scholarly journals Heat transfer from a moving fluid sphere with internal heat generation

2014 ◽  
Vol 18 (4) ◽  
pp. 1213-1222
Author(s):  
Silvia Alexandrova ◽  
Maria Karsheva ◽  
Abdellah Saboni ◽  
Christophe Gourdon
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Generation ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Viscosity Ratio ◽  
Fluid Sphere ◽  
Péclet Number ◽  
Convection Equation

In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0<Re<100), Peclet number (0<Pe<10000) and viscosity ratio (0<k<10), are presented. For a circulating drop with Re?0, steady creeping flow is assumed around and inside the sphere. In this case, the average temperatures computed from our numerical analysis are compared with those from literature and a very good agreement is found. For higher Reynolds number (0<Re<100), the Navier-Stokes equations are solved inside and outside the fluid sphere as well as the unsteady conduction-convection equation including heat generation inside the fluid sphere. It is proved that the viscosity ratio k (k = ?d/?c) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing k for a fixed Peclet number and a given Reynolds number. It is also observed that the average Nusselt number is increasing as Peclet number increases for a fixed Re and a fixed k.

Effect of Variation of Pin-fin Height on Jet Impingement Heat Transfer on a Rotating Surface

2021 ◽  
Author(s):  
Pratik S. Bhansali ◽  
Srinath V. Ekkad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Gas Turbine ◽  
Average Nusselt Number ◽  
Jet Impingement ◽  
Impinging Jet ◽  
Rotating Disc ◽  
Disc Surface ◽  
Pin Fins

Abstract Heat transfer over rotating surfaces is of particular interest in rotating machinery such as gas turbine engines. The rotation of the gas turbine disc creates a radially outward flow on the disc surface, which may lead to ingress of hot gases into the narrow cavity between the disc and the stator. Impingement of cooling jet is an effective way of cooling the disc and countering the ingress of the hot gases. Present study focusses on investigating the effect of introducing pin-fins over the rotating disc on the heat transfer. The jet Reynolds number has been varied from 5000 to 18000, and the rotating Reynolds number has been varied from 5487 to 12803 for an aluminum disc of thickness 6.35mm and diameter 10.16 cm, over which square pins have been arranged in an inline fashion. Steady state temperature measurements have been taken using thermocouples embedded in the disc close to the target surface, and area average Nusselt number has been calculated. The effects of varying the height of the pin-fins, distance between nozzle and the disc surface and the inclination of the impinging jet with the axis of rotation have also been studied. The results have been compared with those for a smooth aluminum disc of equal dimensions and without any pin-fins. The average Nusselt number is significantly enhanced by the presence of pin fins. In the impingement dominant regime, where the effect of disc rotation is minimal for a smooth disc, the heat transfer increases with rotational speed in case of pin fins. The effect of inclination angle of the impinging jet is insignificant in the range explored in this paper (0° to 20°).

Numerical Analysis of Heat Transfer Enhancement in a Micro-Channel Due to Mechanical Stirrers

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
M. Sreejith ◽  
S. Chetan ◽  
S. N. Khaderi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Peclet Number ◽  
Periodic Case ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Fluidic Channel ◽  
Enhancement Of Heat Transfer ◽  
Péclet Number

Abstract Using two-dimensional numerical simulations of the momentum, mass, and energy conservation equations, we investigate the enhancement of heat transfer in a rectangular micro-fluidic channel. The fluid inside the channel is assumed to be stationary initially and actuated by the motion imparted by mechanical stirrers, which are attached to the bottom of the channel. Based on the direction of the oscillation of the stirrers, the boundary conditions can be classified as either no-slip (when the oscillation is perpendicular to the length of the channel) or periodic (when the oscillation is along the length of the channel). The heat transfer enhancement due to the motion of the stirrers (with respect to the stationary stirrer situation) is analyzed in terms of the Reynolds number (ranging from 0.7 to 1000) and the Peclet number (ranging from 10 to 100). We find that the heat transfer first increases and then decreases with an increase in the Reynolds number for any given Peclet number. The heat transferred is maximum at a Reynolds number of 20 for the no-slip case and at a Reynolds number of 40 for the periodic case. For a given Peclet and Reynolds number, the heat flux for the periodic case is always larger than the no-slip case. We explain the reason for these trends using time-averaged flow velocity profiles induced by the oscillation of the mechanical stirrers.

