Uniform Wall Heat Flux Research Articles

Effect of viscous dissipation in heating/cooling of grade three fluid in a pipe subjected to uniform surface temperature

Forced convection in Newtonian and non-Newtonian fluids flowing through pipes maintained at uniform heat flux or uniform wall temperature are important for understanding heat transfer characteristics in design and thermal management of heat exchangers. Convective heat transfer in both Newtonian and non-Newtonian fluids flowing through pipes and parallel plates, subjected to uniform wall heat flux condition, were extensively studied by researchers. But for uniform wall temperature, studies on non-Newtonian fluids in pipes are rarely considered. Forced convective heating and cooling of a third-grade fluid, flowing in a pipe subjected to uniform (constant) wall temperature is considered. Effect of viscous dissipation is included in the energy equation. Separate energy conservation equations for heating and cooling are formulated and their dimensionless forms are obtained. Numerical solutions by shooting technique are obtained for the governing equations. The same equations are also solved by the least square method and semi-analytical solutions are yielded. Least square method is a widely used semi-analytical tool used for solving non-linear differential equations. Results of the numerical solution and semi-analytical solutions are compared and are observed to be in close agreement. This validates the numerical solution. Few important observations are presented. For heating, when the non-Newtonian parameter increases from 0 – 0.1, the peak temperature drops from 1.15 – 0.55 which occurs at the centre. In case of cooling, when non-Newtonian parameter increases from 0 – 0.1, the difference in central line temperature and wall temperature increases to 0.17 from 0.09. For change in the non-Newtonian parameter from 0.2 – 0.3, both for heating and cooling the peak temperature change is not drastic. Heat transfer coefficient, in case of heating, differs by nearly 3.5 when the non-Newtonian parameter increases from 0 – 0.1.

Experimental Study on Heat Transfer Enhancement of 3D-Printed Mini Tubes Under Three Different Flow Directions

In this study, 864 heat transfer experimental data points and 216 pressure drop experimental data points were used to compare the heat transfer and friction factor behavior of 3D-printed and traditional tubes under uniform wall heat flux boundary condition. Experiments were conducted in the entire flow region that covers laminar, transition, and turbulent regions. The inside diameter of the test tubes is around 2 mm, and the average inside wall surface roughness for traditional and 3D-printed tubes is 2.211 μ m and 35.249 μ m , respectively. Comparing with the traditional tubes, in the upper transition and the turbulent regions, the Nusselt numbers and Colburn j -factors of the 3D-printed tube under three different flow directions were enhanced by an average of 52.67% and 51.59% respectively. The greater relative roughness of the 3D-printed tube enhanced the heat transfer but also increased the pressure drop significantly. The friction factors for the 3D-printed tube in these regions also increased by an average of 154.44% compared with the traditional tube. The results also show that the effect of different flow directions on heat transfer and pressure drop of the 3D-printed tube is insignificant relative to roughness. Moreover, the 3D-printed tube has an earlier transition compared with the traditional tube.

Investigation of Laminar Forced and Mixed Convection in Horizontal Mini Tubes with Uniform Wall Heat Flux Boundary Condition

In this study, a numerical model is established to study the forced and mixed convection heat transfer in the laminar region for horizontal mini tube with different diameters (1.2 mm to 3.0 mm) under the uniform wall heat flux boundary condition. The Reynolds number is set from 100 to 2,000 and the uniform wall heat flux boundary condition is set at 10 and 20 kW/m2. The model is verified with well-established correlation to guarantee good accuracy. The existence of mixed convection is examined by (1) the ratio between the heat transfer coefficients at the top and the bottom of the tube, and (2) the temperature contour plot. Based on the simulation results, the existence of buoyancy superimposed on the main flow is strongly related to the tube diameter, the dimensionless location, the Reynolds number, and the heat flux applied. Under the same heating condition, for small diameter tube with insufficient length, buoyancy effect can never establish. The existing flow regime maps for macro tube were used to predict the forced and mixed convection regimes from the simulated mini tube results and discrepancy was found. A new flow regime map is hence developed for mini tubes, and it classified the simulation results with good accuracy.

