Some exact solutions for rotating flows of a generalized Burgers’ fluid in cylindrical domains

The velocity field and the adequate shear stress corresponding to the flow of a generalized Burgers’ fluid model, between two infinite co-axial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions J₁( ? ), J₂( ? ), Y₁( ? ) and Y₂( ? ), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers’, Oldroyd-B, Maxwell, second grade, Newtonian fluids and large-time transient solutions for generalized Burgers’ fluid are also obtained as special cases of the present general solutions. The effect of various parameters on large-time and transient solutions of generalized Burgers’ fluid is also discussed. Furthermore, for small values of the material parameters, λ₂ and λ₄ or λ₁, λ₂, λ₃ and λ₄, the general solutions corresponding to generalized Burgers’ fluids are going to those for Oldroyd-B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Flow pattern and molecular visualization of DNA solutions through a 4:1 planar micro-contraction

The present work explores unusual flow behavior of entangled fluids in an abrupt contraction flow device. Fluorescent imaging was carried out on four different entangled DNA solutions with concentrations ranging from 0.1 to 1.0% (with a wide range of entanglements per chain Z = 7–55). For weakly entangled solutions (Z < 30), vortex flow was dominant at high flow rates. However, for well-entangled DNA solutions (Z ≥ 30), unusual time dependant shear banding was observed at the contraction entrance. Upon reducing the slip length by adding sucrose to the well-entangled DNA solution, vortex flow became dominant again. In vortex flow, most DNA chains remained coiled at the corner in regular recirculation. However, when jerky-shear-banding flow developed, significant stable stretching of DNA chains occurred at the center-line, with quasi-periodic switching between stretching and recoil at the corner.     

Flow of drag-reducing surfactant solutions in rough pipes

The paper reports the results of experimental study of the flow of hexadecyltrimethylammonium chloride (CTAC) solutions with addition of sodium salicylate (NaSal) in the rough pipes. Measurements were performed in the range of the surfactant concentration from 200 to 400 ppm at a constant molar ratio CTAC/NaSal of 1:2. Five pipes of the relative roughness k/D varying from 1.2 × 10^?2 to 5.6 × 10^?2, obtained by the covering of inner surface of the pipes with glued silicon carbide particles of different size, were studied. The roughness was observed to increase the drag of flow of CTAC/NaSal solutions already at Reynolds numbers higher than 800. With increasing relative roughness k/D, the critical value of Reynolds number, at which the drag reduction disappears, was found to decrease. However, no influence of the roughness on the critical shear stress was noted. The ratio of the critical Reynolds number for rough pipes to that of hydraulically smooth pipes was independent of the surfactant concentration. The degree of drag reduction by the flow of surfactants was greater in rough pipes than in smooth pipes.     

Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid

A non-similar boundary layer analysis is presented to study the flow, heat and mass transfer characteristics of non-Darcian mixed convection of a non-Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium with the effect of Soret and Dufour and in the presence of either surface injection or suction. The value of the mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian fluids, from pseudoplastics to dilatant fluids. The numerical solution of the problem is derived using a Runge–Kutta integration scheme with Newton–Raphson shooting technique. Distributions for velocity, temperature and concentration, as well as for the rate of wall heat and mass transfer, have been obtained and discussed for various physical parametric values.     

Unsteady gravity-driven slender rivulets of a power-law fluid

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle α to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 < α < π/2) in the case x < 0 with t < 0, and diverging pendent rivulets (when π/2 < α < π) in the case x > 0 with t > 0, where x denotes a coordinate measured down the plane and t denotes time. Numerical and asymptotic methods are used to show that for each value of the power-law index N there are two physically realisable solutions, with cross-sectional profiles that are ‘single-humped’ and ‘double-humped’, respectively. Each solution predicts that at any time t the rivulet widens or narrows according to |x | ^{(2N+1)/2(N+1)} and thickens or thins according to |x | ^N/(N+1) as it flows down the plane; moreover, at any station x, it widens or narrows according to |t | ^?N/2(N+1) and thickens or thins according to |t | ^?N/(N+1). The length of a truncated rivulet of fixed volume is found to behave according to |t | ^N/(2N+1).     

