Results For Local Nusselt Number Research Articles

NUMERICAL STUDY FOR A THREE DIMENSIONAL LAMINAR NATURAL CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL HEATED HORIZONTAL AND INCLINED SQUARE PLATE AND WITH A CIRCULAR HOLE

A theoretical study for a three-dimensional natural convection heat transfer from an isothermal horizontal , vertical and inclined heated square flat plates (with and without circular hole) has been done in the present work. The study involved the numerical solution of the transient Navier-Stokes and energy equations by using finite deference method (F.D.M.). The complete Navier-Stokes equation are transformed and expressed in terms of vorticity-vector potential. The Energy and Vorticity equations were solved by using an Alternating Direction Implicit (ADI) method because they are transient equations of parabolic portion, and the Vector potential is solved by using an equations Successive Over-Relaxation (S.O.R) method because it is from elliptic portion. The numerical solution is capable of calculating the Vector potential, three components of Vorticity and temperature field of the calculation domain. The numerical results were obtained in rang of Grashof number (103≤Gr≤5x104 ) with Prandtl number of (0.72) for square flat plate and the other consist a circle hole with ratio 0.6 and 0.8 diameter of the hole to main square side length. The numerical results showed that the main process of heat transfer is conduction for Grashof number less than 103 and convection for Grashof number larger than 103 and the results of local Nusselt number show fairly large dependence on inclination angle. For horizontal plate facing upward and downward, average Nusselt number is proportional to one-fifth power of Rayleigh number, and there is a significant difference in heat transfer rates between the upward and downward cases. For horizontal plate with circle hole facing upward for Grashof number 104 , the effect of core portion caused a limited increment in the heat transfer rate, where as for the facing downward case, the effect was larger and the maximum value of heat transfer rates is be for square flat plate with circle hole by ratio 0.6 for all inclination angles. With the increase of Grashof number to 5x104 heat transfer rates decrease except the square horizontal flat plate with circle hole by ratio 0.6 . The average Nusselt number increases with the increase of inclination of plates facing upward to reach to the higher average Nusselt number at vertical position then decrease with increase of inclination of plates. And the maximum value of average Nusselt number is depended on the ratio of diameter of the hole to main square side length, showed that the maximum temperature gradient occurs at the external edge of the horizontal plate (with and without circle hole) facing upward and at the lower external edge in inclined case. The numerical results was made through comparison with a previous numerical and experimental work, the agreement was good.

Dual Solution of Sisko Nanofluid Flow with Gyrotactic Microorganisms Over Stretching/Shrinking Sheet in Non-Darcy Porous Medium

The objective of this paper is to determine the dual solution of bioconvection Sisko nanofluid flow comprising gyrotactic micro-organism enclosed in a porous medium. The flow analysis is incorporated with the presence of Darcy–Forchhemier inertia effect, chemical reaction and magnetohydrodynamic flow over a non-linear stretching sheet. With regard to these assumptions the regulating non-linear partial differential equations for the fluid flow are drafted and turned into ordinary differential equations by means of relevant similarity transformation. Fifth order Runge–Kutta Felhberg method with shooting technique is applied to obtain numerical solution of the transformed ordinary differential equations. Graphs are sketched out to observe and interpret variation in velocity, temperature, nanoparticles concentration and density of micro-organism profiles for respective determining factors. Comparison of the obtained results for local Nusselt number with Prandtl number reveals commendable agreement with earlier reported results. Bioconvection Lewis number, Prandtl number, Peclet number and microorganism difference parameter for escalating values discloses a declining behaviour of motile micro-organism density distribution.

