Non-dimensional Heat Transfer Coefficient Research Articles

Numerical analysis of concentric jet impingement heat transfer to the concave surface of the cone

This work includes numerical investigation of concentric jet impingement heat transfer to the concave surface of 30° apex angle conical surface. Heat transfer results are represented in terms of nondimensional heat transfer coefficient Nusselt number along the slant edge of the cone. Turbulence intensity, static pressure distribution along slant edge of the cone, and velocity contours in the domain are also presented for a detail understanding of the flow behavior. Different geometrical parameters like diameter of pipe (10 mm, 14 mm, and 20 mm) and L/D (4.25, 6.25, and 10.25) are considered for heat transfer analysis. Jet Reynolds number is varied between 25000 and 82000 for each diameter and L/D case. It is observed that Nusselt number value is minimum close to the apex of the cone due to stagnation region, then increases with increase in the distance from the apex of the cone and becomes maximum due to maxima in the turbulence intensity and decreases with increases in the distance. Nusselt number value decreases with increase in the L/D. Nusselt number increases with increase in the jet Reynolds number. There is an insignificant influence of the diameter of pipe on Nusselt number for identical jet Reynolds number and L/D.

Numerical investigation of forced convection heat transfer from a sphere at low Prandtl numbers

Direct numerical simulations of the flow and forced convective heat transfer around a sphere at Reynolds numbers between Re=500 and Re=1000 are performed. We investigate the effects of the Prandtl number (Pr) on the forced convective heat transfer from a sphere for various fluids having Pr=0.01,0.1,0.7. At the larger Prandtl number, the convective transport due to the vortex shedding process dominates over the diffusive transport. As the Prandtl number decreases, diffusive effects become important. Moreover, the thermal boundary layer increases with decrements of the Prandtl number, which results in a reduction in the local and mean non-dimensional heat transfer coefficient. It is seen that at Re=500 and Re=750, the vortex shedding process is asymmetric, which results not only in a non-zero lift coefficient, but in an asymmetric temperature field in the wake of the sphere at Pr≥0.1. The dual asymmetry in the flow and the convective heat transfer is smooth out when the Prandtl number reaches Pr=0.01 as the heat diffusion dominates and asymmetries in the vortex formation zone are no longer relevant in the heat transport. The descend in Prandtl number also produces an attenuation of the temperature fluctuations and thereby, in the turbulent heat transfer. As a direct consequence, two factors emerge at Pr=0.01: (1) a lower decay ratio of the temperature in the wake centreline, and (2) a larger wake spread compared to higher Prandtl numbers.

Unsteady natural convection of nano-encapsulated phase change materials (NEPCMs) inside a random porous medium considering local thermal non-equilibrium condition

A local thermal non-equilibrium analysis is undertaken to simulate unsteady free convective heat transfer inside a square enclosure filled with a random porous medium. There is a time-varying temperature profile at the hot wall. The fluid is a suspension comprising nano-encapsulated phase change materials (NEPCM) particles dispersed in water while aluminum foam, copper foam, or glass balls are considered for the solid matrix. It is found that when the hot wall temperature reaches its minimum value during one oscillation period, most of the cavity is occupied by the NEPCM particles in the solidious phase. For the metallic foams, the heat transfer of the medium is substantially higher than the NEPCM particles. Meanwhile, the Nusselt number of the glass balls is much lower than the suspension. A rise in the dimensionless frequency or amplitude of the temperature profile as well as approaching the dimensionless fusion temperature to 0.5 elevates Nusselt number of the suspension. However, no general conclusion can be drawn for their consequences on the heat transfer in the solid matrix. Among the current alterable parameters, only the contributions of the non-dimensional interface heat transfer coefficient and the non-dimensional amplitude of the temperature profile are found significant.

Local thermal non-equilibrium (LTNE) effects on thermal-free convection in a nanofluid-saturated horizontal elliptical non-Darcian porous annulus

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are out of local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy–Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

AbstractThis article displays a numerical investigation on natural convection within non‐Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10–4 ≤ Fs/Pr* ≤ 10–2), thermal conductivity ratio (0.1 ≤ K r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K r.

