Studies on isothermal steady-state frictional pressure drop for flow of petroleum base oils SN70, SN150, diesel, and water are carried out in spiral coils with diameter to length ratio, 0.00042, 0.00047, 0.00073, 0.00164, 0.00189, 0.003, and 0.0037. An attempt is made to correlate friction factors with a better and more appropriate dimensionless group for flow of Newtonian fluids through spiral-coiled tubes. An innovative approach of correlating heat transfer data with the newly established dimensionless group is presented. Heat transfer experiments are performed for spiral coils with diameter to length ratio 0.000474, 0.00042, 0.001896, 0.00198, 0.000942, and 0.00164 in laminar flow regime. Suitable correlations for friction factors and Nusselt numbers are proposed. Relationship between pressure drop and heat transfer is studied. The incapability of the conventional analogy equations to estimate the heat and momentum transfer coefficients for laminar flow through straight or curved tubes is explained based on the viscous and form drag existing in straight and curved pipe flow. The limitations of the existing analogy equations are examined critically. A new general analogy equation is derived for laminar flow through spiral and straight tubes considering the influencing geometrical parameters of the tube.

This work examines the steady two-dimensional mixed convection boundary layer flow of non-Newtonian Carreau fluid embedded in a porous medium. The impermeable wedge is at rest over which the momentum and thermal boundary layers form due to the motion of Carreau fluid with a large Reynolds number. We consider local thermal nonequilibrium for which the temperature of the solid porous medium is different from that of the fluid phase, and hence, a single heat-transport equation is replaced by a two-temperature model. The governed equations for flow and heat transfer are converted into a system of ordinary differential equations using a similarity approach. It is observed that local thermal nonequilibrium effects are dominant for small interphase heat transfer rate and porosity scaled conductivity parameters. It is shown that the temperature at any location of the solid porous medium is always higher than that of the fluid phase. When these parameters are increased gradually, the local thermal equilibrium phase is recovered at which the temperatures of the fluid and solid are identical at each pore. A similar trend is noticed for both shear-thinning and shear-thickening fluids. The results further show that heat exchange between the fluid and solid porous medium is similar to both assisted and opposed flows and Carreau fluid. The velocity and temperature fields for the various increasing fluid index, Grashof number, and permeability show that the thickness of the momentum and thermal boundary layer is thinner.

The effect of pulsating laminar flow of a Bingham plastic fluid on heat transfer from a constant temperature cylinder is studied numerically over wide ranges of conditions as Reynolds number (0.1 ≤ Re ≤ 40) and Bingham number (0.01 ≤ Bn ≤ 50) based on the mean velocity, Prandtl number (10 ≤ Pr ≤ 100), pulsation frequency (0 ≤ ω* ≤ π ), and amplitude (0 ≤ A ≤ 0.8). Results are visualized in terms of instantaneous streamlines, isotherms, and apparent yield surfaces at different instants of time during a pulsation cycle. The overall behavior is discussed in terms of the instantaneous and time-averaged values of the drag coefficient and Nusselt number. The size of the yielded zone is nearly in phase with the pulsating velocity, whereas the phase shift has been observed in both drag coefficient and Nusselt number. The maximum augmentation (∼30%) in Nusselt number occurs at Bn = 1, Re = 40, Pr = 100, ω * = π , and A = 0.8 with respect to that for uniform flow. However, the increasing yield stress tends to suppress the potential for heat transfer enhancement. Conversely, this technique of process intensification is best suited for Newtonian fluids in the limit of Bn → 0. Finally, a simple expression consolidates the numerical values of the time-averaged Nusselt number as a function of the pertinent dimensionless parameters, which is consistent with the widely accepted scaling of the Nusselt number with ∼Pe 1/3 under these conditions.

Turbulent flow and convective heat transfer of kerosene in coiled pipes with different wall boundary conditions and curvature radii of coiled pipes are numerically studied. The Reynolds-averaged Navier–Stokes equations are solved by finite volume method and the realizable k– ε model is applied for turbulence modeling. The fluid media is aviation kerosene with an inlet supercritical pressure of 3 MPa and an inlet temperature of 400 K. The present results provide temperature and velocity fields as well as distributions of turbulence kinetic energy and streamlines at different axial locations along the flow direction. The Nusselt number at the outer side of the pipe wall is higher than that at the inner side by 75%. Compared to a straight pipe with the same pipe radius of 6 mm and inlet flow conditions, the coiled pipe with a curvature radius of 192.5 mm can increase the averaged heat transfer coefficient by 28.5%. Meanwhile, it is found that when the curvature ratio increases, the effect of secondary flow in the cross section of pipe is more significant and the heat transfer effect at different locations of the pipe wall also changes significantly. In addition, the present results also reveal that heat transfer deterioration takes place for the kerosene flow in coiled pipe with an increased wall heat flux due to the state change of kerosene from liquid to supercritical.

