedge and viscous dissipation is also included. The numerical code is validated with previous Newtonian studies available in the literature. Graphical and tabulated results are analyzed to study the behavior of the fluid velocity, temperature, concentration, shear stress, heat transfer rate, entropy generation number, and Bejan number for various emerging thermophysical parameters, namely Weissenberg number (We), power‐law index (n), mixed convection parameter (λ), pressure gradient parameter (m), Prandtl number (Pr), Biot number (γ), Hartmann number (Ha), Brinkmann number (Br), Reynolds number (Re), and temperature gradient (Π). It is observed that velocity, entropy, Bejan number, and surface heat transfer rate are reduced with the increase in the Weissenberg number, but temperature and local skin friction are increased. An increase in pressure gradient enhances velocity, entropy, local skin friction, and surface heat transfer rate, but reduces temperature and Bejan number. An increase in an isothermal power‐law index (n) is observed to increase velocity, Bejan number, and surface heat transfer rate, but it decreases temperature, entropy, and local skin friction. An increase in the magnetic parameter (Ha) is found to decrease temperature, entropy, surface heat transfer rate, and local skin friction, and it increases velocity and Bejan number. The research is applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water‐soluble solution thermal treatment.

Significance of Joule heating and viscous heating on heat transport of MoS2–Ag hybrid nanofluid past an isothermal wedge

The problem of flow and heat transport of magneto-composite nanofluid over an isothermal wedge has not been addressed in the literature up to yet. Thus, this article features the laminar transport of Newtonian composite nanomaterial (C2H6O2–H2O hybrid base liquid + MoS2–Ag hybrid nanoparticles) in the presence of exponential space- and temperature-dependent heat source past an isothermal wedge. An incompressible and electrically conducting fluid is assumed. The effects of Joule heating and viscous heating are also accounted. Single-phase nanofluid model and boundary layer approximation are utilized to govern the equations of flow and heat transport phenomena. The solution of the simplified coupled system of dimensionless constraints is obtained by using the Runge–Kutta–Fehlberg method based on the shooting technique. Detailed analysis of active quantities of interest has been presented and discussed. The interesting physical quantities (friction factors and Nusselt number) are estimated. Also, the slope of the data point is calculated in order to estimate the amount of decrease/increase in physical quantities.

Heat and mass transfer from an isothermal wedge in nanofluids with Soret effect

A mathematical model for the two-dimensional steady incompressible convective heat and mass transfer from an isothermal wedge immersed in a nanofluid is presented. The model used for the nanofluid incorporates the effects of the volume fraction parameter. Two types of nanofluids, silver-water and gold-water nanofluids, are considered in this study. Suitable transformations are used to convert the partial differential equations into highly nonlinear ordinary differential equations, which have been solved numerically using the Matlab bvp4c function. A comparison is made with results available in the literature and found to be in good agreement. Results pertaining to the skin friction coefficient, Nusselt number, Sherwood number as well as the velocity, temperature and concentration profiles for selected values of parameters describing the model have been discussed.

Direct numerical simulation of transitional mixed convection flows: Viscous and inviscid instability mechanisms

Receptivity studies using direct numerical simulation require computations of equilibrium flow and its response to deterministic excitation. Equivalent flow problem, without heat interaction for zero-pressure gradient boundary layer, has been studied with respect to wall-excitation by a finite difference high accuracy method based on the solution of Navier-Stokes equation in Sengupta and Bhaumik [Phys. Rev. Lett.107, 154501 (2011)] and Sengupta et al. [Phys. Rev. E85, 026308 (2012)]. One of the key features of this study has been that the same methodology is used for computing the equilibrium flow and the disturbance field. Computation of equilibrium flow was performed by solving Navier-Stokes equation to include the leading edge of the plate, so that the effects of leading edge singularity and the growth of the boundary layer is included in the nonlinear framework. When the same methodology is attempted for mixed convection flows past horizontal plate (with Boussinesq approximation to model heat transfer effects) some of the equilibrium flow features could not be explained with linear viscous instability theory results. For horizontal hot flat plate with adiabatic wall conditions, the equilibrium flow could be computed and its receptivity could be correlated with linear spatial theory for lower buoyancy parameter. Here, we focus on receptivity of mixed convection flows to wall excitation for the following cases which do not allow computing the equilibrium flows from the solution of Navier-Stokes equation: (i) Aadiabatic horizontal flat plate cooled significantly at the leading edge only and (ii) strongly heated isothermal wedge flow for a wedge angle of 60°. The cold plate case is particularly interesting as the linear spatial theory indicates enhanced stabilization for higher magnitude of the buoyancy parameter. Results presented for the cold plate case indicates disturbance growth outside the shear layer. This prompted us to re-investigate various mechanisms of instability present for mixed convection flows. There is no definitive study for inviscid mechanism in this respect and the present effort not only fills this void, but also explains the relative roles of viscous and inviscid mechanisms for strong heat transfer effects, within the Boussinesq approximation.

