Laminar Convection Heat Research Articles

Natural-Convection Heat Transfer in Channels With Isoflux Convex Surfaces

Numerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 104) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.

A heuristic approach to optimal arrangement of multiple heat sources under conjugate natural convection

Steady state numerical computations and experiments were performed to study three-dimensional, conjugate laminar natural convection heat transfer from multiple identical heat generating modules (heat sources) in a vertical duct. The heat sources were mounted on a wall at different positions in a defined grid of 5 × 5 positions. Air is used as the cooling medium. The governing flow and energy equations were solved using FLUENT 6.3. The optimum geometric configuration of the five heat sources that maximizes the heat transfer was determined by the introduction of a dimensionless distance parameter and an exhaustive search. The heuristic procedure based on the geometric parameter was tested for varying number of heat sources and for different heat source strengths. Experiments were performed to study the effect of modified Grashof number and the duct spacing on maximum temperatures of different configurations in order to support the numerical findings. Additionally, the temperatures of the heat sources arranged in the optimum configuration obtained by the heuristic approach have been experimentally validated.

Entropy generation analysis for Couette Poiseuille flow through parallel-plates microchannel

This paper presents the first and second laws of thermodynamics analysis for laminar forced convective heat transfer of a Newtonian fluid in a microchannel between parallel plates. Hydrodynamically and thermally fully developed flow with constant properties is examined. Two different forms of the thermal boundary-conditions are considered. The velocity and temperature profiles are analytically determined as a function of the Brinkman and the Knudsen number. The present results are in an excellent agreement with those available in the literature. Entropy generation is shown to decrease with an increase in Kn while increasing Br and Br/Ω results in increasing entropy generation.

Additional Description of Laminar Heat Convection in Tube with Uniform Wall Temperature

Cx = cross average of x, which can be We r,We , We z, Wc r, Wc , or Wc z ei;j = velocity gradient, a second-order tensor f = friction factor h = heat transfer coefficient er, e , ez = unit vector with respect to the r, , z direction Nu = Nusselt number q = components of the heat flux vector q = heat flux vector R = radius of the tube r, , z = coordinate axes Sx = span-averaged value of x, which can beWe r, We ,We z,Wc r,Wc , orWc z T = temperature t = time v = velocity vector vr, v , vz = components of the velocity vector Wc r = velocity’s contribution to the convection of qr, vr @qr @r v @qr r@ vz @qr @z v q r Wc = velocity’s contribution to the convection of q , vr @q @r v @q r@ vz @q @z v qr r We r = velocity gradient’s contribution to the convection of qr, @vr @r qr @v @r q @vz @r qz We z = velocity gradient’s contribution to the convection of qz, @vr @z qr @v @z q @vz @z qz Wc z = velocity’s contribution to the convection of qz, vr @qz @r v @qz r@ vz @qz @z We = velocity gradient’s contribution to the convection of q , @vr r@ qr @v r@ v r vr r q @vz r@ qz = thermal diffusivity = thermal conductivity r = operator

Analysis of Laminar Mixed Convective Heat Transfer in Horizontal Triangular Ducts

Numerical simulations for fluid flow and heat transfer in triangular ducts are carried out. Flow is considered to be laminar, hydrodynamically, and thermally developing. Heat transfer by both forced and natural convection is taken into account. Simulations are carried out for constant wall temperature cases which are at a higher temperature than the inlet temperature of the fluid. The effect of Rayleigh number on bulk mean temperature and Nusselt number is studied. Isotherm and secondary velocity profile formed because of natural convection is shown at different locations with varying Rayleigh number. The effect of the apex angle of the triangular duct on Nusselt number and bulk mean temperature is studied. Results are compared with the cases of mixed convective heat transfer in a square duct.