CONVECTIVE HEAT TRANSFER INSIDE A ROTATING HELICAL PIPE FILLED WITH SATURATED POROUS MEDIA

In this paper, we study the hydrothermal characteristics of flow inside a rotating helical pipe filled with saturated homogeneous porous medium. The analysis is being carried out for the case of small curvature and torsion. Using the perturbation approach, velocity and temperature fields are solved for both uniform wall heat flux and uniform wall temperature boundary conditions. Perturbation expansion up to the third order is carried out to investigate the effect of rotation on the flow. The influence of rotation on velocity is noticed as early as the first order, and on temperature solution, it has an effect in the third order. The influence of rotation on the Nusselt number does not appear till third order, and it is discovered that the Nusselt number grows as dimensionless curvature increases. Moreover, the theoretical results have been verified against experimental data from existing literature for the special case of zero rotation and curvature of the pipe. The available experimental data align well with and support the theoretical results in this limiting case.

Numerical analysis of the binder angle effect on convective heat transfer and pressure drop in drilled-hollow sphere architected foams

Due to their capability of generating customized microstructures, additive manufactured cellular materials are promising to being employed in heat transfer devices. To this aim, among printable cellular materials Drilled-Hollow Spheres Architected (DHSA) foams are investigated. However, at the present status, limited data on pressure drop and heat transfer in DHSAs are available. Starting from hollow spheres, a metal DHSA foam is generated with CAD software in this study. Forced air convective heat transfer in the foam is investigated numerically, under the assumptions of air incompressible laminar flow and uniform wall heat flux from the solid to the fluid phase. Mass, momentum and energy equations in the fluid region are written and solved numerically, for various values of the foam binder angle and the velocity of the inlet air. The convective heat transfer coefficients, the pressure drop and the friction factor are predicted. The effects of the binder angle and the air inlet velocity on heat transfer and pressure drop are highlighted.

Dean number only can not determine characteristics of fluid flow and heat transfer in helically coiled tubes with large curvature

The majority of reported findings indicate that the fluid flow and heat transfer characteristics within helically coiled tubes (HCTs) with small curvature can be determined solely by Dean number. Due to a scarcity of published investigations pertaining to HCTs with large curvature, the extent to which Dean number can ascertain the attributes of HCTs with large curvature remains uncertain. However, the advancement of technology has enabled the production and utilization of HCTs with large curvature. Consequently, there is a significant demand for understanding the fluid flow and heat transfer characteristics of HCTs with large curvature. The present study employs a numerical approach to investigate the characteristics of laminar fluid flow and heat transfer in HCTs with large curvature, where the ratio of coil radius to tube radius (D/d) is less than 5. The findings indicate that the fluid flow and heat transfer characteristics in HCTs cannot be solely determined by Dean number. In addition to the (D/d)0.5 included in Dean number, the fluid flow friction factor is also influenced by (D/d)−0.1902. When considering uniform wall temperature boundary, Nusselt number is mainly determined by Dean number. However, for uniform wall heat flux boundary, Nusselt number is additionally influenced by (D/d)0.1222.

Thermohydraulic performance study of the effect of winglet inserts and a corrugated wall in a rectangular channel