Analytical Study of the Convection Heat Transfer From an Isothermal Wedge Surface to Fluids

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

Analytic study of magnetohydrodynamic flow and boundary layer control over a wedge

A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter 5m and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.

Influence of radiation on mixed convection over a wedge in non-Darcy porous medium

The influences of radiation on mixed convection flow of an optically dense viscous fluid along an isothermal wedge embedded in non-Darcy porous medium, in the presence of heat source/sink are numerically investigated. The entire mixed convection regime is covered by a single parameter χ from the pure free convection limit (χ=0) to the pure forced convection limit (χ=1). Forchheimer’s extension is employed to describe the fluid flow in the porous medium and the Rosseland diffusion approximation is considered to describe the radiative heat flux in the energy equation. The governing equations, including internal heat source/sink, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by the Keller box method. The effect of the radiation parameter, mixed convection parameter, Forchheimer number and heat source/sink parameter on the velocity and temperature profiles as well as on the local Nusselt number is presented and analyzed. The results are compared with those known from the literature and excellent agreement between the results is obtained.

Stability of mixed-convection boundary-layer flow on a porous wedge

A theoretical analysis is presented of the stability characteristics of laminar forced–free mixed-convection boundary-layer flow past an isothermal wedge with uniform suction or injection. The nonsimilar boundary-layer equations for the basic steady flow are solved numerically with a difference-differential scheme in combination with an iterative method for solving the resulting ordinary differential equations. The disturbance equations are then solved numerically on the basis of linear stability theory. The neutral stability curves and the disturbance amplitude of the velocity component and of the temperature are presented graphically for values of the buoyancy parameter ζ, the pressure-gradient parameter m, and the suction/injection parameter X. The results indicate the important role of the suction/injection parameter on the characteristics of both basic flow and disturbance flow. PACS No.: 47.20.–k

Turbulent film condensation on a vertical wedge

The present paper develops for the study of turbulent film condensation on a vertical wedge plate. It begins by considering the case of vapour flow past an isothermal wedge. Potential flow theory is used to determine the high tangential velocity of the vapour, and the Colburn analogy is used to define the local liquid–vapour interfacial shear which occurs when the high velocity vapour flows across the wedge surface. The paper then presents a discussion of the results obtained for the local dimensionless film thickness and heat transfer characteristics. Finally, the results developed in this study are compared with those generated by previous theoretical results.

Effect of radiation on the flow and heat transfer over a wedge with variable viscosity

A boundary layer analysis is presented to investigate numerically the effect of radiation on flow of an optically dense viscous fluid and heat transfer over an isothermal wedge in this paper. The similar governing equations are obtained by using a suitable transformation and solved by Runge–Kutta method. Numerical results for the dimensionless velocity profiles, the dimensionless temperature profiles, the local friction coefficient and local Nusselt number are graphically presented for different values of the radiation parameter R *, surface temperature parameter θ w and viscosity/temperature parameter θ r. It is shown that increasing θ r and R * tends to increasing the local Nusselt number and local friction coefficient.