Effect of gravity on the mechanical properties of lunar regolith tested using a low gravity simulation device

Simulations of the bearing capacity and shear strength of regolith under Earth’s gravity produce different results from those under low gravity. A low-gravity simulation device was developed in this study, and an internal stress model of regolith simulant was established to correct the errors. The model revealed additional force on both shear plane in the shear test and the press plate area in the pressure–sinkage test. The sinkage and shear test results showed that low gravity decreased the deformable index n, frictional modulus k_φ and cohesion c, whereas there were no obvious changes to the cohesive modulus k_c and internal friction angle φ. The sinkage generally increased as the gravity decreased under a consistent normal load larger than 50 N, but when the wheel load was lower than 50 N, the sinkage of the TYII-1 simulant was larger under 1 G than 1/6 G. Gravity had little effect on the shear strength of the regolith. However, the tractive thrust of the TYII-1 simulant was lower under 1/6 G than 1 G. The smaller difference was due to differences in the way the soils responded to changes in the gravity level for the TYII-2 simulant.     

Drag reduction for liquid flow through micro-apertures

Pressure drops in the flow through micro-orifices and capillaries were measured for silicone oils, aqueous solutions of polyethylene glycol (PEG), and surfactant aqueous solutions. The diameter of micro-orifices ranged from 5 μm to 400 μm. The corresponding length/diameter ratio was from 4 to 0.05 and capillary diameters were 105 μm and 450 μm. The following results were obtained: silicone oils of 10^?6 m²/s and 10^?5 m²/s in kinematic viscosity generated a reduction of pressure drop (RPD), that is, drag reduction, similar to the RPD of water and a glycerol/water mixture reported in the previous paper by the present authors. When RPD occurred, the pressure drop (PD) of silicone oils of 10^?6 m²/s and 10^?5 m²/s had nearly the same magnitude. Namely, the difference in viscosity did not influence RPD. A 10³ ppm aqueous solution of PEG20000 provided almost the same PD as that of PEG8000 for the 400 μm to 15 μm orifices, but a greater PD than that of PEG8000 for the 10 μm to 5 μm orifices. A non-ionic surfactant and a cationic surfactant were highly effective in RPD compared with anionic surfactants: the non-ionic and cationic surfactant solutions had PD one order of magnitude lower than that of water under some flow conditions in the concentration range from 1 ppm to 10⁴ ppm, but the anionic surfactant solutions did not generate RPD except in the case of the smallest orifice of 5 μm in diameter. The PD of the non-ionic surfactant solution showed a steep rise at a Reynolds number (Re_t) for 400 μm to 15 μm orifices. The Re_t provides the relationship Re_t = K/D, where D is the orifice diameter, and K is a constant of 2 × 10^?2 m for the 100–20 μm orifices irrespective of liquid concentration. Capillary flow experiment revealed that the PEG, non-ionic and cationic surfactant solutions generated RPD also in a laminar flow through the capillary of 105 μm in diameter, but not in the flow through the capillary of 450 μm in diameter. In order to clarify the cause of RPD, an additional experiment was carried out by changing the orifice material from metal to acrylic resin. The result gave a different appearance of RPD, suggesting that RPD is related to an interfacial phenomenon between the liquid and wall. The large RPDs found in the present experiment are very interesting from both academic and practical viewpoints.     

