Radiation effect on free convection laminar flow along a vertical flat plate with streamwise sinusoidal surface temperature

The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical flat plate with streamwise sinusoidal surface temperature has been investigated in this study. Using the appropriate variables; the basic governing equations are transformed to convenient form and then solved numerically employing two efficient methods, namely, Implicit finite difference method (IFD) together with Keller box scheme and Straight forward finite difference (SFFD) method. Effects of the variation of the physical parameters, for example, conduction-radiation parameter (Planck number), surface temperature parameter, and the amplitude of the surface temperature, are shown on the skin friction and heat transfer rate quantitatively are shown numerically. Velocity and temperature profiles as well as streamlines and isotherms are also presented and discussed for the variation of conduction-radiation parameter. It is found that both skin-friction and rate of heat transfer are enhanced considerably by increasing the values of conduction radiation parameter, Rd

Nonlinear nanofluid flow over heated vertical surface with sinusoidal wall temperature variations

The nonlinear density temperature variations in two-dimensional nanofluid flow over heated vertical surface with a sinusoidal wall temperature are investigated. The model includes the effects of Brownian motion and thermophoresis. Using the boundary layer approximation, the two-dimensional momentum, heat, and mass transfer equations are transferred to nonlinear partial differential equations form and solved numerically using a new method called spectral local linearisation method.The effects of the governing parameters on the fluid properties and on the heat and nanomass transfer coefficients are determined and shown graphically

Numerical study of nonlinear heat transfer from a wavy surface to a high permeability medium with pseudo-spectral and smoothed particle methods

Motivated by petro-chemical geological systems, we consider the natural convection boundary layer flow from a vertical isothermal wavy surface adjacent to a saturated non-Darcian high permeability porous medium. High permeability is considered to represent geologically sparsely packed porous media. Both Darcian drag and Forchheimer inertial drag terms are included in the velocity boundary layer equation. A high permeability medium is considered. We employ a sinusoidal relation for the wavy surface. Using a set of transformations, the momentum and heat conservation equations are converted from an (x, y) coordinate system to an (x,η) dimensionless system. The two-point boundary value problem is then solved numerically with a pseudo-spectral method based on combining the Bellman–Kalaba quasi linearization method with the Chebyschev spectral collocation technique (SQLM). The SQLM computations are demonstrated to achieve excellent correlation with smoothed particle hydrodynamic (SPH) Lagrangian solutions. We study the effect of Darcy number (Da), Forchheimer number (Fs), amplitude wavelength (A) and Prandtl number (Pr) on the velocity and temperature distributions in the regime. Local Nusselt number is also computed for selected cases. The study finds important applications in petroleum engineering and also energy systems exploiting porous media and undulating (wavy) surface geometry. The SQLM algorithm is shown to be exceptionally robust and achieves fast convergence and excellent accuracy in nonlinear heat transfer simulations

An Experimental Investigation on the Flow Behaviour in a Transpired Air Collector

An experimental investigation of the flow dynamics in a transpired air collector channel with a corrugated surface is presented. Particle image velocimetry (PIV) was used to obtain twodimensional velocity fields to compare the effects of surface heating on the flow for five flow rates. Mean velocity and turbulent property profiles are presented and compared. Proper orthogonal decomposition and wavenumber spectrum analyses were also conducted to investigate the underlying interactions between the turbulent structures that comprise the complex flow behaviour observed in corrugated flows. Results show that the corrugated waveform was the primary source of turbulence at all flow rates and heating conditions, which produced enhanced turbulent properties in its vicinity. However, under an applied heat flux, the flow at the lowest flow rate the flow was primarily buoyancy driven, where buoyancy induced stabilities and heating effects were strongest

A Theoretical Nonlinear Dynamical Model of Coupled Heat and Momentum Transfer in Forced Convection Film Boiling

In film boiling, a layer of vapor completely blankets the heated surface and prevents liquid contact with the surface. Film boiling is usually considered undesirable because it is an inefficient mode of heat transfer and can lead to temperatures in excess of those allowed for many materials. Because film boiling may inhibit desired heat transfer in several processes including metals manufacturing, cryogenic engineering, and electronic cooling, it is useful to consider how the film boiling vapor layer may be destabilized or altered such that time-averaged heat transfer is improved

Increased heat transfer to elliptical leading edges due to spanwise variations in the freestream momentum: Numerical and experimental results

A study of the effect of spanwise variation in momentum on leading edge heat transfer is discussed. Numerical and experimental results are presented for both a circular leading edge and a 3:1 elliptical leading edge. Reynolds numbers in the range of 10,000 to 240,000 based on leading edge diameter are investigated. The surface of the body is held at a constant uniform temperature. Numerical and experimental results with and without spanwise variations are presented. Direct comparison of the two-dimensional results, that is, with no spanwise variations, to the analytical results of Frossling is very good. The numerical calculation, which uses the PARC3D code, solves the three-dimensional Navier-Stokes equations, assuming steady laminar flow on the leading edge region. Experimentally, increases in the spanwise-averaged heat transfer coefficient as high as 50 percent above the two-dimensional value were observed. Numerically, the heat transfer coefficient was seen to increase by as much as 25 percent. In general, under the same flow conditions, the circular leading edge produced a higher heat transfer rate than the elliptical leading edge. As a percentage of the respective two-dimensional values, the circular and elliptical leading edges showed similar sensitivity to span wise variations in momentum. By equating the root mean square of the amplitude of the spanwise variation in momentum to the turbulence intensity, a qualitative comparison between the present work and turbulent results was possible. It is shown that increases in leading edge heat transfer due to spanwise variations in freestream momentum are comparable to those due to freestream turbulence