This numerical study investigates the enhancement of heat transfer and pressure drop characteristics in rectangular channels with transverse corrugations and longitudinal winglet vortex generators. Numerical simulations cover a range of Reynolds numbers (Re) (5000–20000) using channels with uniform wall heat flux and fixed wavelength. The study evaluates the influence of geometrical parameters (corrugated channel amplitude and winglet length) on flow and temperature characteristics, average Nusselt number (Nu), and pressure drop. Corrugated channels alone create stationary transverse vortices that impede heat transfer. However, integrating winglet vortex generators introduces beneficial longitudinal vortices, disrupting stationary vortices, perturbing the thermal boundary layer, enhancing near-wall turbulence, and improving fluid mixing and heat transfer compared to smooth and corrugated channels. At Reynolds number (Re)20,000, corrugated channels with winglets exhibit 167.7 % and 61.8 % higher Nusselt numbers compared to smooth and corrugated channels, respectively. However, this enhanced heat transfer accompanies increased pressure drop. Both heat transfer and pressure drop rise with higher Reynolds numbers (Re), corrugation amplitude, and winglet length. This study provides insights into heat transfer mechanisms in corrugated channels and the potential for improvement through winglet vortex generators.

Convective heat transfer across silicon rods under uniform wall heat flux in a laboratory-scale Siemens reactor

The effects of operating and geometric parameters on convective heat transfer (CHT) in Siemens reactor with a laboratory-scale are investigated. A dimensionless analysis of the CHT is performed considering the flow characteristics, rod diameter (d), rod length (L), number of rods, and the distance between adjacent silicon rods. A dimensionless parameter (Hou) is proposed to represent the number of rods and the distance between adjacent rods. Additionally, three dimensionless parameters that affect the CHT, namely, the Rayleigh number, d/L, and Hou, are obtained. The two-factor interaction effects of the dimensionless parameters on the CHT are analyzed, and their relationships are determined for calculating the CHT flux. Based on these relationships, the Nusselt number is calculated for 7- and 8-rod laboratory-scale Siemens reactors, and the relative errors between the predicted and calculated results are 1.4 and 3.2 %, respectively.

Fully developed opposing mixed convection of a Jeffery tri‐hybrid nanofluid between two parallel inclined plates subjected to wall‐slip condition

AbstractWe analyze the effect of wall slip on the fully developed reverse mixed convection of Jeffery nanofluids between two inclined parallel plates with uniform wall heat flux conditions. The theory of tri‐hybrid water‐based nanoparticles with unique shapes, namely, cylindrical (copper), spherical (titanium oxide), and platelet (aluminum oxide) for heat transfer enhancement is utilized since it has better heat performance applicable in a dynamic of fuels and coolant in automobiles as compared with regular Newtonian fluid and nanofluid. The equations describing the above transport phenomena are nondimensional through appropriate scale transformations. Analytical solutions for velocity, temperature, and pressure distributions are obtained. Four different flow regimes including no reversal, bottom reversal, top reversal, and on both walls reversal are found for different combinations of buoyancy and pressure. Particularly, we notice that the wall slip significantly affects flow reversal. Furthermore, we notice that Magyari 's conclusion that the results of the homogeneous nanofluid flow model can be recovered from the corresponding Newtonian fluid model has great limitations. Besides, the effect of several physical factors on velocity and temperature distributions and important physical quantities, including skin friction coefficient and Nusselt number, are analyzed and graphically discussed.

Heat transfer mechanism in ribbed twisted-oval tubes

This paper presents the fluid flow and heat transfer mechanisms in ribbed twisted-oval tubes. Simulations were conducted for a uniform heat-flux wall condition in turbulent flow (5000 ≤ Re ≤ 20,000). Optimal conditions were evaluated from the following parameter ranges: rib arrangement (vertical and horizontal); number of ribs, N = 1, 2, 4; rib height ratios, RR = 0.025–0.1; spiral depth ratios, DR = 0.05–0.14 and twist pitch ratios, PR = 1.5–5.0. It was determined that the ribbed twisted-oval tubes generated stronger swirl flow than a conventional twisted-oval tube, indicated by their greater turbulent kinetic energy. With increasing RR, DR and N, the turbulent kinetic energy significantly increased while the opposite trend was observed as PR became larger. The greater turbulent kinetic energy led to better fluid mixing between the core and near wall region, which directly varied with the heat transfer between the two regions. The optimal parameters that provided a maximal thermal performance factor (TPF), 1.32, were PR = 3.5, DR = 0.1, RR = 0.075, N = 4 and Re = 5000.