Numerical study on coalescence of two pre-existing coplanar flaws in rock

Crack propagation and coalescence processes are the fundamental mechanisms leading to progressive failure processes in rock masses, in which parallel non-persistent rock joints are commonly involved. The coalescence behavior of the latter, which are represented as pre-existing coplanar flaws (cracks), is numerically investigated in the present study. By using AUTODYN as the numerical tool, the present study systematically simulates the coalescence of two pre-existing coplanar flaws in rock under compression. The cumulative damage failure criterion is adopted in the numerical models to simulate the cumulative damage process in the crack initiation and propagation. The crack types (shear or tensile) are identified by analyzing the mechanics information associated with the crack initiation and propagation processes. The simulation results, which are generally in a good accordance with physical experimental results, indicate that the ligament length and the flaw inclination angle have a great influence on the coalescence pattern. The coalescence pattern is relatively simple for the flaw arrangements with a short ligament length, which becomes more complicated for those with a long ligament length. The coalescence trajectory is composed of shear cracks only when the flaw inclination angle is small (such as β ? 30°). When the pre-existing flaws are steep (such as β ? 75°), the coalescence trajectory is composed of tensile cracks as well as shear cracks. When the inclination angle is close to the failure angle of the corresponding intact rock material, and the ligament length is not long (such as L ? 2a), the direct shear coalescence is the more favorable coalescence pattern. In the special case that the two pre-existing flaws are vertical, the model will have a direct tensile coalescence pattern when the ligament length is short (L ? a), while the coalescence between the two inner flaw tips is not easy to achieve if the ligament length is long (L ? 2a).     

Direct numerical simulation of a NACA0012 in full stall

This work aims at investigating the mechanisms of separation and the transition to turbulence in the separated shear-layer of aerodynamic profiles, while at the same time to gain insight into coherent structures formed in the separated zone at low-to-moderate Reynolds numbers. To do this, direct numerical simulations of the flow past a NACA0012 airfoil at Reynolds numbers Re = 50,000 (based on the free-stream velocity and the airfoil chord) and angles of attack AOA = 9.25° and AOA = 12° have been carried out. At low-to-moderate Reynolds numbers, NACA0012 exhibits a combination of leading-edge/trailing-edge stall which causes the massive separation of the flow on the suction side of the airfoil. The initially laminar shear layer undergoes transition to turbulence and vortices formed are shed forming a von Kármán like vortex street in the airfoil wake. The main characteristics of this flow together with its main features, including power spectra of a set of selected monitoring probes at different positions on the suction side and in the wake of the airfoil are provided and discussed in detail.     

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.     

Positive frictional pressure gradient in vertical gas-high viscosity oil slug flow

The present study describes the wall shear stress and the falling liquid film behavior in upward vertical slug flow of air and high viscosity oil. The frictional pressure gradient is directly related to the wall shear stress, and it is usually negative (opposite to the overall flow direction). However, in vertical slug flow, the average total wall shear stress of a slug unit may be negative (in the same direction of the overall flow), resulting in a positive frictional pressure gradient. However, this does not mean, by any way, generation of additional energy or violation of the second law of thermodynamics.The positive frictional pressure gradient phenomenon, reasons and required conditions were explained in this paper. A simplified model was developed and validated against recent experimental data of air-high viscosity oil slug flow in a 50.8 mm ID vertical pipe. The oil viscosity was in the range of 127 mPa s to 580 mPa s. Positive frictional pressure gradient appears when the liquid film wall shear stress supersede the wall shear stress in the slug body. The rate of increase of both wall shear stresses (with respect to the mixture Reynolds number) depend, not only, on the mixture Reynolds number but also, highly, on the liquid viscosity.     

Analysis of an organized turbulent structure using a pattern recognition technique in a drag-reducing surfactant solution flow

This work presents the investigation for an organized turbulent structure in a drag-reducing flow of dilute surfactant solution by utilizing a particle image velocimetry system to perform the pattern recognition technique on a trajectory in four quadrants of streamwise and wall-normal velocity fluctuations. The pattern recognition is added to a new algorithm in order to directly capture the spatial rotation motion. The Reynolds number based on the channel height and bulk mean velocity was set to 1.5 × 10⁴. Surfactant solution with a weight concentration of 150 ppm was employed and the drag reduction rate was 65%. In the drag-reducing flow, we observe increased frequencies of occurrence of the flow events that correspond to a meandering motion in the wall-normal direction of the high-and low-speed regions. Three findings from investigation of the ensemble-averaged Reynolds shear stress and vortex structure are as follows: (i) the Reynolds shear stress in the large fluctuation range occurs in the narrow region; (ii) Size, strength, arrangement and inclination in the spatial vortex structure in the drag-reducing flow differ from those of the water; and (iii) all trajectory contributions for the wall friction coefficient decrease. Finally, we interpreted that the viscoelasticity characterizing the viscoelastic stress and relaxation time in rheological properties of the flow changes specific elementary vortex for the drag-reducing flow, and the trajectories of each flow pattern change drastically.     