NUMERICAL INVESTIGATION OF MHD CASSON NANOFLUID FLOW TOWARDS A NON LINEAR STRETCHING SHEET IN PRESENCE OF DOUBLE-DIFFUSIVE EFFECTS ALONG WITH VISCOUS AND OHMIC DISSIPATION

The intention behind carrying out this research work is to analyze the steady Magnetohydrodynamic (MHD) boundary layer flow with Casson nanofluid in presence of Viscous and Ohmic dissipation effects towards a non-linear stretching sheet. Two phase representation of nanofluid studied the consequence of Brownian motion along with thermophoresis. The major purpose of study is to investigates the significant role of prominent fluid parameters especially yield stress, slip velocity, thermophoresis, Brownian motion, Eckert number, Schmidt number, magnetic parameter and non-linear stretching parameter on profile of velocity, temperature distribution and concentration while keeping the other parameters under study constant. Runge-Kutta Fehlberg (RKF) approach was adopted to numerically solve the non-linear governing equations and the linked boundary conditions by use of shooting technique. In present study, we use MATLAB for finding the final outcomes and relating the concluding results for local Nusselt number -θ_δ^' (0) with extant outcomes in literature as a limiting case in the absence of thermophoresis and Brownian motion and an excellent agreement is noted. Over all the consequence of prominent fluid parameters are explained via graphs, whereas distinction of several valuable engineering quantities like skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated. The finding of present study helps to control the rate of heat transportation as well as fluid velocity in any manufacturing processes and industrial applications to make desired quality of final product.

Heat transfer flow of Cu-water and Al2O3-water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller-box method

Natural convection boundary layer flow over a solid sphere in micropolar nanofluid with prescribed wall temperature is studied. Copper (Cu) and alumina (Al2O3) in water-based micropolar nanofluid has been considered. Tiwari and Das’s nanofluid model with realistic empirical correlations are considered to analyze the nanoparticles effects on natural convective flow. The nonlinear partial differential equations of the boundary layer are first transformed into a non-dimensional form and then solved numerically using an implicit finite difference scheme known as Keller-box method. The effects of nanoparticles volume fraction, Prandtl number, micro-rotation parameter on temperature, velocity and angular velocity are plotted and discussed. Further, numerical results for the local Nusselt number and the local skin friction coefficient are obtained. It is found that Cu has a low heat transfer rate as compare to Al2O3 water-based micropolar nanofluid with increasing micro-rotation parameter. The present results of local Nusselt number and the local skin friction for viscous fluid are found to be in good agreement with the literature.

Numerical Simulation of Natural Convection in a Square Cavity Utilizing Nanofluid and Subjected to Air Stream Cooling

In the present paper the natural convection in a squarecavity utilizing Cu-water nanofluid is examined numerically.The cavity is exposed to cooling air stream with free streamtemperature (T∞) from left wall and its right and bottom wallskept with cold and hot temperatures (TC) and (TH) respectively,while the cavity top wall considered as adiabatic. The nanofluidflow inside the cavity is assumed to be laminar and obeying toBoussinesq approximation. The governing equations are solvedby finite volume method using ANSYS FLUENT code. Theresults are accomplished with a range of nanofluid volumefraction =0–0.16, Rayleigh number Ra=103–105 and freestream Reynolds number Re∞=103–104. The effects of thesevariables are displayed on the stream function (), isotherms ()contours and average Nusselt number (Nuavg). The results showthe heat transfer rate augmented with increasing , Ra and Re∞.Also, the increment in both  and Ra increases the circulationinside the cavity while increasing Re∞ produces secondaryvortices and reduces circulation at the main vortex of the cavity.The results of local Nusselt number (Nu) and isotherms () arecompared with other studies and show good agreement withmaximum error values 14.28% and 3.2% respectively.

Particle shape effects on ferrofuids flow and heat transfer under influence of low oscillating magnetic field

The purpose of this study is to theoretically examine nanoparticle shapes behavior on mass and heat flow of ferrofluid over a rotating disk with the presence of low oscillating magnetic field. Ferrofluid is prepared by water and iron nanoparticles of three different shapes like sphere, oblate ellipsoid and prolate ellipsoid. The problem has been formulated by employing the controllable force into the fundamental hydrodynamic equations and its effect along with particle shape factor on physical properties of fluid is discussed. These equations are converted into a system of ordinary differential equations by employing appropriate similarity approach and then solved by HAM based Bvph2 package. Effects of particle shape, particle volume fraction and magnetization parameter on axial, radial and tangential velocities along with temperature profile are demonstrated through graphically. The results for local Nusselt number are calculated and analyzed and the path for enhancement in heat transfer is also proposed.

Effects of operational and geometrical uncertainties on heat transfer and pressure drop of ribbed passages

In this paper uncertainty quantification of turbulent flow and heat transfer through ribbed channels of gas turbine blades is presented and discussed. The uncertainty quantification method is first validated using the Ishigami function and then applied to turbulent flow and heat transfer through a ribbed pipe. Combination of four operational and geometrical uncertain variables (Re, Pr, P/h and D/h) are considered. Results for local Nusselt number, average Nusselt number and non-dimensional pressure drop using a polynomial chaos expansion of order 3 are presented and discussed. Uncertainty quantification results for the local Nusselt number showed that the regions located on top and immediately after the rib are more sensitive to the uncertain input variables. To tackle the curse of dimensionality, the sparse polynomial chaos expansion is further employed in this study. Results for quantities of interest showed that the sparse polynomial chaos method reduces the computational cost by at least 50% in comparison to the full polynomial chaos expansion method. Furthermore, results show that the sparse PCE works better for the non-dimensional pressure drop than the average Nusselt number. Results of sensitivity analysis for non-dimensional pressure-drop showed that, in agreement with the empirical correlations, this quantity is independent of Reynolds number. Also, results of sensitivity analysis for local Nusselt number showed that generally the major variability of Nusselt number is due to the blockage ratio.

Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet

This present study describes the combine effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous stretching sheet. Similarity transformation variables have been used to model the governing equations of momentum, energy, solute, and nanoparticle concentration. Successive linearization method (SLM) and Chebyshev spectral collocation method (CSC) are applied to solve the resulting coupled ordinary nonlinear differential equations. The numerical comparison has also presented for skin friction coefficient and local Nusselt number as a special case for our study. Physical features for all the pertinent parameters such as porosity parameter, Prandtl number, radiation parameter, Lewis number, modified Dufour parameter, Brownian motion parameter, thermophoresis parameter, Dufour solute Lewis number, nano-Lewis number and Williamson fluid parameter are discussed with the help of graphs. Numerical results of local Nusselt number, Sherwood number are also presented with the help of tables.

Radiation Effect on MHD Mixed Convection Flow Along an Isothermal Vertical Wedge Embedded in a Porous Medium with Heat Generation

This paper study the effect of radiation on a steady mixed convection flow of a viscous incompressible electrically conducting and radiating fluid over an isothermal vertical wedge embedded in a porous medium. The governing nonlinear partial differential equations and their boundary conditions are transformed into a nonsimilar form by using a suitable dimensionless variables. The system of nonsimilar equations is solved numerically using a finite difference method. The present results of local Nusselt number are compared with previously published work for the case of Darcy solution. The comparison is found to be in excellent agreement. The present results showed that as the wedge angle parameter increases the local Nusselt number increases. Increasing in the value of the square of the Hartmann number leads to decreasing the value of the local Nusselt number. Increasing in the value of the radiation parameter leads to an increase in the value of the local Nusselt number. Increasing in the value of the heat generation parameter leads to decreasing the value of the local Nusselt number. Increasing in the value of the radiation parameter in the presence of the square of the Hartmann number and the heat generation parameter has a similar effect on the local Nusselt number presented above but with less values.

Soret and Dufour effects on heat and mass transfer by natural convection from a vertical truncated cone in a fluid-saturated porous medium with variable wall temperature and concentration

This work studies the Soret and Dufour effects on the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a fluid-saturated porous medium. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary layer equations are solved by the cubic spline collocation method. Results for local Nusselt number and the local Sherwood number are presented as functions of Soret parameters, Dufour parameters, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to decrease the local Nusselt number, while it tends to increase the local Sherwood number. An increase in the Soret number leads to an increase in the Nusselt number and a decrease in the Sherwood number from a vertical truncated cone in a fluid-saturated porous medium. The local Nusselt number and the local Sherwood number of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents.

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10 5 to 1.2 × 10 7. The entrance sections used were long tube with length of 2520 mm ( L/ D h = 63) and short tube with length of 504 mm ( L/ D h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.

Natural convection heat and mass transfer from a vertical truncated cone in a porous medium saturated with a non-Newtonian fluid with variable wall temperature and concentration

This work presents a boundary-layer analysis about the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a porous medium saturated with non-Newtonian power-law fluids. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary-layer equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of power-law indexes, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. The heat and mass transfer rates of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents. Moreover, an increase in the power-law index of fluids tends to decrease the heat and mass transfer from a vertical truncated cone in a porous medium saturated with non-Newtonian power-law fluids.

Natural convection of a micropolar fluid from a vertical truncated cone with power-law variation in surface temperature

This work presents a boundary-layer analysis about the natural convection heat transfer near a vertical truncated cone with power-law variation in surface temperature in a micropolar fluid. The transformed boundary layer governing equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of vortex viscosity parameter, the surface temperature exponent, and the Prandtl number. The heat transfer rates of the truncated cones with higher surface temperature exponents are higher than those with lower surface temperature exponents. Moreover, the heat transfer rate from a vertical truncated cone in Newtonian fluids is higher than that in micropolar fluids.

PREDICTION OF THREE DIMENSIONAL NATURAL CONVECTION FROM A HORIZONTAL ISOTHERMAL SQUARE PLATE

A theoretical study of a three-dimensional natural convection heat transfer from an isothermal horizontal square plate, with upper and lower heated surfaces is present. The transient Navier–Stokes and energy equations were solved by using finite deference method (F.D.M). The complete Navier–Stokes equations are transformed and expressed in terms of vorticity–vector potential and solved using an Alternating Direction Implicit (ADI) method for the parabolic portion of the problem, and Successive Over–Relaxation (SOR) method for the elliptic portion .A computer program in (FORTRAN 77) was built to carry out the solution. The numerical results were obtained for laminar flow range of Grashof number up to (105) in up ward–facing and downward–facing with Prandtl number of (0.72). The results of local Nusselt number have maximum values at the outer edge of plate for two cases upward and downward facing heating.The comparison of the results of average Nusselt number with numerical data for downward facing and experimental data for upward facing shows acceptable agreement. It may be noted that the present data are generally different with experimental data, since the available data are extrapolated to high Grashof number. Thus the deviation may be large with present data.

Free convection and radiation for a vertical wall with varying temperature embedded in a porous medium

Free convection with and without radiation past a vertical plate embedded in a saturated porous medium has been analysed. The partial differential equations are non-dimensionalised and solved using Finite Element Method. Temperature distribution in the porous medium has been studied for constant and varying wall temperatures. For non-isothermal case, the wall temperature has been assumed as power law function. Numerical results for local Nusselt number are presented for the case of, with and without radiation. It is found that the local Nusselt number decreases with the height of the vertical plate for an isothermal wall temperature. However, local Nusselt number increases with the height of the plate for linearly varying wall temperature and it also increases with radiation.

Heat Transfer in Turbulent Flow Past a Surface-Mounted Two-Dimensional Rib

Heat transfer measurements and predictions are reported for a turbulent, separated duct flow past a wall-mounted two-dimensional rib. The computational results include predictions using the standard k–ε model, the algebraic-stress (A-S) functionalized k–ε model, and the nonlinear k–ε model of Speziale (1987). Three different prescriptions for the wall functions, WF I, WF II, and WF III given, respectively, by Launder and Spalding (1974), Chieng and Launder (1980), and Johnson and Launder (1982), are examined. The experiments include laser-Doppler flow measurements, temperature measurements, and local Nusselt number results. For WF I, the nonlinear model yielded improved predictions and displayed the most realistic predictions of the streamwise turbulence intensity and the mean streamwise velocities near the high-speed edge of the separated layer and downstream of reattachment. However, no significant improvements in the surface heat transfer predictions were obtained with the nonlinear model. With WF I and WF II, the models underpredicted the local Nusselt numbers and overpredicted the flow temperatures. With WF III, the predicted results agree with the experimental Nusselt numbers quite well up to reattachment, after which it substantially overpredicted the Nusselt numbers. The AS functionalized model using only the high Re formulation and curvature corrections in Cartesian coordinates improved the temperature predictions substantially, with the predicted flow temperatures agreeing quite well with the measured temperatures.

