Values Of Local Nusselt Number Research Articles

MHD flow and heat transfer of couple stress fluid over an oscillatory stretching sheet with heat source/sink in porous medium

This article presents the MHD flow and heat transfer of a couple stress fluid over oscillatory stretching sheet embedded in a porous medium in the presence of heat source/sink. The unsteady flow problem is reduced to two coupled partial differential equations using dimensionless variables. Homotopy analysis method is employed to obtain the solution of these equations. Based on the solution of these equations an extensive analysis is performed to investigate the effects of various flow parameters on velocity and temperature fields, skin friction coefficient and Nusselt number. It is found that the presence of couple stress in viscous fluid increases the amplitude of oscillations in velocity and skin friction coefficient. It is also noticed that temperature increases by increasing heat source parameter. Moreover, the numerical values of local Nusselt number are calculated and shown in tabular form. It is found that the Nusselt number increases by increasing Prandtl number while it decreases by increasing couple stress parameter.

Experimental Analysis of Laminar Flow and Heat Transfer in Multi-Port Finned Mini-Channel

Due to their high heat transfer rate, small scale channels have been a popular area of study for the past three decades, especially for heat exchangers. In this study, fluid flow and heat transfer in a multi-port finned minichannel with a rectangular cross section was investigated experimentally under the constant heat flux boundary condition. The minichannel, which has a length of 638 mm, consists of 16 ports, 14 of which are identical finned rectangular channels with a width of 2.10 mm and a height of 5.85 mm while the remaining two ports at the outer edges of the channel were considered to be identical with the other ports. Deionized water was used as the working fluid with Reynolds number ranging between 75 and 190 in a single port. In order to correctly evaluate local heat transfer and friction coefficient values, thermal entrance effects and varying thermo-physical properties of the working fluid were taken into consideration throughout the study. Local Nusselt number varying with dimensionless axial thermal length, friction factor and average Nusselt number values varying with Reynolds number, and temperature distribution along the wall were evaluated to study fluid flow and heat transfer of the finned minichannel. The results were compared to theoretical values and presented graphically. Local Nusselt number values indicated fairly good agreement with theory while friction factor was overestimated. This was considered to be due to the effect of fins. In addition, three correlations were suggested in order to evaluate friction factor, local Nusselt number and average Nusselt number for the minichannel in given ranges of parameters. Keywords: Fin; Convective Heat Transfer; Laminar; Multi-Port; Nusselt Number DOI: 10.17350/HJSE19030000032 Full Text:

Three-dimensional flow of an elastico-viscous nanofluid with chemical reaction and magnetic field effects

Magnetohydrodynamic (MHD) three-dimensional flow of an elastico-viscous nanofluid under the influence of mass transfer and chemical reaction is studied. The flow is produced by a bidirectional stretching sheet. Effects of thermophoresis and Brownian motion are also present. In the presence of constant applied magnetic field, the fluid is electrically conducting. Using appropriate transformations, the governing nonlinear partial differential equations are converted into highly nonlinear coupled ordinary differential equations. Homotopy Analysis method (HAM) is employed to find the series solution of the acquired system of equations. h-curves have been drawn to discuss the convergence of HAM solution. Effects of velocity, temperature and concentration profiles on the emerging important parameters is portrayed and discussed graphically. Numerical values of local Nusselt number, skin friction and Sherwood number with different parameters are calculated and examined. It is observed that temperature profile increases and concentration profile decreases with increasing values of Brownian motion parameter Nb. It is also noticed that both velocity components decrease with an increase in viscoelastic parameter k.

Radiative Three-Dimensional Flow with Chemical Reaction

Abstract We discuss the three-dimensional boundary layer flow of Maxwell nanofluid in the present article. The flow is caused due to bidirectional stretching surface. An applied magnetic field is taken into account. Heat and mass transfer characteristics are considered in the presence of thermal radiation, Brownian motion, thermophoresis and chemical reaction effects. Mathematical modelling is made under a low magnetic Reynolds number and Rosseland’s approximation. Expressions of series solutions for velocities, temperature and concentration are developed. Impacts of influential parameters on the temperature and concentration are sketched and examined. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. We found that an increase in thermophoresis and Brownian motion parameters enhanced the temperature field and thermal boundary layer thickness. The concentration field reduced gradually when we enhance the values of Lewis number and chemical reaction parameter. The values of local Nusselt number are higher for a larger radiation parameter.

Magnetohydrodynamic (MHD) mixed convection stagnation point flow of a nanofluid over a vertical plate with viscous dissipation

In this study, magnetohydrodynamic effects on the mixed convection flow of nanofluid particles, namely, Cu (copper) and Al2O3 (alumina) near a stagnation region over a vertical plate in the presence of viscous dissipation is investigated. The governing equations of the nanofluid flow model proposed by Tiwari and Das (Int. J. Heat Mass Transfer, 50, 2002 (2007). doi:10.1016/j.ijheatmasstransfer.2006.09.034) are converted into a dimensionless nonlinear system of ordinary differential equations by using the similarity transformation. The solution of the resulting equations is obtained numerically by using a very efficient implicit scheme known as the Keller box method. A comparison with previous studies is shown in tabular form and excellent agreement is found. The effects of pertinent parameters like magnetic parameter M, Eckert number Ec, and volume fraction parameter ϕ on velocity, temperature, skin friction coefficient, and local Nusselt number with fixed value of Prandtl number Pr = 6.2 are shown graphically and discussed. These results show that the skin friction coefficient increases for both nanoparticles in assisting and opposing flow cases because of increasing absolute values of M and Ec, on the other hand heat transfer rate is enhanced in the opposing flow case and reduced in the assisting flow case. The values of skin friction coefficient for both nanoparticles, namely, Cu and Al2O3 increase with the increase in volume fraction parameter ϕ in both assisting and opposing flow cases and Cu has a higher value than Al2O3. The same behavior is observed for local Nusselt number in opposing flow, but in assisting flow the value of local Nusselt number decreases with the increase of ϕ in the presence of magnetic and viscous dissipation effects and Cu has a smaller value than Al2O3.

Three-Dimensional Flow of Jeffrey Nanofluid with a New Mass Flux Condition

AbstractThe three-dimensional (3D) boundary layer flow of Jeffrey nanofluid subject to the convective boundary condition is analyzed. The flow is induced by a bidirectional stretching surface. Effects of thermophoresis and Brownian motion are considered. Newly developed boundary condition with the zero nanoparticles mass flux is employed. Mathematical modeling is made under boundary layer approach. Similarity variables are used to convert the governing partial differential equations into the nonlinear ordinary differential equations. The resulting nonlinear ordinary differential equations have been solved for the velocities, temperature, and nanoparticles concentration. Graphs are plotted to examine the influence of various physical parameters on the dimensionless temperature and nanoparticles concentration distributions. Numerical values of local Nusselt number are tabulated and discussed. It is found that the effects of the Biot number on the temperature and nanoparticles concentration are quite similar...

Flow of Burgers’ fluid over an inclined stretching sheet with heat and mass transfer

Effects of heat and mass transfer in the flow of Burgers fluid over an inclined sheet are discussed. Problems formulation and relevant analysis are given in the presence of thermal radiation and non-uniform heat source/sink. Thermal conductivity is taken temperature dependent. The nonlinear partial differential equations are simplified using boundary layer approximations. The resultant nonlinear ordinary differential equations are solved for the series solutions. The convergence of series solutions is obtained by plotting the ħ -curves for the velocity, temperature and concentration fields. Results of this work describe the role of different physical parameters involved in the problem. The Deborah numbers corresponding to relaxation time (β1 and β2) and angle of inclination (α) decrease the fluid velocity and concentration field. Concentration field decays as Deborah numbers corresponding to retardation time (β3) and mixed convection parameter (G) increase. Large values of heat generation/absorption parameters A/B, and the temperature distribution across the boundary layer increase. Numerical values of local Nusselt number, −θ′(0), and local Sherwood number, −ϕ′(0), are computed and analyzed. It is found that θ′(0) increases with an increase in β3.

Interaction of magnetic field in flow of Maxwell nanofluid with convective effect

Magnetohydrodynamic (MHD) three-dimensional flow of Maxwell nanofluid subject to the convective boundary condition is investigated. The flow is generated by a bidirectional stretching surface. Thermophoresis and Brownian motion effects are present. Fluid is electrically conducted in the presence of a constant applied magnetic field. Unlike the previous cases even in the absence of nanoparticles, the correct formulation for the flow of Maxwell fluid in the presence of a magnetic field is established. Newly proposed boundary condition with the zero nanoparticles mass flux at the boundary is employed. The governing nonlinear boundary layer equations through appropriate transformations are reduced in the nonlinear ordinary differential system. The resulting nonlinear system has been solved for the velocities, temperature and nanoparticles concentration distributions. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt number are computed and analyzed. It is observed that the effects of magnetic parameter and the Biot number on the temperature and nanoparticles concentration are quite similar. Both the temperature and nanoparticles concentration are enhanced for the increasing value of magnetic parameter and Biot number.

