Case Of Uniform Heat Flux Research Articles

New Jet impingement flow-scale sets wall approach, Proximity limits & wall-jet heat transfer

A new scale is here identified as dominant in laminar jet impingement flow and heat transfer, namely, the height of the stagnation zone, zw. This being the point at which the jet “senses” the approaching wall, which corresponds to the location of marginal static pressure rise above the impinged plate. It is shown that this new profile-specific scale emerges from the virtual origin concept in Glauert's wall-jet solution, and physically constrained expressions are derived for both. Reynolds analogy is then conducted for the cases of uniform-heat-flux and -wall-temperature. This leads to a new prediction of the wall-jet heat transfer, valid upon convergence to quasi-self-similarity – within a diameter or two of the stagnation point. The convergence distance depends on incoming velocity profile and flow rate, as captured by the new virtual origin expression. The analysis also reveals that the convergence to self-similarity is delayed in the uniform heat flux case, even though eventually heat transfer is about one-third higher.The new scale also led to a successful description of the deceleration during wall-approach, as an interpolation between near-wall (Homann solution) and far-field (inviscid flow) asymptotes. Consequently, the new scale is shown to give the proximity limits for nozzle-to-plate distance. This being the distance at which the incoming jet becomes distorted due to constriction and back-pressure. Here found to correspond to around 2/5 of the stagnation zone height.All these findings are confirmed and validated through simulations, experimental measurements and literature data; and simple expressions are derived for prediction and design purposes.

Flow due to a porous stretching/shrinking sheet with thermal radiation and mass transpiration

AbstractThis study investigates the behavior of carbon nanotubes (CNT) approaching an unsteady flow of a Newtonian fluid over a stagnation point on a stretching surface employing porous media. It flows when the liquid begins to move with the progression of time. Heat exchange with the environment has an impact on the flow. The implicitly limited component technique is used to solve the nondimensional partial differential equation with an associated boundary layer, which is an unstable system. Analytically, the solutions, as well as the required boundary conditions, are obtained. The effects of mass transpiration, volume fraction, and heat radiation on Newtonian fluid flow through porous media are explored. Single‐ and multi‐walled CNTs are used as well as water, as base fluids in the experiment. The impact of thermal radiation and heat source/sink is shown in the energy equation, which is solved under four different cases: uniform heat flux case, constant wall temperature case, general power‐law wall heat flux case, and general power‐law wall temperature case. By supplying distinct physical characteristics, a theoretical analysis of the existence and nonexistence of unique and dual solutions may be explored. These physical parameters determine the velocity distribution and temperature distribution. Prescribed surface temperature (PST) and prescribed wall heat flux (PHF) heat transfer solutions can be written using confluent hypergeometric equations, and generic power‐law PST and PHF situations can also be expressed using confluent hypergeometric equations. The graphical representations assist in the discussion of the current study's findings.

Forced Convection Heat Transfer from a Flat Plate at Different Locations between Plates Array.(Dept.M)

A forced convection heat transfer experiment was conducted to study the heat transfer from hot rectangular flat plate ( 155 x 115mm ) to an air stream. The hot plate was situated between unheated plates array at various locations in the flow direction. The study was mainly concerned with the effect of the plate location on the average film coefficient of the transfer. An experimental test rig was designed and constructed for this investigation. The experiments covered the plate locations of x= 12.5, 22.5, 32. 5, 42.5 and 62.5mm, and extended over a range of Revonolds number from about 6,680 to 107, 170. A correlation between the average Nusselt number, the Reynodls number and the hot plate dimensionless location (X) was deduced. The experiments were performed for the case of uniform heat flux. A comparison with the available work in the literature review was also made.

Forced Convection Heat Transfer from a Flat Plate between Array with Lateral Air Flow.(Dept.M)

An experimental work on heat transfer by forced convection was conducted in order to study the heat transfer from hot rectangular tlat p late (155 x 115 mm) to an air stream. The hot place was situated between unheated p laces array at various locations in the flow direction. The air flow stream enters the tunnel ducc laterally from one side and from two sides. The study was mainly concerned with the effect of the lateral air flow on the average film coefficient of heat transfer . An exp erimental test rig was designed and constructed for chis investigation. The experiments covered the place locations of x = 12.5, 22.5, 32.5, 42.5 and 62.5 mm. and extended over a range of Reynolds number from about 6,800 to 109.000. Two correlations between the average Nusselt numoer and the Reynolds umbes were deduced, one was for the case of air entering the tunnel duct laterally from one side and the other was for the case of air entering the duco from two sides. The exp eriments were performed for the case of uniform heat flux. A comparison with the available work in the literature review was also made.

On the use of LES-based turbulent thermal-stress models for rod bundle simulations

An alternative methodology is proposed here to overcome the excessive cost of large eddy simulations (LES) of full-length heated rod bundle calculations, while improving the inaccurate results typically obtained with Reynolds-averaged Navier–Stokes equations (RANS). While the cost of the full-length LES is generally too high, LES of a small section of a single rod is usually affordable. The idea presented here consists of using the information granted by the small LES calculation to determine the appropriate turbulence viscosity or turbulent thermal diffusivity that can be used to solve only for the temperature field in a pseudo-RANS approach. The study has been performed with single-rod simulations with a P/D of 1.12 and 1.24, considering rod lengths that are representative of reactor applications, for the cases of uniform heat flux and a more realistic cosine-like axial heat distribution. The spectral element code Nek5000 has been used for all LES, RANS, and pseudo-RANS simulations. The recently proposed Nek5000 steady-state solver has been used for solving the temperature field in the pseudo-RANS approach and has proved significantly faster than transient schemes. Prediction of thermal quantities is compared with classical linear and nonlinear RANS models. LES for the full-length rods has also been performed and is used as a reference. Results of the proposed method show significant improvements with respect to those obtained with RANS.

Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers

Double U-pipe boreholes are the second most used type of ground heat exchangers after single U-pipe boreholes. The borehole thermal resistance is a key design and performance parameter for the double U-pipe boreholes. Another parameter that is particularly important for double U-pipe boreholes is the internal thermal resistance between the U-pipes. There is, however, a general lack of methods that can be used to calculate the thermal resistances of the double U-pipe boreholes. This article presents explicit multipole formulas for calculating thermal resistances of double U-pipe boreholes with symmetrically positioned pipes. The presented formulas include zeroth- and first-order expressions for the borehole thermal resistance and the internal thermal resistance. The internal thermal resistance formulas cover various possible flow configurations of the heat carrier fluid in the double U-pipes. The accuracy of the presented zeroth- and first-order formulas is established by comparing them to the original 10th-order multipole method. The article also presents thermal network models for computing effective borehole thermal resistance of double U-pipe boreholes from the multipole resistances. Formulas for calculating effective borehole thermal resistance of double U-pipe boreholes are presented for two idealized cases of uniform heat flux and uniform average wall temperature along the borehole.

Prediction of the minimum point of the pressure drop in a narrow rectangular channel under a transversely non-uniform heat flux

It is necessary to accurately predict the minimum point of pressure drop to ensure the safety of nuclear reactors. However, the non-uniform heat flux distribution along the transverse direction is encountered when the plate-type nuclear fuels are used. This study shows the effect of a transversely non-uniform heat flux on the minimum point of the pressure drop. The pressure drop-flow rate curve under the non-uniform heat flux was obtained by the experiment, and the trend of curve was different with the one of uniform heat flux case. Under the non-uniform heat flux, even when the inlet mass flow rate decreased, the value of the pressure drop was constant for a while with the development of a two-phase flow. With further reduction of inlet mass flow rate, the pressure drop started to decrease until the minimum point of the pressure drop was reached. Moreover, the inlet mass flow rate at the minimum point of pressure drop is much lower than that in the uniform heat flux case. For a detail analysis, the numerical approach is proposed along with the application of multi-channel concept. A single narrow rectangular channel is divided along the transverse direction, and the heat flux is given non-uniformly to the divided channels. Although the pressure drop is separately calculated for each divided channel, the mass is transferred between the channels. In the calculation, the mass flow rate is non-uniformly distributed in the transverse direction. If the mass flow rate is uniformly distributed, the non-uniform heat flux causes an unbalanced pressure drop because of the non-uniform distribution of void fraction. As a result, at the edges where the void fraction is high, the mass flow rate is transferred to the middle of channel to balance the pressure drop in transverse direction. When the void fraction in the middle becomes significantly large, the minimum point of the pressure drop can be obtained.

Influence of circumferential solar heat flux distribution on the heat transfer coefficients of linear Fresnel collector absorber tubes

The absorber tubes of solar thermal collectors have enormous influence on the performance of the solar collector systems. In this numerical study, the influence of circumferential uniform and non-uniform solar heat flux distributions on the internal and overall heat transfer coefficients of the absorber tubes of a linear Fresnel solar collector was investigated. A 3D steady-state numerical simulation was implemented based on ANSYS Fluent code version 14. The non-uniform solar heat flux distribution was modelled as a sinusoidal function of the concentrated solar heat flux incident on the circumference of the absorber tube. The k–ε model was employed to simulate the turbulent flow of the heat transfer fluid through the absorber tube. The tube-wall heat conduction and the convective and irradiative heat losses to the surroundings were also considered in the model. The average internal and overall heat transfer coefficients were determined for the sinusoidal circumferential non-uniform heat flux distribution span of 160°, 180°, 200° and 240°, and the 360° span of circumferential uniform heat flux for 10m long absorber tubes of different inner diameters and wall thicknesses with thermal conductivity of 16.27W/mK between the Reynolds number range of 4000 and 210,000 based on the inlet temperature. The results showed that the average internal heat transfer coefficients for the 360° span of circumferential uniform heat flux with different concentration ratios on absorber tubes of the same inner diameters, wall thicknesses and thermal conductivity were approximately the same, but the average overall heat transfer coefficient increased with the increase in the concentration ratios of the uniform heat flux incident on the tubes. Also, the average internal heat transfer coefficient for the absorber tube with a 360° span of uniform heat flux was approximately the same as that of the absorber tubes with the sinusoidal circumferential non-uniform heat flux span of 160°, 180°, 200° and 240° for the heat flux of the same concentration ratio, but the average overall heat transfer coefficient for the uniform heat flux case was higher than that of the non-uniform flux distributions. The average axial local internal heat transfer coefficient for the 360° span of uniform heat flux distribution on a 10m long absorber tube was slightly higher than that of the 160°, 200° and 240° span of non-uniform flux distributions at the Reynolds number of 4000. The average internal and overall heat transfer coefficients for four absorber tubes of different inner diameters and wall thicknesses and thermal conductivity of 16.27W/mK with 200° span of circumferential non-uniform flux were found to increase with the decrease in the inner-wall diameter of the absorber tubes. The numerical results showed good agreement with the Nusselt number experimental correlations for fully developed turbulent flow available in the literature.

Effect of non-uniform heating on entropy generation for the laminar developing pipe flow of a high Prandtl number fluid

Non-uniform distribution of heat flux as a wall boundary condition is used for laminar developing pipe flow to find the optimum case in which minimum entropy is generated. Several cases are solved for the same amount of heat rate but with different heat flux distribution and entropy generation is determined for each one. It is shown that entropy generation in the cases with decreasing heat flux distribution is always more than the cases with the same amount of heat flux at sections but with increasing distribution. In addition, it is found that the generated entropy for the cases with decreasing heat flux distribution is always more than the case of uniform heat flux. It is also seen that the optimum case is not the case with uniform heat flux distribution and the least generated entropy is due to a case with increasing heat flux distribution.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].

Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium

A theoretical analysis is presented to investigate thermally and hydrodynamically fully developed forced convection in a duct of rectangular cross section filled with a hyper-porous medium. The Darcy-Brinkman model was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e., the H boundary condition in the terminology of Kays and Crawford (1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, NY), is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Natural convection flow of micropolar fluid from a permeable uniform heat flux surface in porous medium

Natural convection flow of micropolar fluid along a vertical and a permeable semi-infinite plate embedded in a porous medium have been considered. A nonsimilarity solution is obtained for the case of uniform heat flux. A finite-difference scheme was used to solve the system of transformed governing equations. The obtained results are presented. A parametric study illustrating the influence of the Prandtl number, micropolar parameters, Darcy number, inertia coefficient and wall mass transfer on the velocities and temperature fields, skin friction, couple stress as well as the Nusselt number are investigated. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed. It is found that the enhancement of the wall heat transfer represented by increasing in the Nusselt number. But the values of the skin friction parameter and couple stress decrease as the suction parameter increases. Furthermore, the presence of inertia coefficient tends to decreases the local Nusselt number. In comparison to the Newtonian fluids, we found that the micropolar fluid enhances the skin friction and reduces the heat transfer rate.

Variable viscosity and thermal conductivity effects on combined heat and mass transfer in mixed convection over a UHF/UMF wedge in porous media: the entire regime

Mixed convection along a wedge embedded in a fluid-saturated porous media incorporating the variation of viscosity and thermal conductivity has been investigated for the case of uniform heat flux (UHF) and uniform mass flux (UMF). The governing equations, reduced to local nonsimilarity boundary layer equations using suitable transformations, have been solved numerically employing finite difference method. The entire regime of the mixed convection is included, as the mixed convection parameter χ varies from 0 (pure free convection) to 1 (pure forced convection). The numerical results for the dimensionless temperature, dimensionless concentration, local Nusselt (Sherwood) number are obtained. The decay of the dimensionless temperature and concentration profiles has been observed. The local Nusselt (Sherwood) number increase for the increase in buoyancy ratio N and for the decrease in wedge angle parameter λ. Also the local Nusselt number decreases for the increase of ε or γ and the local Sherwood number increases for the increase of γ and decreases for the increase of ε. The variations of the local Nusselt (Sherwood) number with the increase of χ have the phenomenon of minimum. It is observed that the Lewis number has a more pronounced effect on the local Sherwood number than it has on the local Nusselt number.

Forced Convection of a Power-Law Fluid in a Porous Channel—Integral Solutions

The integral method based on the boundary layer analysis is used to conduct a theoretical study of the primary hydrodynamic and heat transfer mechanisms for forced convection of a power-law fluid in a porous channel for both cases of uniform heat flux (UHF) and uniform wall temperature (UWT) boundary conditions. The flow in the porous medium is modeled using the modified Brinkman—Forchheimer-extended Darcy model for power-law fluids. The results indicate that for a high-permeability porous medium, the thickness of the momentum boundary layer depends on the Darcy number, inertia parameter, and power law index, but for a low-permeability porous medium it depends only on the Darcy number. Consequently in the non-Darcy regime, the effects of power law index on hydrodynamic and heat transfer behaviors in the porous channel are significant, whereas in the Darcy regime, the effects of Darcy number are predominant. Also the hydrodynamic behavior of shear thickening fluids (n > 1.0) is more sensitive to the Darcy number whereas the behavior of shear thinning fluids (n < 1.0) is more sensitive to the inertia parameter in the non-Darcy regime. Based on the fully developed Nusselt number solutions, the valid region for the applicability of the present integral method is illustrated graphically. The valid region of the integral solutions covers the Darcy regime for any value of the power law index within the range considered, while in the non-Darcy regime, the valid region for a shear thinning fluid becomes smaller than that for a shear thickening fluid as the inertia parameter decreases.

The effect of uniform lateral mass flux on free convection about a vertical cone embedded in a saturated porous medium

The effect of uniform lateral mass flux on natural convection about a cone embedded in a saturated porous medium is numerically analyzed. The surface is maintained at a uniform wall temperature (UWT) or uniform heat flux (UHF). The transformed governing equations are solved by Keller box method. Numerical data for the dimensionless temperature profiles and the local Nusselt number are presented for a wide range of the mass flux parameter. In general, it has been found that the local surface heat transfer rate increases owing to suction of fluid. This trend reversed for blowing of fluid. The mass flux parameter is found to have a more pronounced effect on the local Nusselt number for the case of UWT than it does for the case of UHF.

The Effect of the Thermal Boundary Condition on Transient Method Heat Transfer Measurements on a Flat Plate With a Laminar Boundary Layer

The heat transfer coefficient distribution on a flat plate with a laminar boundary layer is investigated for the case of a transient thermal boundary condition (such as that produced with the transient measurement method). The conjugate problem of boundary layer convection with simultaneous wall conduction is solved numerically, and the predicted transient local heat transfer coefficients at several locations are determined. The numerical solutions for the surface temperature are used to determine the Nusselt number that would be measured in a transient method experiment for a range of (nondimensionalized) surface measurement temperatures (liquid crystal temperatures when they are used as the surface sensor). These predicted transient method results are compared to the well-known results for uniform temperature and uniform heat flux thermal boundary conditions. Measurements are made and compared to the numerical predictions using a shroud (transient) experimental technique for a range of nondimensional surface temperatures. The numerical predictions and measurements compare well and both demonstrate the strong effect of the (nondimensional) surface temperature on transient method measurements. Transient method measurements will give heat transfer coefficients that range from as low as that of the uniform temperature case to higher than that of the uniform heat flux case (a 36 percent difference). These results demonstrate the importance of the temperatures used with the transient method.

Effects of wall transpiration on mixed convection in a radial outward flow inside rotating ducts

The present work treats the transport phenomena in a radial outward flow inside rotating ducts with rotation-induced buoyancy and wall transpiration effects. Using the vorticity-velocity method, the three-dimensional Navier-Stokes equations and the energy equation were solved simultaneously. Predicted results are presented for air flowing in a rectangular duct over a wide range of governing parameters. In this work, both the thermal boundary conditions of uniform wall temperature (UWT) and uniform heat flux (UHF) are considered. The results disclose that the axial variations of the peripherally averaged friction factor and Nusselt number are closely related to the emergence, disappearance, growth and decay of the rotation-induced secondary vortices. The Nu is enhanced with an increase in the rotation number Ro. Predicted results also show that near the entrance, the fRe increases with an increase in the wall Reynolds number Re w . But as the flow goes downstream, the fRe decreases with Re w . Additionally, the fRe and Nu for the UWT case are lower than those for the UHF case near the inlet but surpass them downstream.

Effect of Uniform Suction or Injection on Stability of Free-Convection Boundary Layer. (Case of Uniform Heat Flux).

Effect of Uniform Suction or Injection on Stability of Free-Convection Boundary Layer. (Case of Uniform Heat Flux).

A forced convection subcooled boiling model for nonuniform axial heat fluxes

The modeling of convective subcooled boiling of water flowing in round tubes subjected to nonuniform axial heat fluxes is described. The effects of different axial heat flux profiles are modeled using a local hypothesis; i.e. flow and thermal development are assumed to occur very rapidly in the subcooled boiling (SCB) flow regime. A computer code has been developed to predict the pressure drop, heat transfer coefficient and wall temperature for nonuniform axial heat fluxes, starting with a well-validated code for uniform axial heat fluxes. The predictions for some common nonuniform axial heat profiles are compared to the uniform heat flux case.

Free convection in a saturated porous medium adjacent to a vertical impermeable wall subjected to a non-uniform heat flux

Boundary layer analysis is performed for free convection in a fluid-saturated porous medium adjacent to a vertical impermeable wall subjected to a non-uniform heat flux. The wall heat flux is assumed to be an arbitrary function of the distance along the surface. The solutions are obtained in the form of perturbations to the uniform heat flux case. Using the differentials of the wall heat flux, which are functions of the distance along the surface, as perturbation elements, universal functions are obtained. These universal functions can be used to estimate the heat transfer for any type of wall heat flux variation. For the wall heat flux variation as a power function of the distance from the origin, the solutions obtained by using these universal functions have been compared with those obtained by similarity analysis and the agreement is found to be good. Further, solutions are presented for wall heat flux varying exponentially and sinusoidally but comparison could not be drawn due to non-availability of solutions in the literature.