Experimental Analysis Of The Influential Factors On Mixed Convection Flow In Horizontal Pipes

Abstract It has been speculated that a forced pipe flow is always assisted by free convection owing to the dependency of fluid properties on its temperature. The purpose of the current study is to experimentally examine the effect of different-sized smooth horizontal pipes on mixed convection of water in internal flows under uniform heat flux wall conditions. Infra-red thermal imaging is used to measure outer surface temperature in axial and circumferential direction. Reynolds number range is taken between 1000 and 18000 on three test sections of the diameter of 8mm, 13.8 mm, and 17.8 mm. The outcome of varying tube diameter, mass flux, and heat flux on mixed flow characteristics is studied. The strength of free convection is illustrated by the ratio of top to bottom local heat transfer coefficient. It is found to be maximum at the tube outlet by 50% and 80% for 8mm and 13.8mm tube diameter than the inlet. The laminar Nusselt number is 3 to 6 times the analytical value of Nu=4.36 under UHF condition. The Nusselt number increases with the increase in the tube diameter. The temperature distribution in the turbulent regime remains constant from the top to the bottom point. However, it significantly differs in laminar flow. A suitable correlation is suggested for the variation of the Nusselt number under the laminar regime showing the emphasis of free convection on forced convection.

Heat transfer and pressure drop investigation for prescribed heat fluxes on both the inner and outer wall of an annular duct

The rising cost of energy has made the need for the design of energy-efficient thermal equipment a necessity. It was therefore the purpose of this study to experimentally determine the heat transfer and pressure drop during the forced convective turbulent flow of water in a horizontal concentric annular flow passage with various prescribed uniform wall heat fluxes. Unilateral heating from either the inner or outer wall of the annulus, as well as bilateral heating on both walls simultaneously, were considered. Compared to unilateral heating conditions, bilateral heating resulted in enhanced heat transfer coefficients. When the difference in temperature between the fluid and the walls was considered, the factors of diabatic friction were correlated to within 1%.

Numerical Study on the Heat Transfer Characteristics of Cu-Water and TiO2-Water Nanofluid in a Circular Horizontal Tube

A numerical simulation of convective heat transfer coefficient (hconv) was studied with Cu-Water and TiO2-Water nanofluids flowing through a circular tube subjected to uniform wall heat flux boundary conditions under laminar and turbulent regimes. Four different concentrations of nanofluids (ɸ = 0.5, 1, 1.5 and 2%) were used for the analysis and the Reynolds number (Re) was varied from laminar (500 to 2000) to turbulent flow regime (5000 to 20,000). The dependence of hconv on Re and ɸ was investigated using a single-phase Newtonian approach. In comparison to base fluid, average hconv enhancements of 10.4% and 7.3% were noted, respectively, for the maximum concentration (ɸ = 2%) and Re = 2000 for Cu-Water and TiO2—water nanofluids in the laminar regime. For the same ɸ under the turbulent regime (Re = 20,000), the enhancements were noted to be 14.6% and 13.2% for both the nanofluids, respectively. The random motion (Brownian motion) and heat diffusion (thermophoresis) by nanosized particles are the two major slip mechanisms that have more influence on the enhancement of hconv. In addition, the Nusselt number (Nu) of the present work was validated for water with the Shah and Dittus Boelter equation and found to have good agreement for both the regimes.