This paper studies the local thermal nonequilibrium (LTNE) model for two-dimensional mixed convection boundary-layer flow over a wedge, which is embedded in a porous medium in the presence of radiation and viscous dissipation. It is considered that the temperature of the fluid and solid phases is not identical; hence, we require two energy equations: one for each phase. The motion of the mainstream and wedge is approximated by the power of distance from the leading boundary layer. The flow and heat transfer in the LTNE phase is governed by the coupled partial differential equations, which are then reduced to nonlinear ordinary differential equations via suitable similarity transformations. Numerical simulations show that when the interphase rate of heat transfer is large, the system attains the local thermal equilibrium (LTE) state and so is for porosity scaled conductivity. When LTNE is strong, the fluid phase reacts faster to the mainstream temperature than the corresponding solid phase. The state of LTE rather depends on radiation and viscous dissipation of the model. Further, numerical solutions successfully predicted the upper and lower branch solutions when the velocity ratio is varied. To assess which of these solutions is practically realizable, an asymptotic analysis on unsteady perturbations for a large time leading to linear stability needs to be performed. This shows that the upper branch solutions are always stable and practically realizable. The physical dynamics behind these results are discussed in detail.

The asymptotic limit for perimeter averaged convection is generalized for short ducts of arbitrary cross section. A correction factor to Lévêque's original analysis is derived in terms of the state of wall shear stress under conditions of fully developed flows for walls of constant temperature (T) and constant heat flux (H 1 and H 2 ). This analysis is performed for four duct geometries: elliptic, rhombic, rectangular, and regular polygons. The magnitude of this correction is greatest for the H 2 wall condition and for ducts having walls with acute corners. The results of this analysis can be incorporated into a generalized correlation for the full Graetz problem in ducts of arbitrary cross section.

This paper reports the results of a numerical study that determined the Nusselt number for hydrodynamically and thermally fully developed, laminar, dissipative flows of pseudoplastic and dilatant fluids through circular conduits. Two boundary conditions were considered, constant heat flux and constant temperature. Constitutive equations were used that describe the entire flow curve, from the zero-shear rate through the infinite shear rate Newtonian regions, so that computed Nusselt numbers are valid for whatever shear rates may exist in the flow field. Nusselt numbers are reported as a function of a dimensionless shear rate parameter that establishes the region of the flow curve where the system is operating and are shown to be bound by the Newtonian and power law values. The conditions required for the system to perform at these asymptotic limits are quantified.

The flow and heat transfer performance of Bingham fluid with thermally dependent viscosity across a heated circular tube have been numerically investigated (2408 ≤ Re B ≤ 5852, 9 ≤ Pr ≤ 23 and 10 ≤Bn ≤ 90). The modified bi-viscous Bingham model was used to solve the problem of discontinuous-viscous properties, and a function of temperature known as Arrhenius law was introduced. The results show that unyield regions include a circular shape, pyramid shape, and zones enclosing yield regions at high Reynolds number. Under constant wall temperature boundary, unyield region of temperature-dependent model at rear of circular tube is smaller due to a higher shear rate and lower average viscosity. On the surface of circular tube, local skin drag coefficient first increases and then decreases, and local Nusselt number decreases near rear stagnation point of circular tube illustrating unyield regions of Bingham fluid weaken heat transfer performance. Empirical correlations of average Nusselt number and drag coefficient were obtained based on effects of Reynolds number and Bingham number.

A series of rotating convection experiments have been conducted in a novel configuration, which comprises a cylindrical annulus with spot heating on the bottom outer edge and uniform cooling on the inner surface. Such a system provides bi-directional thermal gradients in both radial and vertical directions, thereby reenacting the thermal gradient patterns encountered in the atmosphere. Bulk heat transfer characteristics are studied by quantifying the overall Nusselt number, Nu, for a range of Taylor number, Ta, heating rate, Q, and Rayleigh number, Ra. Temperature measurements are carried out at different locations with the help of thermocouples. The Nusselt number is found to be quite sensitive to the buoyancy and relatively insensitive to the rotation rate. The correlation for Nu as a function of Ra revealed different power law exponents for low and high Ta values. The varying exponent is attributed to the presence of baroclinic eddies at high Ta, which in turn is verified with the help of flow visualization. The heat transfer characteristics in this new configuration are significantly different compared to other conventional rotational convection systems, where thermal gradients are present in only one direction.