Determination of Heat Transfer Coefficient and Thermal Dispersion of a Representative Porous Structure Based on Pore Level Simulations

In the present work, pore level simulations were performed to calculate heat transfer coefficient and thermal dispersion coefficient of a consolidated porous structure. A three-dimensional cubic unit cell structure, made up of six cuboid struts was selected to represent the idealized porous structure. To analyze fluid flow and heat transfer through the porous structure, governing fluid flow and energy equations were solved using the finite-volume method. A parametric study was carried out to investigate the effects of Reynolds number, Prandtl number, and porosity on heat transfer coefficient of the considered structure. A separate parametric study explored the variation of stream-wise dispersion coefficient with Reynolds number, Prandtl number, thermal conductivity ratio of the solid and the fluid phase, and porosity. Finally, generalized correlations for both non-dimensional heat transfer coefficient and stream-wise dispersion coefficients were proposed. It is observed that the obtained heat transfer coefficient follows two distinct trend lines for both porosities considered in the present investigation. For the considered operating conditions, the stream-wise dispersion coefficient is found to be proportional to square of Peclet number.

STUDY OF HEAT TRANSFER OF A HEATER FOR VARIOUS INSTALLATION METHODS

Analysis of numerically simulated convective heat transfer for a variety of heater installations is presented. A critical review of the existing method of energy effi ciency assessment, which is based on empirical coeffi cients, is given. Numerically verifi ed nondimensional heat transfer coeffi cients for eight installations of the heater are presented. The results were validated with the adopted experimental data. Sensitivity analysis of heat transfer intensity towards heat carrier temperature for a variety of heater installations is presented.

Scales of natural convection on a convectively heated vertical wall

Natural convection on a convectively heated vertical wall, one of the fundamental issues of heat and mass transfer in many engineering applications, is investigated in this work. The configuration is governed by the Rayleigh number (RaL or Ra), the Prandtl number (Pr), and the non-dimensional convective heat transfer coefficient (CiL or Ci). A scaling analysis for the dynamics of the boundary layer flow and heat transfer is carried out. The scales of the velocity/thickness of the boundary layer flow and the temperature/thickness of the thermal boundary layer related to the non-dimensional governing parameters are obtained. The scales are validated using the numerical results by large eddy simulation. The results show that the non-dimensional velocity of the boundary layer flow is proportional to CiL2/5RaL2/5; the thickness from the wall to the layer of the maximal velocity is inversely proportional CiL1/5RaL1/5; the non-dimensional thickness of the thermal boundary layer is inversely proportional CiL1/5RaL1/5; the non-dimensional temperature in the thermal boundary layer is proportional to CiL4/5RaL−1/5. The reduction factor describing the thermal resistance of the thermal boundary layer is further discussed, which is proportional to Ci4/5Ra−1/5.

Heat transfer characteristics of impinging methane diffusion and partially premixed flames

Flame jet impingement heat transfer is a well-established technique for obtaining high heat transfer rates in many domestic and industrial applications. The flame structure and the heat transfer characteristics of the impinging methane diffusion flame and partially premixed flame are experimentally investigated. The heat transfer characteristics of the impinging methane flame are determined using the minimization technique wherein the target surface is impinged by a methane flame from the bottom and is simultaneously cooled from the top by air jets of different Reynolds number. At steady state, one-dimensional energy balance across the impingement surface provides an over-determined system of equations which when solved using the minimization technique give the heat transfer coefficient of the flame jet, the reference temperature and the emissivity of the gas/flame beneath the impingement surface.The stagnation point heat transfer coefficient and reference temperature are found to be maximum for the case of flame just touching the impingement surface. The radial variation of the non-dimensional heat transfer coefficient and reference temperature is found to have a Gaussian profile. For low H/d’s where the flame is impinging the target surface, the temperature at the stagnation zone is lower than in the radial position as the hot jet turns in the radial direction and impinges at a distance slightly away from the stagnation region.The separation of heat transfer components indicates that the heat transfer is convective dominant with radiation accounting to 10% of the total incident heat flux in the case of methane diffusion flame and 3.5% in the case of partially premixed flame. Re-radiation becomes a significant component of heat transfer, accounting to 25–30% of the incident heat flux, due to higher wall temperatures. The present study also investigates the effect of tube burner to plate spacing.

Analytical study of the heat transfer coefficient of the impinging air jet during cold spraying

A semi-empirical analytical model was developed to determine the convective heat transfer coefficient of an impinging air jet generated by a cold spraying nozzle. A low-pressure cold spraying unit was utilized to produce hot air jets that impinged upon a flat substrate surface. An infrared camera was used to measure the surface temperature of the substrate at different time intervals. A method involving Green's functions was employed to solve a transient two-dimensional heat conduction problem to obtain an expression for the temperature distribution within the substrate. By coupling the analytical results of temperature distribution and experimental surface temperature data, the radial variation of the non-dimensional heat transfer coefficient of the impinging air jets upon the substrate was estimated. The results showed that the maximum values of the heat transfer coefficient were present close to the stagnation point of the air jets. It was found that the heat transfer coefficient was independent of the time that the cold spray nozzle remained stationary over the substrate surface. It was found further that by increasing the stand-off distance of the nozzle, the radial variations of the heat transfer coefficient became negligible, compared to those for small stand-off distances. The close agreement between the experimental results and the predictions of the model suggested that the estimated heat transfer coefficient of the cold spray gas jet can be used to estimate the surface temperature of the substrate at any time.

Numerical investigation on possibility of heat transfer enchancement using reduced weight fin configuration

ABSTRACTThe heat transfer augmentation using extended surfaces (fins) is nothing new in the field of convective heat transfer, yet another milestone in this area is the usage of lesser weight porous fins to overcome the shortcoming of rigid fins in intrinsic passages. The present numerical analysis is focussed towards the heat transfer augmentation of concentric tube heat exchanger with the help of circumferentially attached porous fin. The analysis is aimed at predicting the effect of the following parameters fin height, spacing, conductivity and Darcy number (Da) on the non-dimensional convective heat transfer coefficient (Nu). Darcy's model is adopted for simulation and the finite volume method is adopted for discretisation. It is found that the permeability and height of the fin significantly affect the flow field. The heat transfer augmentation is inferred from the results and it is very high at large values of Da.

Modelling of heat and mass transfer from spheroidal drops with non-uniform surface temperature

The heating and evaporation of single component spherical and spheroidal (oblate and prolate) drops in gaseous quiescent environment are modelled, accounting for the effect of a non-uniform distribution of the temperature at the drop surface. The analytical solution to the species conservation equations in the proper coordinate system (spherical/spheroidal) is used to numerically solve the energy equation. The effect of temperature disuniformity on the local non-dimensional heat transfer coefficient and global heat and evaporation rates is calculated for different drop temperature disuniformity, mean surface temperature, drop deformation, gas temperature and pressure and liquid species.

Calculation of the Maximum Slope Angles of the Temperature Curve for the Single-Flow Non-Stationary Method of Deriving the Thermal Characteristics of Heat Transfer Surfaces

Results are presented for the solution of the problem of gas flow in a porous body with the presence of a temperature “step” in the range 1–100 of the non-dimensional heat-transfer coefficient, while accounting for longitudinal thermal conductivity. The problem was solved using the numerical finite difference method. Maximum slope angles were derived for temperature curves that can be used to obtain the thermal characteristics of high-compact heat transfer surfaces with the single-flow non-stationary method. Recommendations were provided regarding the range of applicability of the method, taking into account the new received results.

Improving the cooling performance of automobile radiator with ethylene glycol water based TiO2 nanofluids

In this paper, the performance of ethylene glycol and water based TiO2 nanofluids as an automobile radiator coolant is determined experimentally. Forced convective heat transfer coefficient of TiO2 nanofluids has been measured and compared with the data of base fluid in an automobile radiator. Nanofluids were prepared taking 40% ethylene glycol and 60% water with volume concentrations of 0.1%, 0.3% and 0.5% of TiO2 nano powder. All the experiments were conducted in the range of Reynolds numbers from 4000 to 15,000. In all the experiments the nanofluids made to flow through the radiator tubes with elliptical cross section and airflows with constant speed in the crosswise direction in between the tubes of a tube bundle. Results demonstrate that increasing the fluid circulation rate can improve the heat transfer performance while the fluid inlet temperature to the radiator has little or no effect. Nanofluids investigated in the present work with low concentrations enhanced the heat transfer rate up to 37% in comparison with base fluid. The results of the investigation are presented graphically in terms of non-dimensional heat transfer coefficient as a function of volume concentration, temperature and flow rate.

Multi-Objective Optimization of Turbulent Tube Flows Over Diamond-Shaped Turbulators

In this paper, experimentally derived correlations of heat transfer and pressure drop are used in a Pareto-based multi-objective optimization approach to find the best possible combinations of heat transfer and pressure drop in a tube fitted with diamond-shaped turbulators in tandem arrangements. The design variables are two geometrical parameters of diamond-shaped turbulators, namely, cone angle and tail length ratio, Reynolds number, and Prandtl number. The objectives are maximizing the nondimensional heat transfer coefficient and minimizing the nondimensional pressure drop in a round tube fitted with diamond-shaped turbulators. It is shown that some interesting and important relationships as useful optimal design principles involved in the thermal performance of round tube fitted with diamond-shaped turbulators can be discovered by the Paret- based multi-objective optimization approach.

Pareto based multi-objective optimization of turbulent heat transfer flow in helically corrugated tubes

In this study, by using the empirical correlations for heat transfer and pressure drop and also employing a multi-objective optimization (MOO) approach, the best possible combinations of heat transfer and pressure drop in helically corrugated tubes will be discovered. The design variables are two geometrical parameters of helically corrugated tubes, namely pitch to diameter ratio (PDH) and rib height to diameter ratio (eDH), Reynolds number (Re) and Prandtl number (Pr). The objectives are maximizing the non-dimensional heat transfer coefficient (Nu) and minimizing the non-dimensional pressure drop (f Re) in turbulent flow in helically corrugated tubes. It will be shown in the results that by using the multi-objective optimization approach, very important relations can be obtained which can be used in the thermal design of fluid flow in helically corrugated tubes.

Numerical Simulation of the Fluid Flow, Heat Transfer, and Solidification During the Twin-Roll Continuous Casting of Steel and Aluminum

The commercialization of aluminum twin-roll casting was realized in the early 1950s, while it is still a dream for engineers to produce steel strip by this process. In the present paper, a two-dimensional mathematical model is employed to study the fluid flow, heat transfer, and solidification during the twin-roll casting for both steel and aluminum. The turbulent flow in the pool is examined using the Lam and Bremhorst low-Reynolds-number turbulence model. In order to facilitate the comparison and analysis, a new transformed coordinate system (r, φ) is established. Characteristics of the momentum boundary layer and the solidification front are described. Reasons of the formation of the wedge-shaped zone near the surface of rotating roll are given. In the transformed coordinate system (r, φ), the effect of the centrifugal force induced by the rotating roll is presented using the velocity component in the r direction and the pressure gradient in the r direction. At last, the evaluation of the solidified shell in the pool is analyzed. The results show that the twin-roll casting is a roll-rotating-driven process. The variation of the thickness of the momentum boundary layer can be divided into three stages and its thickness is very uniform at the last stage. Near the roll surface, there exists a wedge-shaped zone induced by the near-roll-surface shear flow that washes the mushy zone front, which increases the depth of the liquid pool and decreases the length of the rolling region. The rotating roll gives rise to the stirring effect to the pool region and the metal is moving away from the roll surface in the positive radial velocity region, and the effect of the centrifugal force becomes weak in the lower part of the pool. At the solidification front, the non-dimensional effective heat transfer coefficient distribution in steel twin-roll casting is larger than that in aluminum twin-roll casting. Considering that the turbulence level is determined by the flow pattern in the pool region, which demonstrates the importance of the geometry of the feeding system in steel twin-roll casting. The evaluation of the solidified shell in aluminum twin-roll casting is a parabolic growth, while in steel twin-roll casting, the parabolic growth only occurs in the lower part of the pool.

Fundamental assessments and new enabling proposals for heat transfer correlations and flow regime maps for shear driven condensers in the annular/stratified regime

Modern-day applications need mm-scale shear-driven flow condensers. Condenser designs need to ensure large heat transfer rates for a variety of flow conditions. For this, good estimates for heat-transfer rate correlations and correlations for the length of the annular regime (beyond which plug-slug flows typically occur) are needed. For confident use of existing correlations (particularly the more recent ones supported by large data sets) for shear-pressure driven internal condensing flows, there is a great need to relate the existing correlation development approaches to direct flow-physics based fundamental results from theory, computations, and experiments. This paper addresses this need for millimeter scale shear driven and annular condensing flows. In doing so, the paper proposes/compares a few new and reliable non-dimensional heat-transfer coefficient correlations as well as a key flow regime transition criteria/correlation

Conjugate Heat Transfer Study at Interior Surface of NGV Leading Edge with Combined Shower Head and Impingement Cooling

A computational study on conjugate heat transfer is carried out to present the behavior of nondimensional temperature and heat transfer coefficient of a Nozzle Guide Vane (NGV) leading edge. Reynolds number of both mainstream flow and coolant impinging jets are varied. The NGV has five rows of film cooling holes arranged in shower head manner and four rows of impingement holes arranged in staggered manner. The results are presented by considering materials of different thermal conductivity. The results show that the mainstream flow affects the temperature distribution on the interior side of the vane leading edge for high conductivity material whereas it has negligible effects for low conductivity material. The effect of changing blowing ratio on internal heat transfer coefficient and internal surface temperature is also presented.

Influence of Viscous Dissipation on Mixed Convection in a Non-Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid-saturated non-Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far-field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite-difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non-dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21083