Radiation Effect on Mixed Convection over an Isothermal Wedge in Porous Media: The Entire Regime

Numerical solutions are presented for the effect of radiation on mixed-convection flow of optically dense viscous fluids about an isothermal wedge embedded in a saturated porous medium. The partial differential equations are transformed into the nonsimilar boundary-layer equations, which are solved by the Keller box method. Numerical results for the dimensionless temperature profiles and the local Nusselt number parameter are presented for the combined convection parameter X, the wedge angle parameter A, the radiation-conduction parameter R d , and the surface temperature parameter H. The entire regime of the mixed convection is included, when X varies from 0 (pure free convection) to 1 (pure forced convection). As X varies from 0 to 1, the variation of the local Nusselt number parameter has the phenomenon of minimum. As the wedge angle parameter λ increases, the local Nusselt number parameter increases. When the radiation effect becomes significant (for the case of large values of R d and H), the local Nusselt number parameter is also greatly increased

Magnetohydrodynamic free convection flow over a wedge in the presence of a transverse magnetic field

This paper presents the main results of a theoretical study focusing on the effects of a uniform magnetic field on the free convection flow of an electrically conducting fluid past an isothermal wedge. A very efficient numerical method has been used to solve the non-similar boundary layer equations. A range of values for the magnetic field parameter, wedge angle parameter and Prandtl number were considered. Flow and heat transfer characteristics are presented and discussed.

Impingement heat transfer from wedge surface

An experimental investigation is made to study the heat transfer characteristics of slot jet impingement on a wedge whose included angle is 90°. Local and average heat transfer rates from the wedge surfaces have been measured. The experiments have been conducted with isothermal wedge surface at Reynolds numbers ranging from 5 680 to 16 600. The effects of varying the flow rate, width of the nozzle, distance of the wedge vertex from the nozzle exit, eccentricity of the wedge vertex to the jet axis on the flow properties of the fluid have been investigated. A correlation has been proposed considering the relevant dimensionless parameters and then compared with experimental data.

Heat transfer from an isothermal wedge in an air-water mist flow

An analysis has been made to investigate the influence of droplet trajectories and size distribution of polydisperse droplets on the heat transfer mechanism from an isothermal heated wedge put in air-water mist flow. To simplify the calculating process, an approximate calculation method with equivalent diameter theory is used. In the method, the equations of the water film flow have been solved by an integration method, while the equations of the gas flow have been solved by a finite difference method. The interface conditions between the water film and the gas layer have been determined by iterating the solutions of water and gas flows.

Numerical Solution of the Hypersonic Wake behind a Wedge

SummaryA numerical method which solves the time-dependent Navier-Stokes equations for plane, two-dimensional, compressible flow problems is presented. The method was applied to obtain the steady-state flow field about a flat-based 20° wedge at a free-stream Mach number of 6.05, a free-stream Reynolds number (based on the base height of the wedge) of 1.41 × 104, and a Prandtl number of 0.75. Two wedge surface temperature boundary conditions were investigated: adiabatic and isothermal walls. Convergence of the numerical solutions was demonstrated using two different finite-difference meshes. Numerical errors in the static pressure, velocity, and static temperature were generally less than 8 per cent in the wake of the body. Comparisons with experimental results and other independent theories were also made. For the isothermal wedge, calculated pressures on the surface of the body (including its base), static pressure profiles, pitot pressures profiles, and velocity profiles in the near wake were in agreement with corresponding experimental data. A comparison of static temperature profiles in the near wake of the isothermal wedge produced significant differences between numerical and experimental results near the wake shock. It was found that these differences could be explained in terms of uncertainties in the accuracy of the experimental measurements and thermal boundary conditions on the wedge surface. For the adiabatic wedge, the ramp boundary layer profiles and pressure distribution were in agreement with theoretical predictions coming from hypersonic interaction theory.

Combined forced and natural convection flow for the wedge geometry

This paper considers simultaneously the phenomena of forced and natural flow effects over an isothermal wedge. The analysis is restricted to situations in which the natural convection effects may be considered as a perturbation of the purely forced flow situation. Using this technique, a number of wedge angles are considered for laminar boundary-layer type flow. A Prandtl number of 0·73 was used and numerical results are presented for calculating surface shear and heat-transfer rates. Boundary-layer separation is also considered.