A detailed computational analysis is carried out on the heat transfer and pressure loss of a turbulent flow in detached pin fin arrays with various clearance values for the Reynolds number range of 20,000–80,000 and the rotation number range of 0–0.3. Clearances exist at the midheight of the detached pin fins, which account for 10%, 15%, and 20% of the full pin fin's height, respectively. The clearances release the fluid stagnation and reduce the bulk flow turbulent mixing level, which significantly reduces the pressure loss. Compared with the pin fin arrays, the pressure loss is decreased by up to 30.5% with the increase of the clearance value for the detached pin fin arrays. Also, the detached pin fin arrays show a maximum increase in the total Nusselt numbers by about 13.5%. Furthermore, the rotation effects can increase the friction factors as well as the Nusselt numbers simultaneously in both the pin fin arrays and the detached pin fin arrays. A higher rotation number can promote the heat transfer enhancement and uniformity in the detached pin fin channels.

This study investigates the mean flow and radial heat-transfer behaviors in semiclosed rotating disk cavity within the canned reactor coolant pump. The flow in the semiclosed cavity contains the Stewartson type flow at inner region and the Batchelor type flow at outer region. The heat is radially transported from the outer rim of the semiclosed disk cavity to discharge-hole through the nondirect discharge (ND) portion of the superimposed flow from inlet. The effects of rotating Reynolds numbers, cavity aspect ratio and radial location of discharge-hole on the discharge ratio, pumping mass flow rate, local wall shear stress and radial heat-transfer coefficient are examined in the semiclosed rotating cavity flow, respectively. Based on the radial heat transfer behaviors of pumping secondary flow, an equivalent thermal network is proposed and validated by experiments, which can effectively predict the radial temperature distribution from the discharge hole to periphery with the viscous-heating and nonisothermal effects.

Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.

New generalized correlations for predicting the average fanning friction factor f and average Nusselt number Nu for laminar flow in plain plate-fin compact cores of rectangular cross section are presented. These are based on extended experimental data, as well as three-dimensional computational simulations, obtained for a broad range of fin density and geometrical attributes. The results indicate that while the fully developed forced convection scales only with the interfin channel cross-sectional ratio α (fin spacing by fin height), the entrance region hydrodynamic and thermal performance is additionally a function of the fin-core length L, flow Reynolds number Re, and fluid Prandtl number Pr. The developing flow and convection is further shown to scale as: ( f Re ) ∼ ( L / d h Re ) 1 / 2 , and Nu ∼ ( L / d h Re ) 1 / 2 Pr 1 / 3 ϕ ( α ) , where f, Re, and Nu are all based on the hydraulic diameter d h of the interfin flow channel. Generalized correlations for both ( f Re ) and Nu are developed by the corresponding scaling of the forced convection behavior and asymptotic matching of the entrance or developing flow (short fin-core flow length) and the fully developed flow (large fin-core flow length) region performance. Finally, the predictions from these correlations are found to be within ±15% of all available experimental data for air, water, and glycol (0.71 ≤ Pr ≤ 10), and fin cores with 0 < α ≤ 1.

A novel finite volume method about the boundary layer flow and heat transfer of fractional viscoelastic fluid over a moving plate with convective boundary condition is developed. The fractional Maxwell model and fractional Fourier's law are employed in the constitutive relations. Numerical solutions are obtained and validated by exact solutions of special case with source terms. The effects of fractional parameters on the flow and heat transfer characteristics are analyzed. Results show that the viscoelastic fluid performs shear-thickening property with the increase of fractional parameter. Moreover, the variations of the average Nusselt number demonstrate that the viscoelastic fluid characterized by fractional Fourier's law has short memory in heat conduction process.

The combined entry problem for the simultaneous development of heat and momentum transfer in a circular tube has been resolved over an extended range of inverse Graetz number Z H ≥ 10 − 6 and for a wide range of Prandtl numbers 0.1 ≤ Pr ≤ 500 . For the historical range of Z H ≥ 5 × 10 − 4 and 0.7 ≤ Pr ≤ 50 , earlier studies are within 5% of the current benchmark calculations, but for the new extended range of conditions, the best authoritative sources were in error by as much as 33%. Four new correlations are proposed for the local and average Nusselt numbers, and for the constant temperature and constant heat flux wall condition, which are accurate to 2.2% for all values of inverse Graetz number and Pr ≥ 0.5 . In contrast, legacy correlations typically had a 10–20% error range when compared to the results of this work, with many exhibiting larger errors and only few achieving errors as low as 5–10%.