Heat Transfer Intensification in a Heat Exchanger by Means of Twisted Tapes in Rib and Sawtooth Forms

This experimental study aimed to intensify the aerothermal performance index (API) in a round tube heat exchanger employing twisted tapes in rib and sawtooth forms (TTRSs) as swirl/vortex flow generators. The TTRSs have a constant twist ratio of 3.0, a constant rib pitch ratio (p/e) of 1.0, and six different sawtooth angles (α = 20°, 30°, 40°, 50°, 60°, and 70°). Experiments were carried out in an open flow using air as the working fluid for Reynolds numbers between 6000 and 20,000 in the current study, which was conducted in a heated tube under conditions of uniform wall heat flux. A typical twisted tape (TT) was also tested for comparison. The experimental results suggest that TTRSs yield Nusselt numbers ranging from 1.42 to 2.10 times of those of a plain tube. TTRSs with larger sawtooth angles (α) offer superior heat transfer. The TTRSs with α = 20°, 30°, 40°, 50°, 60°, and 70° respectively, enhance average Nusselt numbers by 158%, 162%, 166%, 172%, 180%, and 187% with average friction factors of 3.51, 3.55, 3.60, 3.67, 3.75 and 3.82 times higher than a plain tube. Additionally, TTRSs with sawtooth angles (α) of 20°, 30°, 40°, 50°, 60°, and 70° offer APIs in the ranges of 0.99 to 1.19, 1.01 to 1.21, 1.03 to 1.26, 1.05 to 1.31, 1.07 to 1.42, and 1.09 to 1.48, respectively, which are higher than those of the typical twisted tape (TT) by around 5%, 7%, 11%, 16%, 25%, and 31%, respectively. This demonstrates that twisted tapes in rib and sawtooth form (TTRSs), with appropriate geometries, give a promising trade-off between enhanced heat transfer and an increased friction loss penalty.

Review and Analysis of Electro-Magnetohydrodynamic Flow and Heat Transport in Microchannels

This paper aims to develop a review of the electrokinetic flow in microchannels. Thermal characteristics of electrokinetic phenomena in microchannels based on the Poisson–Boltzmann equation are presented rigorously by considering the Debye–Hückel approximation at a low zeta potential. Several researchers developed new mathematical models for high electrical potential with the electrical double layer (EDL). A literature survey was conducted to determine the velocity, temperature, Nusselt number, and volumetric flow rate by several analytical, numerical, and combinations along with different parameters. The momentum and energy equations govern these parameters with the influences of electric, magnetic, or both fields at various preconditions. The primary focus of this study is to summarize the literature rigorously on outcomes of electrokinetically driven flow in microchannels from the beginning to the present. The possible future scope of work highlights developing new mathematical analyses. This study also discusses the heat transport behavior of the electroosmotically driven flow in microchannels in view of no-slip, first-order slip, and second-order slip at the boundaries for the velocity distribution and no-jump, first-order thermal-slip, and second-order thermal-slip for the thermal response under maintaining a uniform wall-heat flux. Appropriate conditions are conferred elaborately to determine the velocity, temperature, and heat transport in the microchannel flow with the imposition of the pressure, electric, and magnetic forces. The effects of heat transfer on viscous dissipation, Joule heating, and thermal radiation envisage an advanced study for the fluid flow in microchannels. Finally, analytical steps highlighting different design aspects would help better understand the microchannel flow’s essential fundamentals in a single document. They enhance the knowledge of forthcoming developmental issues to promote the needed study area.

A Conservation-Based Transitional Boundary Layer Model

Abstract A simple, flow-physics-based model of flat-plate, transitional boundary layer skin friction and heat transfer is presented. The model is based on the assumption of negligible time-, spanwise-, and streamwise-average wall-normal velocity at the top of the boundary layer. This results in a threefold increase in boundary layer thickness over the transition region. This simple velocity assumption and its boundary-layer growth implications seem to be reasonably consistent with more sophisticated (direct numerical simulation (DNS)) modeling simulations. Only two modeling parameters need to be assumed, the Reynolds numbers at the onset and at the completion of transition, for which there is guidance based on freestream turbulence intensity for smooth plates. Several experimental datasets for air are modeled. New criteria are proposed to help define the onset and completion of transition: zero net vertical (wall-normal) velocity or mass flux (integrated in time and space, spanwise and streamwise) at the top of the boundary layer, and tripling of boundary layer thickness. Also presented is a minor improvement to a previously published unheated starting length factor for flat-plate laminar boundary layers with uniform wall heat flux.