Experimental Investigation on Convective Heat Transfer Enhancement of Laminar Slot Jet Impingement in the Presence of Porous Medium

2016 ◽  
Author(s):  
Sampath Kumar Chinige ◽  
Arvind Pattamatta
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Porous Medium ◽  
Porous Media ◽  
Nusselt Number ◽  
Heat Sink ◽  
Average Nusselt Number ◽  
Jet Impingement ◽  
Transfer Enhancement ◽  
Porous Obstacle

An experimental study using Liquid crystal thermography technique is conducted to study the convective heat transfer enhancement in jet impingement cooling in the presence of porous media. Aluminium porous sample of 10 PPI with permeability 2.48e−7 and porosity 0.95 is used in the present study. Results are presented for two different Reynolds number 400 and 700 with four different configurations of jet impingement (1) without porous foams (2) over porous heat sink (3) with porous obstacle case (4) through porous passage. Jet impingement with porous heat sink showed a deterioration in average Nusselt number by 10.5% and 18.1% for Reynolds number of 400 and 700 respectively when compared with jet impingement without porous heat sink configuration. The results show that for Reynolds number 400, jet impingement through porous passage augments average Nusselt number by 30.73% whereas obstacle configuration enhances the heat transfer by 25.6% over jet impingement without porous medium. Similarly for Reynolds number 700, the porous passage configuration shows average Nusselt number enhancement by 71.09% and porous obstacle by 33.4 % over jet impingement in the absence of porous media respectively.

scholarly journals Natural Convection Flow along an Isothermal Vertical Flat Plate with Temperature Dependent Viscosity and Heat Generation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Md. Mamun Molla ◽  
Anita Biswas ◽  
Abdullah Al-Mamun ◽  
Md. Anwar Hossain
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Nusselt Number ◽  
Wall Shear Stress ◽  
Heat Generation ◽  
Average Nusselt Number ◽  
Variation Parameter ◽  
Viscosity Variation ◽  
Wall Shear ◽  
Vertical Flat Plate

The purpose of this study is to investigate the natural convection laminar flow along an isothermal vertical flat plate immersed in a fluid with viscosity which is the exponential function of fluid temperature in presence of internal heat generation. The governing boundary layer equations are transformed into a nondimensional form and the resulting nonlinear system of partial differential equations is reduced to a convenient form which are solved numerically using an efficient marching order implicit finite difference method with double sweep technique. Numerical results are presented in terms of the velocity and temperature distribution of the fluid as well as the heat transfer characteristics, namely, the wall shear stress and the local and average rate of heat transfer in terms of the local skin-friction coefficient, the local and average Nusselt number for a wide range of the viscosity-variation parameter, heat generation parameter, and the Rayleigh number. Increasing viscosity variation parameter and Rayleigh number lead to increasing the local and average Nusselt number and decreasing the wall shear stress. Wall shear stress and the rate of heat transfer decreased due to the increase of heat generation.

Effects of Nanoparticle Shape on Slot-Jet Impingement Cooling of a Corrugated Surface With Nanofluids

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Öztop
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Jet Impingement ◽  
Heat Transfer Characteristics ◽  
Impingement Cooling ◽  
Corrugated Surface ◽  
Nanoparticle Shapes

Numerical study of jet impingement cooling of a corrugated surface with water–SiO2 nanofluid of different nanoparticle shapes was performed. The bottom wall is corrugated and kept at constant surface temperature, while the jet emerges from a rectangular slot with cold uniform temperature. The finite volume method is utilized to solve the governing equations. The effects of Reynolds number (between 100 and 500), corrugation amplitude (between 0 and 0.3), corrugation frequency (between 0 and 20), nanoparticle volume fraction (between 0 and 0.04), and nanoparticle shapes (spherical, blade, brick, and cylindrical) on the fluid flow and heat transfer characteristics were studied. Stagnation point and average Nusselt number enhance with Reynolds number and solid particle volume fraction for both flat and corrugated surface configurations. An optimal value for the corrugation amplitude and frequency was found to maximize the average heat transfer at the highest value of Reynolds number. Among various nanoparticle shapes, cylindrical ones perform the best heat transfer characteristics in terms of stagnation and average Nusselt number values. At the highest solid volume concentration of the nanoparticles, heat transfer values are higher for a corrugated surface when compared to a flat surface case.

Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2011 ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
V. Soloviev
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermally developing and periodically fully-developed flow in a parallel-plate channel comprised of superhydrophobic walls. The superhydrophobic walls considered in this paper exhibit alternating micro-ribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: 1) Increases in the cavity fraction lead to decreases in the average Nusselt number; 2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and 3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully-developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

Finite element thermal analysis of a moving porous fin with temperature-variant thermal conductivity and internal heat generation

2020 ◽  
Vol 1 (1) ◽  
pp. 110
Author(s):  
Gbeminiyi Sobamowo ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element ◽  
Heat Generation ◽  
Peclet Number ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Péclet Number ◽  
Porous Fin

This paper focuses on finite element analysis of the thermal behaviour of a moving porous fin with temperature-variant thermal conductivity and internal heat generation. The numerical solutions are used to investigate the effects of Peclet number, Hartmann number, porous and convective parameters on the temperature distribution, heat transfer and efficiency of the moving fin. The results show that when the convective and porous parameters increase, the adimensional fin temperature decreases. However, the value of the fin temperature is amplified as the value Peclet number is enlarged. Also, an increase in the thermal conductivity and the internal heat generation cause the fin temperature to fall and the rate of heat transfer from the fin to decrease. Therefore, the operational parameters of the fin must be carefully selected to avoid thermal instability in the fin.

Mixed convective heat transfer and heat generation simulation in lid-driven enclosure filled with porous medium

2021 ◽  
pp. 2150106
Author(s):  
Basma Souayeh ◽  
Najib Hdhiri
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Generation ◽  
Average Nusselt Number ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Bottom Wall ◽  
Maximum Temperature ◽  
Grashof Number ◽  
Number Formula

Researchers in heat transfer field always attempt to find new solutions to optimize the performance of energy devices through heat transfer enhancement. Among various methods which are implemented to reinforce the thermal performance of energy systems, one is utilizing porous media in heat exchangers. In this study, characteristics of laminar mixed convection in a porous two-sided lid-driven square cavity induced by an internal heat generation at the bottom wall have been carried out by using a numerical methodology based on the finite volume method and the full multigrid acceleration. The two-sided and top walls of the enclosure are assumed to have cold temperature while the remaining walls of the bottom wall are insulated. The working fluid is air so that the Prandtl number equates 0.71. The behavior of different physical parameters is shown graphically so that computations have been conducted over a wide range of pertinent parameters; (10[Formula: see text] Ri [Formula: see text]), Darcy number ([Formula: see text] Da [Formula: see text]), internal Rayleigh number ([Formula: see text] Ra[Formula: see text]), the porosity ([Formula: see text]) and the Grashof number (10[Formula: see text] Gr [Formula: see text]). Results revealed that heat transfer mechanism and the flow characteristics inside the enclosure are strongly dependent on the Grashof number. For instance, the best heat transfer rates at the considered values of internal Rayleigh numbers are obtained for a high Grashof number. Furthermore, an increase of internal heat generation (RaI) leads to a higher flow and temperature intensities for Grashof numbers ranging from [Formula: see text] to [Formula: see text] and a specific Richardson number value. Besides, an increase in porosity values ([Formula: see text]) leads to an obvious decrease in the average Nusselt number. Maximum temperature [Formula: see text] is optimal for high ([Formula: see text]) value. A correlation expression for the average Nusselt number relative to the internal heat source was established in function of two control parameters such as Darcy and Richardson numbers.

Buoyancy Driven Flow, Heat Transfer and Entropy Generation Characteristics for Different Heater Geometries Placed in Cryogenic Liquid: A CFD Study

2021 ◽  
pp. 1-20
Author(s):  
Someshwar Ade ◽  
Sushil Rathore
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Entropy Generation ◽  
Heat Generation ◽  
Average Nusselt Number ◽  
Cryogenic Liquid ◽  
Heat Generation Rate ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer

Abstract The present work reports 3D computational study of buoyancy driven flow and heat transfer characteristics for a localized heater (analogous to superconductor) submerged in cryogenic liquid nitrogen in an enclosure. Seven different heater geometries are considered and the effect of heater geometry on flow and heat transfer characteristics are illustrated. The heater is generating heat at a constant rate (W/m3). Continuity, momentum and energy equations are solved using finite volume method. Liquid flow and heat transfer features are demonstrated with the help of velocity vector and temperature contours. Rayleigh number, average Nusselt number, maximum vertical velocity of fluid flow, average velocity of fluid flow are the parameters which are considered for comparing seven different geometries of heater. Additionally, an analysis of the entropy generation owing to transfer of heat and friction due to fluid flow are reported. Furthermore, the dependency of average Nusselt number, maximum velocity of fluid, entropy generation owing to transfer of heat and fluid friction as a function of heat generation rate is illustrated graphically. The results of this study indicate that heater geometry can considerably affect the transfer of heat, fluid flow features and entropy generation under same heat generation rate in the heater. Highest average Nusselt number on heater surface is obtained when heater geometry is circular; whereas lowest value of total entropy generation in the domain is obtained when heater geometry is equilateral triangle.

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