Soret effect on mixed convection heat and mass transfer along a semi-infinite horizontal plate in the presence of heat generation and chemical reaction

The aim of this work is to study Soret and chemical reaction effects on laminar mixed convection boundary-layer flow and heat and mass transfer past a semi-infinite horizontal flat plate in the presence of heat generation. A transformation is introduced that reduces the equations governing the flow to a system of nonlinear coupled ordinary differential equations. The transformed equations are solved numerically using the fourth-order Runge–Kutta integration scheme coupled with the shooting method. Graphical results for the velocity, temperature, and concentration profiles for various parametric conditions are presented and studied. The effects of the chemical reaction parameter, Soret parameter, and the heat generation parameter on the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form and discussed.PACS Nos.: 44.20+b, 44.20+Cb

Comparison of Mixed Convection in a Square Cavity with an Oscillating versus a Constant Velocity Wall

This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.

Contribution Analysis of Dimensionless Variables for Laminar and Turbulent Flow Convection Heat Transfer in a Horizontal Tube Using Artificial Neural Network

The artificial neural network (ANN) method has shown its superior predictive power compared to the conventional approaches in many studies. However, it has always been treated as a “black box” because it provides little explanation on the relative influence of the independent variables in the prediction process. In this study, the ANN method was used to develop empirical correlations for laminar and turbulent heat transfer in a horizontal tube under the uniform wall heat flux boundary condition and three inlet configurations (re-entrant, square-edged, and bell-mouth). The contribution analysis for the dimensionless variables was conducted using the index of contribution defined in this study. The relative importance of the independent variables appearing in the correlations was examined using the index of contribution based on the coefficient matrices of the ANN correlations. For the turbulent heat transfer data, the Reynolds and Prandtl numbers were observed as the most important parameters, and the length-to-diameter and bulk-to-wall viscosity ratios were found to be the least important parameters. The method was extended to analyze the more complicated forced and mixed convection data in developing laminar flow. The dimensionless parameters influencing the heat transfer in this region were the Rayleigh number and the Graetz number. The contribution analysis clearly showed that the Rayleigh number has a significant influence on the mixed convection heat transfer data, and the forced convection heat transfer data is more influenced by the Graetz number. The results of this study clearly indicated that the contribution analysis method can be used to provide correct physical insight into the influence of different variables or a combination of them on complicated heat transfer problems.

Natural convection analysis for both protruding and flush-mounted heaters located in triangular enclosure

A numerical was performed analysis on laminar natural convection heat transfer and fluid flow in both protruding heaters (PHs) and flush-mounted heaters (FMHs) located in a triangular enclosure using finite-difference technique. The heaters were isothermal and the temperature of the inclined wall was lower than that of the heaters while the remaining walls of the triangular enclosure were adiabatic. Results are presented according to the location of the heaters in two cases. In the first case, the PH was located near the vertical wall and the FMH near the right corner. In the second case, the PH was located near the right corner of the enclosure, whereas the FMH was located close to the vertical wall. The governing parameters on natural convection were Rayleigh number (104≤Ra≤106), dimensionless length of the PH ( W1), dimensionless length of the FMH ( W2), dimensionless height of the PH (Hp), dimensionless distance between the heater and the vertical wall ( S1), dimensionless distance between the PH and the FMH ( S2), and aspect ratio of the triangular enclosure (0.25 ≤AR≤ 1.0). It was found that better heat transfer occured when the PH was located near the right corner of the triangular enclosure, while the other heater was mounted near the left vertical wall. Heaters behaved as a single heater when they were close to each other.

伝熱面付着気泡が層流自然対流熱伝達に及ぼす影響

伝熱面付着気泡が層流自然対流熱伝達に及ぼす影響

Numerical Simulation of Three-Dimensional Combined Convective Radiative Heat Transfer—A Finite Volume Method

Combined laminar forced convection and radiation heat transfer was numerically simulated in a three-dimensional channel flow. A finite volume method was used to solve the steady incompressible Navier-Stokes equations, energy equation, and radiative transfer equation. The effects of Reynolds number, conduction-radiation parameters, absorption coefficient, and scattering albedo on the Nusselt number and bulk temperature profiles along the channel are presented. Radiation was found to play a major impact on temperature field in the range of parameters considered in this study. It was found that the radiation effect is diminished, and thermal penetration is increased with increasing Reynolds number, conduction-radiation parameter, scattering albedo, and decreasing absorption coefficient.

Natural Convection Heat Transfer Through an Interface Separating Two Fluids in An Horizontal Annulus

In this research a theoretical study for laminar steady natural convection heat transfer through concentric horizontal annulus heated from inside, it’s contain two different fluids (pr1:0.7, pr2:7.0) for radius ratio (5) and for Gr numbers (102-105). A vorticity stream function formula was used in the numerical solution by transforming the governing differential equations into this formula, then turned into algebraic equations solved numerically using (Explicit Successive Over Relaxation finite deference method). To declare the movement of the fluids and the distribution of the temperatures through each of them counters for both streamlines and isotherms through the annulus were used, also the results contain calculating the distribution, of local Nu number along the internal cylinder inside the annulus, also a correlation was found to estimate the amount of heat transfer for both fluids. Through this research it’s found that two separating flows forming above and under the separating interface, also it’s found that the highest local Nu number accrue at the separating interface.

Transient Laminar Forced Convection Heat Transfer of power-law Fluids along a Wavy Plate

The transient laminar forced convection of power-law fluids along a wavy surface is studied by the coordinate transformation and the cubic spline collocation method. Effects of the power-law index and the amplitude-wavelength ratio on the Nusselt number and the skin-friction coefficient are examined. The fluid with larger power-law index has larger transient local Nusselt numbers at the leading edge; as the fluid moves downstream from the leading edge, the transient local Nusselt number and the transient mean Nusselt number of dilatant fluids decrease rapidly while those of pseudoplastic fluids increase. The transient local skin-friction coefficient decreases as the power-law index is increased. Moreover, the harmonic curves for the transient local Nusselt number and the transient local skin-friction coefficient have the same wave number as that of the wavy surface.

Experimental Study of Free Convection Heat Transfer from Horizontal Isothermal Cylinders Arranged in Vertical and Inclined Arrays

Laminar free convection heat transfer from vertical and inclined arrays of horizontal isothermal cylinders in air were investigated experimentally. Experiments were carried out using a Mach-Zehnder interferometer. For the vertical array, the cylinder spacing (center to center) varied from 2 to 5 cylinder diameter. The same range of vertical spacing also was used for the inclined array. The horizontal spacing varied from 0 to 2 cylinder diameter in the inclined array. The Rayleigh number based on the cylinder diameter varied between 103 and 3× 103. The effect of vertical and horizontal cylinder spacing and Rayleigh number on the heat transfer from each individual cylinder and the whole array were investigated. It is found that the free convection heat transfer from any individual cylinder in the array depends on its position relative to the others. Heat transfer correlations have been developed for any individual cylinder in the vertical and inclined arrays and for the arrays. Also the experiment was carried out on a single cylinder for a comparison with the results from other research.

Numerical Computation of Laminar Natural Convection Heat Transfer around a Horizontal Compound Tube with External Longitudinal Fins

A new boundary condition treatment at the pseudo-outer boundary is proposed to numerically simulate the laminar natural convection heat transfer around a horizontal finned tube. It may be implemented easily while largely reducing the computational domain size. Numerical tests indicate that by using this boundary condition, the relative errors of the average Nusselt number of the laminar natural convection around a horizontal isothermal cylinder are less than 0.5% when compared with the benchmark solutions. The heat transfer of the laminar natural convection around a horizontal compound tube with different fin heights and a different number of fins are calculated using the conjugated computational method with primitive variables. The key findings are as follows: (1) for a fixed fin number, there exists an optimum relative fin height at which the total heat transfer rate of the finned tube approaches the maximum; (2) for a fixed relative fin height, there exists an optimum fin number at which the total heat transfer rate of the finned tube reaches its maximum; and (3) the tube fin positioning also has some effect on the heat transfer. Positioning a pair of fins in the vertical symmetric plane will deteriorate the overall heat transfer to some extent.