Improving Flat Plate Heat Transfer Using Flexible Rectangular Strips

Many engineering systems involve proper transfer of heat to operate. As such, augmenting the heat transfer rate can lead to performance improvement of systems such as heat exchangers and solar photovoltaics panels. Among the many existing and studied heat transfer enhancement techniques, a well-designed passive turbulence generator is a simple and potent approach to augmenting convective heat transfer. Two of the most recognized passive convective heat enhancers are wings and winglets. Their potency is attributed to the long-lasting induced longitudinal vortices which are effective in scooping and mixing hot and cold fluids. Somewhat less studied are flexible turbulence generators, which could further the heat transfer enhancement compared to their rigid counterpart. In the current study, the flexible rectangular strips are proposed, marrying the long-lasting vortex streets with the periodic oscillation, to maximize heat convection. This study was conducted in a closed-looped wind tunnel with 76 cm square cross-section. The effects of flexible strips on the turbulent flow characteristics and the resulting convective heat transfer enhancement from a heated flat surface are detailed in four papers which are presented as Chapters 3, 4, 5 and 6. In Chapter 3, the effect of the thickness of the strip is detailed. The 12.7 mm wide and 38.1 mm tall rectangular strip was cut from an aluminum sheet with thickness of 0.1, 0.2 and 0.25 mm. The incoming wind velocity was maintained at around 10 m/s, giving a Reynolds number based on the strip width of 8500. It is observed that the thinnest 0.1 mm strip could induce a larger downwash velocity and a stronger Strouhal fluctuation at 3H (strip height) downstream, leading to a better heat transfer enhancement. The peak of the normalized Nusselt number (Nu/Nu0) at 3H downstream of the 0.1 mm strip was around 1.67, approximately 0.1 larger than that of the 0.25 mm strip. In Chapter 4, the height effect of the strip is disclosed. The strip was 12.7 mm wide and 0.1 mm thick, with a height of 25.4 mm, 38.1 mm and 50.8 mm. The Reynolds number in this chapter was also fixed at around 8500, based on the strip width and the freestream velocity. It was found that the shortest, 25.4 mm strip could induce the closest-to-wall swirling vortices, and the largest near-surface downwash velocity toward the heated surface. Thus, the largest heat transfer augmentation was observed. At 9W (strip width) downstream, the 25.4 mm-strip provided the Nu/Nu0 peak of around 1.76, 0.26 larger than that associated with the tallest, 50.8 mm-strip. In Chapter 5, the effect of the transversal space of a pair of strips is expounded. A pair of 0.1 mm thick, 12.7 mm wide, and 25.4 mm tall aluminum rectangular flexible strips was placed side-by-side with a spacing of 1W (strip width), 2W and 3W. The Reynolds number based on the strip width was around 8500. The results showed that the 1W-spaced strip pair induced the strongest vortex-vortex interaction, the largest downwash velocity, and the most intense turbulence fluctuation. These resulted in the most effective heat convection. At Y=0 (middle of the strip pair) and X=9W, the largest Nu/Nu0 value of around 1.50 was identified when using the 1W-spaced strip pair. This was approximately 0.24 and 0.33 larger than that of the 2W- and 3W-spaced strip pairs. Chapter 6 presents the effect of freestream turbulence on the flat plate heat convection enhancement with a 12.7 mm wide, 25.4 mm tall and 0.1 mm thick flexible strip. A 6 mm thick sharp-edged orificed perforated plate (OPP) with holes of 38.1 mm diameter (D) was placed at 10D, 13D and 16D upstream of the strip to generate the desirable levels of freestream turbulence. The corresponding streamwise freestream turbulence intensity at the strip was around 11%, 9% and 7%. The Reynolds number based on the strip width and freestream velocity was approximately 6000. The freestream turbulence was found to diminish the effect of flexible strip in terms of the relative heat transfer enhancement (Nu/Nu0). This is due to the significant increase of Nu0 with the increasing freestream turbulence. In other words, the flexible strip could always improve the heat transfer, and the relative improvement is greatest for the largely laminar freestream case in the absence of the OPP. Chapter 7 summarizes the effect of all the parameters in previous chapters on the convective heat transfer enhancement. The results show that the freestream turbulence intensity (Tu) had the most significant effect in augmenting the averaged Nu/Nu0, and the local Nu/Nu0 correlated best with the local ke. The maximal averaged Nu/Nu0 over 23W downstream, within ±1 and ±4 strip widths cross-stream was found for Tu=7% case and Tu=11% case, respectively. Conclusions are drawn and recommendations are provided in Chapter 8

Boundary Layer Flows

Written by experts in the field, this book, "Boundary Layer Flows - Theory, Applications, and Numerical Methods" provides readers with the opportunity to explore its theoretical and experimental studies and their importance to the nonlinear theory of boundary layer flows, the theory of heat and mass transfer, and the dynamics of fluid. With the theory's importance for a wide variety of applications, applied mathematicians, scientists, and engineers - especially those in fluid dynamics - along with engineers of aeronautics, will undoubtedly welcome this authoritative, up-to-date book

Lift forces on cylindrical bodies in unsteady flows

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