Forced convection behavior of a dielectric fluid (FC-77) in a 2:1 rectangular duct

The present study numerically investigates the effect of variable viscosities of water and a dielectric fluid (FC-77) on the heat transfer and friction factor for laminar flow in a rectangular channel. The present numerical results of local Nusselt numbers for FC-77 significantly exceed the value obtained with a constant-property fluid or water. The increase in the Nusselt numbers for FC-77 results from two factors: the low thermal conductivity of FC-77 and an increased velocity gradient caused by decreasing viscosity near the top wall. However, the actual heat transfer rate for FC-77 is much smaller than for water because of its low thermal conductivity. Also, the present study examines the wisdom of using dimensionless and dimensional heat transfer coefficients in relation to the design of liquid-cooling module involving dielectric fluids or water.

A numerical study of free convective heat transfer in a parallelogram‐shaped enclosure

Two‐dimensional free convective flow in a parallelogram‐shaped enclosure has been studied numerically. The heated and cooled walls of the enclosure are isothermal and inclined at an angle β with respect to gravity. The top and bottom walls of the enclosure are horizontal and adiabatic. Calculations have been made for Rayleigh numbers ranging from 103 to 105 for a variety of wall angles (60° ≤ β ≤60° ) and enclosure aspect ratios 0.5 ≤ A ≤ 3. Average and local Nusselt number results are presented for a Prandtl number of 0.7. Streamline and isotherm contours are also presented.

Laminar heat transfer in a rectangular duct with a non-Newtonian fluid with temperature-dependent viscosity

The present study investigates the effect of the temperature-dependent and shear-thinning viscosity of a non-Newtonian fluid on the behavior of the laminar heat transfer and friction coefficients in a 2:1 rectangular duct. The H1 thermal boundary condition, corresponding to an axially-constant heat flux and a peripherally-constant temperature, was adopted for a top-wall-heated configuration. The present numerical results of local Nusselt numbers for a polyacrylamide (Separan AP-273) solution show 70–300% heat transfer enhancement over those of a constant-property fluid and give excellent agreement with recent experimental results. The heat transfer enhancement from the heated top wall is due to an increased velocity gradient near the wall, which is attributed to the combined effect of the temperature-dependent and shear-thinning viscosity. Two new correlations for the friction factor and the local Nusselt numbers in the 2: 1 rectangular duct are proposed; these correlations cover both thermally-developing and thermally-fully-developed regions. This study also proposes the use of a temperature-dependent shear-thinning fluid in a rectangular duct in the design of a liquid cooling module for the computer industry.

Numerical study of laminar heat transfer with temperature dependent fluid viscosity in a 2:1 rectangular duct

The present study investigates the influence of variable viscosity of temperature-dependent fluids on the laminar heat transfer and friction factor in a 2:1 rectangular duct. The H 1 thermal boundary condition corresponding to axially constant heat flux and peripherally constant temperature was adopted for a top-wall-heated configuration. The governing conservation equations of mass, momentum, and energy were solved using a finite volume method, and the range of the Prandtl number was from 7 to 15000. The present numerical results of local Nusselt numbers for oil showed 70—80% enhancement over those of a constant property fluid and 40—50% enhancement over water, and gave excellent agreement with recent experimental results [ Int. J. Heat Mass Transfer 35, 641—648 (1992)]. The heat transfer enhancement from the heated top wall was due to an increased velocity gradient near the wall. The study proposes a new correlation for local Nusselt numbers in the 2:1 rectangular duct, which covers both thermally developing and thermally fully developed regions. Consequently, a temperature-dependent viscous fluid with a non-circular duct is proposed for use in the design of a liquid cooling module for the computer industry and in compact heat exchangers in general.