The flow around a heated circular cylinder and the wake behind it were studied in wind tunnel flow using two methods of anemometry, i.e., particle image velocimetry (PIV) and constant temperature anemometry (CTA) with a special technique using a rotating slanted hot-wire probe. The Reynolds number ranged from 2000 to 20,000 and the cylinder wall temperatures varied between 27 °C and 177 °C. The wake is characterized by mean wind and fluctuation contour maps. Significant changes in wake patterns were observed while the cylinder was being heated, thus increasing its wall temperatures at low Reynolds numbers. At higher Reynolds numbers, the effects of cylinder heating on wake properties were negligible. The research fills a gap observed in the literature for a certain combination of velocity, cylinder aspect ratio, and cylinder surface temperature.

Stanton number, St, calculations as a function of position, x, are made for turbulent, external boundary layer flow over aerodynamically rough surfaces and also for a fully developed duct flow with rough top and bottom surfaces. This is accomplished with three different forms of generalized Reynolds analogies from the literature and also with a new data correlation developed with the aid of the thermal inner and outer layers. Comparison of these predicted values of St with experimental data, from the literature, is made for several favorable equilibrium, one nonequilibrium, and a zero pressure gradient as well as a duct flow over “real” roughness patterns. Predictions compare reasonably well with the data for some of the generalized Reynolds analogies.

As nonbody-conforming numerical methods using simple Cartesian mesh, immersed boundary methods have become increasingly popular in modeling fluid–solid interaction. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid–fluid interface are satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. A similar path has been followed to model forced convection heat transfer by adding a source term in the energy equation. The added source term will ensure that thermal boundary conditions on the solid–fluid interface are imposed without invoking a boundary conforming mesh. These approaches were developed to handle the Dirichlet boundary condition (constant wall temperature). Few of them deal with the Neumann boundary condition (constant wall heat flux). This paper presents a simple new immersed boundary method. It can deal with the Dirichlet boundary condition, Neumann boundary condition, and conjugated heat transfer by adding an energy source or sink term in the energy conservation equation. The presented approach is validated against the analytical solutions and a very good match is achieved.

Diabatic performance modeling is a prerequisite for engine condition monitoring based on nonsteady-state data points (e.g., Putz et al. 2017, “Jet Engine Gas Path Analysis Based on Takeoff Performance Snapshots,” ASME J. Eng. Gas Turbines Power, 139 (11), p. 111201.). The importance of diabatic effects increases with decreasing engine size. Steady-state diabatic modeling of turbomachinery components is presented using nondimensional parameters derived from a dimensional analysis. The resulting heat transfer maps are approximated using the analytic solution for a pipe. Experimental identification of the maps requires the measurement of casing and gas path temperatures. This approach is demonstrated successfully using a small turboshaft engine as a test vehicle. A limited amount of measurements was needed to generate a steady-state heat transfer map which is valid for a wide range of operating points.

The laminar and turbulent regimes of a boundary layer on a flat plate are often represented with separate correlations under the assumption of a distinct “transition Reynolds number.” Average heat coefficients are then calculated by integrating across the “transition point.” Experimental data do not show an abrupt transition, but rather an extended transition region in which turbulence develops. The transition region may be as long as the laminar region. Although this transitional behavior has been known for many decades, few correlations have incorporated it. One attempt was made by Stuart Churchill in 1976. Churchill, however, based his curve fit on some doubtful assumptions about the data sets. In this paper, we develop different approximations through a detailed consideration of multiple data sets for 0.7 ⩽ Pr ⩽ 257 , 4000 ⩽ Re x ⩽ 4 , 300 , 000 , and varying levels of freestream turbulence for smooth, sharp-edged plates at zero pressure gradient. The result we obtain is in good agreement with the available measurements and applies smoothly over the full range of Reynolds number for either a uniform wall temperature or a uniform heat flux boundary condition. Fully turbulent air data are correlated to ± 11 % . Like Churchill's result, this correlation should be matched to the estimated transition condition of any particular flow. We also review the laminar analytical solutions for a uniform wall heat flux, and point out limitations of the classical Colburn analogy.