Probing the Accuracy of Experimental Data on Nusselt Numbers Within Miniature Heat Sinks

Abstract Achieving accurate experimental data in conjugate heat transfer studies to calculate Nusselt number can be challenging due to its complex three-dimensional thermal hydraulics nature. This study is devoted to evaluating the accuracy and reliability of experimental approaches used to calculate the Nusselt number in miniature heat sinks. It is observed that three major parameters including (1) axial heat conduction within the solid substrate of heat sinks, (2) thermal contact resistance, and (3) assumed uniform wall temperature, as well as wall heat flux distributions, influence the reported experimental data in the literature. The results obtained from the developed analytical and computational models in this study revealed that the assumptions of local uniform wall temperature and heat flux distributions for small-scale heat sinks result in underestimated Nusselt numbers calculated from experiments. At lower Reynolds number (<200) flows in miniature heat sinks with a high solid to fluid thermal conductivity ratio (>> 1), it is shown that the fluid bulk temperature should be measured away from the heat sink inlet and outlet to minimize the effect of axial heat conduction within the solid substrate of the microscale heat sinks on calculated Nusselt numbers. As the third important parameter, the influence of thermal contact resistance on the Nusselt number calculation in a miniature heat sink is studied where thermal slip length is considered. Finally, the concurrent effects of thermal contact resistance and thermal developing region are considered to explicate the obtained trends in the experimental Nusselt numbers dataset.

Application of Superposition Principle for Solving a Nonlinear Energy Equation

Abstract A new procedure to solve a nonlinear energy equation using the superposition principle is proposed. As an example of the utilization of this procedure, forced convection in a tube with temperature-dependent fluid properties was considered. The tube wall was maintained at uniform wall heat flux axially that varies with time, and the average fluid temperature at the outlet was calculated. This problem simulates convection heat transfer inside a solar collector tube. In the proposed procedure, the average fluid temperature at the outlet for a single heat pulse was determined for fluid properties evaluated at 15 different temperatures by solving the energy equation numerically assuming constant fluid properties and subsequently applying the superposition principle. The choice of the temperature at which fluid properties were evaluated as an important parameter in the simulation. This temperature was determined by using the inlet and outlet average fluid temperatures at the previous time-step multiplied by a weighting function. The average fluid temperature at the outlet obtained by this procedure was compared with the temperature obtained by solving the nonlinear energy equation using variable properties to determine the predictive accuracy of this procedure. The results for one-day operation of a sunny day with fluid velocity of 0.6 m/s, showed the highest root-mean-square (RMS) error of 0.25 K, and the highest mean absolute deviation (MAD) error of 0.16 K which agreed well with the result obtained by the numerical simulation of the nonlinear problem using variable properties.

A parametric study of the novel flow divider-type turbulator on heat transfer enhancement in a circular tube

The outcomes of numerical findings on a parametric study of flow divider-type turbulators in forced convection heat transfer mode were presented in this research study. A numerical study has been conducted using air as the working fluid within the Reynolds number range 7000–21000 under uniform wall heat flux boundary conditions. The turbulators were used with a pitch to tube diameter ratio of 0.54, with an alternate angle of twist and the cyclic angle of twist equal to 90°, 45° and, 30°. The CFD simulation outcomes show that the Nusselt number enhances by 2.34–2.40 times, for an alternate angle of twist of 30°. The maximum thermal enhancement efficiency equal to 1.09–1.15 is obtained for turbulators with an alternate angle of twist of 30°. The Nusselt number enhances by 1.67–2.13 times for tubes fitted with a turbulator with the cyclic angle of twist equal to 45°.

Magnetohydrodynamic mixed convection in a non‐Newtonian third‐grade fluid flowing through vertical parallel plates: A semianalytical study of flow and heat transfer

AbstractBuoyancy assisted and buoyancy opposed mixed convection of a third‐grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third‐grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non‐Newtonian third‐grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing.