Local Nusselt Number Decrease Research Articles

Similarity solution of fractional viscoelastic magnetohydrodynamic fluid flow over a permeable stretching sheet with suction/injection

A novel easy‐to‐use similarity technique for spatial fractional partial differential equations is introduced to solve the flow and heat transfer of fractional viscoelastic magnetohydrodynamic (MHD) fluid over a permeable stretching sheet. The proposed method represents a new technique for deriving similarity transformations, which allows the conversion of the fractional partial differential equations to fractional ordinary differential equations. Moreover, using the Grünwald–Letnikov formula, the fourth‐order Runge–Kutta method is adopted here to solve the obtained similarity equations, using the shooting method. The transformed governing equations were found to be dependent on six physical parameters, namely, fractional parameter, magnetic field parameter, generalized local Reynolds number, generalized Prandtl number, the wall suction/injection parameter, and the wall stretching exponential. The results reveal that maximums of the skin friction coefficient and local Nusselt number are obtained for fractional‐order derivative of about 0.5. Moreover, application of a magnetic field on electrically conducting fractional fluid thins the velocity boundary layer and thickens the thermal boundary layer; therefore, the skin friction coefficient increases whereas the local Nusselt number decreases. Furthermore, an increase in any parameters of the local Reynolds number, suction parameter, or the wall stretching exponential leads to thinner boundary layers and higher values of skin friction coefficient and local Nusselt number, whereas imposing injection has opposite effects. Finally, increasing the generalized Prandtl number leads to a thinner thermal boundary layer and higher local Nusselt number for the fractional viscoelastic fluid. It would be of interest to extend the proposed method to other practical problems in the same field.

Numerical investigation on forced, natural, and mixed convective heat transfer of n-decane in laminar flow at supercritical pressures

The present study numerically investigates the forced, natural, and mixed convective heat transfer characteristics of supercritical n-decane in a tube in laminar flow, focusing on the law of mutual coupling of forced and natural convection in mixed convection. Effects of heat flux (100 W/m2–8000 W/m2) and flow direction on heat transfer are investigated. For forced convection, deterioration occurs when the wall temperature reaches the pseudo-critical temperature and the local Nusselt number decreases by up to 17.4% compared to the theoretical value at the heat flux of 2400 W/m2. For natural convection, heat transfer is continuously enhanced with the increase of heat flux. For mixed convection in upward flow, heat transfer is enhanced by the buoyancy of increasing the fluid velocity gradient near the wall. As for the downward flow, buoyancy illustrates the opposite effects. Based on numerical simulation results, the Nusselt number correlations are proposed for forced and natural convection respectively and the correlation for mixed convection is modeled employing a function of the forced and natural convection.

Analysis of thermal radiation in magneto-hydrodynamic motile gyrotactic micro-organisms flow comprising tiny nanoparticle towards a nonlinear surface with velocity slip

This study investigates 2D bioconvection magneto-hydrodynamic (MHD) flow and heat transfer of the non-Newtonian (Casson) nanofluid model. The phenomenon of Brownian motion and thermophoresis containing gyrotactic microorganisms over a nonlinear surface is demonstrated pictorially under the simultaneous impact of thermal radiation and velocity slip. Herein, the flow is electrically conducting where different cases and the effect of convergence parameters such as chemical reactions and heat generation/absorption are studied. The transformed ODEs are tackled numerically by employing the Bvp4c scheme. This method contains three-stage Lobatto IIIa collocation formula that provides continuous solutions up to fifth-order accuracy. The salient features of relevant flow parameters are illustrated through tables and graphs, and the current results are compared with the previous ones, which claim considerable agreement. The main finding reveals an increase in the thermophoresis parameter (Nt) and radiation (R) parameters, uprising the temperature profile which leads to enhancement in the thermal boundary layer. Also, the impact of the magnetic parameter (M) shows decrement in the velocity profile because there exists a Lorentz force that suppresses fluid motion. The friction factor and local Nusselt number decrease for higher values of the Casson parameter (β), whereas increment is illustrated for the suction parameter (S).

The Impingement Flow Study on The Temperature Profile Perforated Plate

This paper presents the impingement flow study on the temperature profile perforated plate. Icing is one of the most hazardous threats in aviation and this leads to unsafe flight conditions. Hence, thermal anti-Icing is very much useful in aircraft to prevent ice accretion on the surface. On the other hand, the hotspot temperature of this technique might destroy the Aluminum-based Bias Acoustic Liner (BAL) plate. Thus, it is highly essential to study the hotspot temperature profile on the perforated plate. This study is concerned with a numerical study of the convective heat exchange between an impinging air jet at temperatures of 70 °C and a structured perforated surface using the Fluent tool. The model is designed in an Aluminium plate with the dimensions of 100 mm x 100 mm x 1mm containing 0.15 cm diameter perforated hole. In addition, the 0.25 cm diameter circular nozzle is maintained at a constant jet-to-target distance of 3.71 cm. In this sense, the standard k-ω turbulence model jet equation is applied to this three-dimensional domain with periodic boundary conditions for the Reynolds numbers ranges from 2000–9000. The simulations are performed based on the gap between two holes and the hole configuration (tandem and staggered) at different jet velocities. The simulation results reveal that there is a rapid increment in heat transfer with Reynolds number and the maximum local Nusselt number decreases by seven and increases to 24 when the Reynolds number varies from 2508.17 to 8778.588 at the surface of the perforated plate. The findings of the hole arrangement on the perforated plate indicate that the tandem hole configuration without a center hole is highly recommended for bias acoustic liners than the staggered configuration. Since the tandem hole arrangement has higher dimensionless temperature, a thicker high temperature layer will be developed at the outer surface. Hence, this kind of perforated plate is more suitable to prevent ice accretion in aircraft applications.

Soret & Dufour and Triple Stratification Effect on MHD Flow with Velocity Slip towards a Stretching Cylinder

The phenomenon of convective flow with heat and mass transfer has been studied extensively due to its applications in various fields. The effects of nonlinear thermal radiation (NLTR), slip, thermal-diffusion (Soret) and diffusion-thermo (Dufour) on magenoto-hydrodynamic (MHD) flow towards a stretching cylinder in the presence of triple stratification (TSF) are investigated in this paper. The governing equations are transformed into an ODE by suitable transformations. The homotopy analysis method (HAM) is used to solve the ODE. The revamping of fluid flow, and heat transfer due to the presence of the Soret and Dufour effect, concentration slip and concentration stratification are analyzed. The temperature and local Sherwood number increases as the Dufour number rises, whereas the local Nusselt number decreases. While elevating the Soret number, the Sherwood number diminishes, whereas the concentration profile rises. The thermal boundary layer thickness enhances when thermal radiation increases. The rate of solute transport reduces while the concentration slip increases.

The Method of Lines Analysis of Heat Transfer of Ostwald-de Waele Fluid Generated by a Non-uniform Rotating Disk with a Variable Thickness

In this article, it is aimed to address one of Ostwald-de Waele fluid problems that either, has not been addressed or very little focused on. Considering the impacts of heat involving in the Non-Newtonian flow, a variant thickness of the disk is additionally considered which is governed by the relation z = a (r/RO+1)-m. The rotating Non-Newtonian flow dynamics are represented by the system of highly nonlinear coupled partial differential equations. To seek a formidable solution of this nonlinear phenomenon, the application of the method of lines using von Karman’s transformation is implemented to reduce the given PDEs into a system of nonlinear coupled ordinary differential equations. A numerical solution is considered as the ultimate option, for such nonlinear flow problems, both closed-form solution and an analytical solution are hard to come by. The method of lines scheme is preferred to obtain the desired solution which is found to be more reliable and in accordance with the required physical expectation. Eventually, some new marvels are found. Results indicate that, unlike the flat rotating disk, the local radial skin friction coefficients and tangential decrease with the fluid physical power-law exponent increases, the peak in the radial velocity rises which is significantly distinct from the results of a power-law fluid over a flat rotating disk. The local radial skin friction coefficient increases as the disk thickness index increases, while local tangential skin friction coefficient decreases, the local Nusselt number decrease, both the thickness of the velocity and temperature boundary layer increase.

Effect of nonlinear thermal radiation on double-diffusive mixed convection boundary layer flow of viscoelastic nanofluid over a stretching sheet

BackgroundThe present exploration deliberates the effect of nonlinear thermal radiation on double diffusive free convective boundary layer flow of a viscoelastic nanofluid over a stretching sheet. Fluid is assumed to be electrically conducting in the presence of applied magnetic field. In this model, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of convection features of the nanofluid. Entire different concept of nonlinear thermal radiation is utilized in the heat transfer process.MethodsAppropriate similarity transformations reduce the nonlinear partial differential system to ordinary differential system which is then solved numerically by using the Runge–Kutta–Fehlberg method with the help of shooting technique. Validation of the current method is proved by having compared with the preexisting results with limiting solution.ResultsThe effect of pertinent parameters on the velocity, temperature, solute concentration and nano particles concentration profiles are depicted graphically with some relevant discussion and tabulated result.ConclusionsIt is found that the effect of nanoparticle volume fraction and nonlinear thermal radiation stabilizes the thermal boundary layer growth. Also it was found that as the Brownian motion parameter increases, the local Nusselt number decreases, while the local friction factor coefficient and local Sherwood number increase.

Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.

Flow and heat transfer of Ostwald-de Waele fluid over a variable thickness rotating disk with index decreasing

This paper investigates the flow and heat transfer of Ostwald-de Waele fluid over a variable thickness rotating disk with style of z=a (r/R0+1)−m. Boundary layer governing partial equations are reduced to a set of semi-similarity ordinary differential equations by modified local von Kármán’s transformation and then solved by Runge–Kutta method coupled with multi-shooting technique. The effects of involved parameters (Ostwald-de Waele fluid physical power law exponent, disk thickness index, Prandtl number) on velocity and temperature fields, local skin friction coefficient and Nusselt number are presented graphically. Some new phenomena are found. Results indicate that, unlike the flat rotating disk, the local radial skin friction coefficients and tangential decrease with the fluid physical power law exponent increases, the peak in the radial velocity rises which is significantly distinct from the results of a power-law fluid over a flat rotating disk. As disk thickness index m increases, the local radial skin friction coefficient increases while local tangential skin friction coefficient decreases, the local Nusselt number decrease, both the thickness of velocity and temperature boundary layer increase.

MHD convective heat transfer with temperature-dependent viscosity and thermal conductivity: a numerical investigation

This paper considers numerical solutions to magneto hydrodynamics convective heat transfer over a permeable stretching wedge with thermal radiation and ohmic heating. Both the viscosity and thermal conductivity are assumed to vary as a linear function of the temperature, and dynamic viscosity is considered in a new form. Using an appropriate transformation, the governing partial differential equations are transformed into ordinary differential equations. Numerical solutions to these equations subject to corresponding boundary conditions are obtained by efficient numerical shooting technique coupled with Runge–Kutta–Fehlberg scheme. The effects of pertinent parameters are shown through tables and graphs, and meanwhile the associated transfer characteristics are analyzed in detail. The results show that: with the increase of viscosity variation parameter or the thermal conductivity, the local skin-friction coefficient increases but the local Nusselt number decreases. The increasing in viscosity variation parameter is to increase the velocity boundary layer thickness and decrease in the magnitude of the velocity gradient. Furthermore, thermal conductivity parameter has the same effect on the thermal boundary layer thickness and the temperature gradient.

Effect of radiation on heat and mass transfer of fluid flow across a horizontal cylinder

The free convective boundary layer flow, heat and mass transfer across an isothermal cylinder in the diffusing species is investigated. The partial differential conservation equations are non-dimensionalized and solved numerically by using an implicit iterative tridiagonal finite-difference method. The effects of radiation parameters on dimensionless velocity, temperature and species concentration distributions are studied, for the case of water (Pr = 7.0), concentration is slightly affected by radiation parameter; Temperatures are however increased by an increase in radiation parameter. Furthermore, the local skin friction, local Nusselt number and local Sherwood number have been analyzed for various parametric conditions. It is found that as the thermal radiation parameter increases the skin-friction coefficient increases and the local Nusselt number decreases. Excellent agreement is obtained with the earlier studies for the purely fluid.

Natural Convective Boundary Layer Flow of Nanofluids Above an Isothermal Horizontal Plate

The natural convective boundary layer flow of a nanofluid over an isothermal horizontal plate is studied analytically. The model used for the nanofluid accounts for the effects of Brownian motion and thermophoresis. The analysis shows that the velocity, temperature, and nanoparticle volume fraction profiles in the respective boundary layers depend not only on the Prandtl number (Pr) and Lewis number (Le) but also on three additional dimensionless parameters: the Brownian motion parameter Nb, the buoyancy ratio parameter Nr and the thermophoresis parameter Nt. The velocity, temperature, and nanoparticle volume fraction profiles for the nanofluid are found to have a weak dependence on the values of Nb, Nr, and Nt. The effect of the above-mentioned parameters on the local skin-friction coefficient and Nusselt number has been studied extensively. It has been observed that as Nr increases, the local skin-friction coefficient decreases whereas local Nusselt number remains almost constant. As Nb or Nt increases, the local skin-friction coefficient increases whereas the local Nusselt number decreases.

Effects of chemical reaction and thermal radiation on unsteady double diffusive convection

Purpose – The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects. Design/methodology/approach – In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled. Findings – Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase. Originality/value – The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.

Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t* >= 5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state. (C) 2010 Elsevier Ltd. All rights reserved.

Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet

We consider the steady state, viscous, incompressible two-dimensional magneto hydrodynamic flow of an electrically conducting power law fluid over a vertical stretching sheet. The stretching of the surface velocity and the prescribed surface temperature are assumed to vary linearly with the distance from the slit. The coupled partial differential equations governing the flow and heat transfer are transformed into non-linear coupled ordinary differential equations by a similarity transformation. The transformed boundary layer equations are solved numerically by Keller-Box method for several sets of values of the parameters governing the flow and heat transfer. The flow and heat transfer characteristics are analysed and discussed for different values of the parameters. We observe that the local skin friction coefficient and the local Nusselt number decrease as the magnetic parameter Mn increase for fixed value of the buoyancy parameter λ. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

Transient Mixed Convection Flow of A Second-Grade Visco-Elastic Fluid over a Vertical Surface

The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement.

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet

An analysis is made for the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching vertical sheet in its own plane. The stretching velocity, the surface temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The transformed boundary layer equations are solved numerically for some values of the involved parameters, namely the magnetic parameter M, the velocity exponent parameter m, the temperature exponent parameter n and the buoyancy parameter λ, while the Prandtl number Pr is fixed, namely Pr = 1, using a finite difference scheme known as the Keller-box method. Similarity solutions are obtained in the presence of the buoyancy force if n = 2m−1. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M increases for fixed λ and m. For m = 0.2 (i.e. n = −0.6), although the sheet and the fluid are at different temperatures, there is no local heat transfer at the surface of the sheet except at the singular point of the origin (fixed point).

Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet

An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation-point. Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent.

Viscous dissipation and Joule heating effects on MHD-free convection from a vertical plate with power-law variation in surface temperature in the presence of Hall and ion-slip currents

An analysis is presented to study the effects of viscous dissipation and Joule heating on MHD-free convection flow past a semi-infinite vertical flat plate in the presence of the combined effect of Hall and ion-slip currents for the case of power-law variation of the wall temperature. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. The governing differential equations are transformed by introducing proper non-similarity variables and solved numerically. The effects of various parameters on the velocity and temperature profiles as well as the local wall shear stresses and the local Nusselt number are presented graphically and in tabular form. It is found that the magnetic field acts as a retarding force on the tangential flow but has a propelling effect on the induced lateral flow. The skin-friction factor for the tangential flow and the local Nusselt number decrease but the skin-friction factor for the lateral flow increases as the magnetic field increases. The skin-friction factor for the tangential and lateral flows are increased while the local Nusselt number is decreased if the effect of viscous dissipation, Joule heating and heat generation are considered. The opposite trend was observed as the temperature power coefficient n is increased. Also, the skin-friction factor for the tangential flow and the local Nusselt number are increased due to the Hall and ion-slip currents, whereas the skin-friction factor for the tangential flow increases when Hall values increase to one and decreases for values of Hall greater than one, but reduces by rising ion-slip values.