Analysis of Micro-Graetz Problem in a Microtube

A theoretical analysis is presented for the problem of hydrodynamically developed, thermally developing, steady, laminar forced convective heat transfer of a Newtonian fluid in the entrance region of a microtube. The viscous dissipation effect, the velocity slip, and the temperature jump at the wall are taken into consideration. Two different thermal boundary conditions are considered: the constant heat flux (H1-type) and the constant wall temperature (T-type). Either wall heating (the fluid is heated) or wall cooling (the fluid is cooled) is considered. The downstream variation and the asymptotic value of the Nusselt number are determined as a function of the Brinkman number and the Knudsen number. For some limiting cases, the results are compared with those existing in the literature and an excellent agreement is observed.

Free Convection Heat Transfer from a Confined Horizontal Elliptic Cylinder

The laminar free convection heat transfer from an isothermal horizontal cylinder of elliptical cross-section confined between two adiabatic walls is investigated by the Mach-Zehnder interferometry technique. The ellipse major axis is vertical, and the minor to major axis ratio is kept constant to 0.53. This paper focuses on the effect of wall spacing and Rayleigh number variation on the local and average free convection heat transfer coefficient from the cylinder surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 9 × 10 2 to 3.2 × 10 3 and wall spacing to cylinder minor axis ratios of 1.9, 2.3, 2.67, 3.17, 3.8, 4.6, 6.12, 8, 13, ∞. Results are indicated with a single correlation that gives the average Nusselt number as a function of the ratio of the wall spacing to cylinder minor axis and the Rayleigh number. There is an optimum distance between the walls in which the Nusselt number is maximum. The experiment was also carried out on a cylinder of circular cross-section with the same periphery and length of the elliptic cylinder to allow a comparison with the results of other research.

A Theoretical Study on Natural Convection in a Concentric Vertical Annulus

The research include a theoretical study of natural laminar study convection heat transfer in a vertical annuls, the surfaces were at constant temperature and the inner cylinder temperature is higher than the outer cylinder temperature. The air used as a working fluid in the annulus. Rayleigh Number was( 71 Ra 5 10 4 ) and the radius ratio were (1.7, 2.0 and 2.3). Alternating direct implicit method (ADI) was used to solve the governing equations numerically, the governing equations were transformed into vorticity-stream function formula then transformed into algebraic equations using finite difference method. The results were declared by using contour diagrams which represent streamlines and isotherms also the results were declared by velocity and temperature distribution through the annulus and local Nusselt number along the inner cylinder.It was found in this research that heat transfer by conduction in low Rayleigh Number, also increasing the thermal boundary layer around the inner cylinder as the fluid moves up while the thermal boundary layer on the outer cylinder increases as the fluid moves down.

Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates

In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette–Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement.

Viscous-dissipation effects on the heat transfer in a Poiseuille flow

In this study, laminar heat-convection in a Poiseuille flow of a Newtonian fluid with constant properties is analyzed by taking the viscous dissipation into account. At first, both hydrodynamically and thermally fully-developed flow case is investigated. Then, consideration is given to thermally-developed laminar forced-convection. The axial heat-conduction in the fluid is neglected. Two different thermal boundary-conditions are considered: the constant heat-flux and the constant wall-temperature. Both the hot-wall and the cold-wall cases are considered. In the literature, the viscous-dissipation effect is commonly represented by the Brinkman number. Several different definitions of the Brinkman number arise depending on the thermal boundary conditions. Either for the thermally fully-developed case or the thermally-developing case (the Graetz problem), temperature distributions and the Nusselt numbers are analytically determined as functions of the Brinkman number.