Natural convection heat transfer under constant heat flux wall in a nanofluid filled annulus enclosure

In this investigation, the Control Volume based Finite Element Method (CVFEM) is used to simulate the natural convection heat transfer of Cu–water nanofluid in an annulus enclosure. The Maxwell–Garnetts (MG) and Brinkman models are also employed to estimate the effect of thermal conductivity and viscosity of nanofluid. The governing parameters are the Rayleigh number, nanoparticle volume fraction and the aspect ratio (ratio of the outer radius to the inner one). Results are presented in the form of isotherms, streamlines, local and average Nusselt numbers. The results indicate that increment of the aspect ratio increases the value of average Nusselt number. Moreover, the angle of turn for the boundary condition of the inner cylinder significantly affects the values of local Nusselt number, average Nusselt number, streamlines and isotherms.

MHD three dimensional flow of viscoelastic fluid with thermal radiation and variable thermal conductivity

The objective of the present work is to model the magnetohydrodynamic (MHD) three dimensional flow of viscoelastic fluid passing a stretching surface. Heat transfer analysis is carried out in the presence of variable thermal conductivity and thermal radiation. Arising nonlinear analysis for velocity and temperature is computed. Discussion to importantly involved parameters through plots is presented. Comparison between present and previous limiting solutions is shown. Numerical values of local Nusselt number are computed and analyzed. It can be observed that the effects of viscoelastic parameter and Hartman number on the temperature profile are similar in a qualitative way. The variations in temperature are more pronounced for viscoelastic parameter K in comparison to the Hartman number M. The parameters N and ɛ give rise to the temperature. It is interesting to note that values of local Nusselt number are smaller for the larger values of ɛ.

Profile shape optimization in multi-jet impingement cooling of dimpled topologies for local heat transfer enhancement

The present study deals with shape optimization of dimples on the target surface in multi-jet impingement heat transfer. Bezier polynomial formulation is incorporated to generate profile shapes for the dimple profile generation and a multi-objective optimization is performed. The optimized dimple shape exhibits higher local Nusselt number values compared to the reference hemispherical dimpled plate optimized shape which can be used to alleviate local temperature hot spots on target surface.

Numerical investigation of twin-jet impingement with hybrid-type turbulence modeling

A Computational Fluid Dynamics (CFD) study of a twin-jet impingement is performed using the Reynolds-Averaged Navier–Stokes (RANS) approach with a dynamic Smagorinsky Large Eddy Simulation (LES). The use of a hybrid RANS–LES (i.e., part of the turbulence is modeled and part of the turbulence is resolved) method potentially offers a compromise between the computational efficiency and the accuracy comparable with that of a pure dynamic LES. In the current study, the SST–SAS (Shear-Stress transport with Scale-Adapted Simulation) k–ω model having hybrid RANS–LES characteristics is utilized for turbulence modeling. Effects of nozzle-to-plate (H/D) and nozzle-to-nozzle (L/D) distances on the pressure distribution and the heat transfer are investigated for 3 × 104 < Re < 5 × 104. Numerical results of SST–SAS and dynamic LES methods are validated against available experimental data. The flow expands radially as H/D increases. Results show that the SST–SAS model can produce fairly accurate results, especially with a lower H/D at which the sub-atmospheric region appears. In addition, the SST–SAS model is capable of predicting the peak values of local Nusselt number at correct locations.

Three-dimensional stretched flow via convective boundary condition and heat generation/absorption

Purpose – The purpose of this paper is to investigate the three-dimensional flow of viscous fluid with convective boundary conditions and heat generation/absorption. Design/methodology/approach – The governing partial differential equations are reduced into ordinary differential equations by applying similarity transformations. Series solutions of velocity and temperature are found by adopting homotopy analysis method (HAM). Findings – The authors found that an increase in ratio parameter and Hartman number increased the values of skin-friction coefficient, but the values of local Nusselt number are reduced with an increase in Hartman number. Practical implications – The present study is a useful source of information for the investigators in the fields of Newtonian fluids and heat transfer. The results obtained are specifically important in processes of polymer industry and metallurgical. Originality/value – Very scarce literature is available on three-dimensional stretched flow with convective boundary conditions. Mathematical modelling for such flow in regime of magnetohydrodynamics is a main concern here. Performed computations to the resulting nonlinear analysis further enhance its novelty.

On Mixed Convection Stagnation Point Flow of Second Grade Fluid with Convective Boundary Condition and Thermal Radiation

Abstract This work focuses on the mixed convection stagnation point flow subject to the convective boundary conditions. Mathematical formulation involves the constitutive equations of thermodynamic second grade fluid. Analysis has been performed when thermal radiation effect is present. Nonlinear flow analysis is computed for the homotopic solutions in the series forms. Behaviors of different arising physical parameters are examined. Numerical values of local Nusselt number are given and analyzed.

NATURAL CONVECTION HEAT TRANSFER INSIDE VERTICAL AND INCLINED OPEN ENDED EQUILATERAL TRIANGULAR CHANNELS

Experimental study of natural convection heat transfer inside smooth and rough surfaces of vertical and inclined equilateral triangular channels of different inclination angles with a uniformly heated surface are performed. The inclination angle is changed from 15o to 90o. Smooth and rough surface of average roughness (0.02mm) are used and their effect on the heat transfer characteristics are studied. The local and average heat transfer coefficients and Nusselt number are obtained for smooth and rough channels at different heat flux values, different inclination angles and different Rayleigh numbers (Ra) 6.48 × 105 ≤ Ra ≤ 4.78 × 106. The results show that the local Nusselt number decreases with increase of axial distance from the lower end of the triangular channel to a point near the upper end of channel, and then, it slightly increases. Higher values of local Nusselt number for rough channel along the axial distance compared with the smooth channel. The average Nusselt number of rough channel is higher than that of smooth channel by about 8.1% for inclined case at θ = 45o and 10% for vertical case. The results obtained are correlated using dimensionless groups for both rough and smooth surfaces of the inclined and vertical triangular channels.

Boundary layer flow of Maxwell fluid with power law heat flux and heat source

Purpose – The purpose of this paper is to investigate the two-dimensional flow of Maxwell fluid with power law heat flux and heat source over a stretched surface. Design/methodology/approach – The governing partial differential equations are reduced into ordinary differential equations by applying similarity transformations. Series solutions of velocity and temperature are found by adopting homotopy analysis method (HAM). Findings – It is found that the velocity decreases by increasing Deborah number and suction parameter. It is also observed that the heat generation parameter leads to a decrease in temperature. Furthermore, the numerical values of local Nusselt number decreased with an increase in Deborah number. Practical implications – A useful source of information for the investigators on the field of non-Newtonian fluids with heat transfer. Originality/value – This paper discusses the boundary layer flow of Maxwell fluid with power law heat flux in the presence of heat source.

Variational formulation on Joule heating in combined electroosmotic and pressure driven microflows

The present study attempts to analyze the extended Graetz problem in combined electroosmotic and pressure driven flows in rectangular microchannels, by employing a variational formulation. Both the Joule heating and axial conduction effects are taken into consideration. Since assuming a uniform inlet temperature profile is not consistent with the existence of these effects, a step change in wall temperature is considered to represent physically conceivable thermal entrance conditions. The method of analysis considered here is primarily analytical, in which series solutions are presented for the electrical potential, velocity, and temperature. For general treatment of the eigenvalue problem associated with the solution of the thermal field, an approximate solution methodology based on the variational calculus is employed. An analytical solution is also presented by considering thin electrical double layer limits. The results reveal non-monotonic behaviors of the Nusselt number such as the occurrence of singularities in the local Nusselt number values when the fluid is being heated from the wall. Moreover, the effect of increasing the channel aspect ratio is found to be increasing both the temperature difference between the wall and the bulk flow and the Nusselt number. In addition, higher wall heat fluxes are obtained in the entrance region by increasing the Peclet number.

Mixed Convection Radiative Flow of Maxwell Fluid Near a Stagnation Point with Convective Condition

AbstractEffects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed. Mathematical modeling is based upon constitutive equations of an incompressible Maxwell fluid. Nonlinear analysis is presented through implementation of homotopy analysis method. Numerical values of Local Nusselt number is computed and analyzed.

Natural convection heat transfer in a nanofluid filled semi-annulus enclosure

To investigate natural convection heat transfer in a semi-annulus enclosure filled with nanofluid, the Control Volume based Finite Element Method (CVFEM) is used. The fluid in the enclosure is Cu–water nanofluid. The inner and outer semi circular walls are maintained at constant temperatures while the two other walls are thermally insulated. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern and isotherms. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and the angle of turn for the enclosure. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The results reveal that there is an optimum angle of turn in which the average Nusselt number is maximum for each Rayleigh number. Moreover, the angle of turn has an important effect on the streamlines, isotherms and maximum or minimum values of local Nusselt number.

Experimental investigation of natural convection heat transfer in narrow vertical rectangular channel heated from both sides

The heat transfer characteristics of the natural convection regime through a vertical rectangular channel simulating a cooling channel of typical material testing reactor have been experimentally investigated. Experiments are performed on demineralized water as coolant passing under atmospheric pressure through narrow rectangular channel of 80 cm length, 7 cm width and 2.7 mm gap thickness under different heat fluxes ranging from 2.7 kW/m 2 to 26.8 kW/m 2 that covers almost all possible heat fluxes in the single-phase liquid. The measured local Nusselt number values are compared with the predictions of two correlations for both natural and combined natural and forced convection regimes respectively. The comparison shows the need for developing new correlation to represent the obtained experimental results and to be utilized for the prediction of the local Nusselt number in thermal–hydraulics and safety analysis of the reactor. The developed correlation fits the experimental data within 5.8% relative standard deviation.