An experimental and numerical study of the localization behavior of tantalum and stainless steel

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material’s local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length is 870–890 μm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 × 10⁴ s⁻¹ in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the shear section. The numerical results for stainless steel suggest that melting temperature was reached throughout the shear band shortly after peak load. Due to sample geometry, the stress state in the shear zone was not pure shear; a significant normal stress relative to the shear zone basis line was developed.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro-contraction

We have studied the flow of thermodynamically ideal solutions of a high molecular weight (M_w = 6.9 MDa) atactic polystyrene in the θ solvent dioctyl phthalate (aPS in DOP) through a micro-fabricated 8:1 planar abrupt contraction geometry. The channel is much deeper than most micro-scale geometries, providing an aspect ratio of 16:1 and a good approximation to 2D flow in the narrow channel. The solutions span a range of concentration 0.03 wt.% < c < 0.6 wt.%, encompassing the dilute to semi-dilute regimes and providing a range of fluid viscosities and relaxation times such that we achieve a range of Weissenberg numbers (8.7 < Wi < 1562) and Reynolds numbers (0.07 < Re < 11.2), giving elasticity numbers between 31 < El < 295. We study the flow using a combination of micro-particle image velocimetry (μ-PIV) to characterize the flow field, pressure measurements to evaluate the non-Newtonian viscosity, and birefringence measurements to assess macromolecular strain. Flow field observations reveal three broad flow regimes characterized by Newtonian-like flow, unstable flow and vortex growth in the upstream salient corners. Transitions between the flow regimes scale with Wi, independent of El, indicating the dominance of elastic over inertial effects in all the fluids. Transitions in the flow field are also reflected by transitions in the relative viscosity (determined from the pressure drop) and the macromolecular strain (determined from birefringence measurements). The strain through the 8:1 contraction saturates at a value of ～4–5 at high Wi. The results of these experiments broaden the limited set of literature on flow through micro-fluidic planar contractions and should be of significant value for optimizing lab-on-a-chip design and for comparison with modeling studies with elasticity dominated fluids.     

Influence of single rectangular groove on the flow past a circular cylinder

In the present study, flow control mechanism of single groove on a circular cylinder surface is presented experimentally using Particle image velocimetry (PIV). A square shaped groove is patterned longitudinally on the surface of the cylinder with a diameter of 50 mm. The flow characteristics are studied as a function of angular position of the groove from the forward stagnation point of the cylinder within 0° ≤ θ ≤ 150°. In the current work, instantaneous and time-averaged flow data such as vorticity, ω streamline, Ψ streamwise, u/U_o and transverse, v/U_o velocity components, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components are utilized in order to present the results of quantitative analyses. Furthermore, Strouhal numbers are calculated using Karman vortex shedding frequency, f_k obtained from single point spectral analysis. It is concluded that a critical angular position of the groove, θ = 80° is observed. The flow separation is controlled within 0° ≤ θ < 80°. At θ = 80°, the flow separation starts to occur in the upstream direction. The instability within the shear layer is also induced on grooved side of the cylinder with frequencies different than Karman vortex shedding frequency, f_k.     

A numerical study of steady and unsteady viscoelastic flow past bounded cylinders

We consider two-dimensional, inertia-free, flow of a constant-viscosity viscoelastic fluid obeying the FENE-CR equation past a cylinder placed symmetrically in a channel, with a blockage ratio of 0.5. Through numerical simulations we show that the flow becomes unsteady when the Deborah number (using the usual definition) is greater than De ≈ 1.3, for an extensibility parameter of the model of L² = 144. The transition from steady to unsteady flow is characterised by a small pulsating recirculation zone of size approximately equal to 0.15 cylinder radius attached to the downstream face of the cylinder. There is also a rise in drag coefficient, which shows a sinusoidal variation with time. The results suggest a possible triggering mechanism leading to the steady three-dimensional Gortler-type vortical structures, which have been observed in experiments of the flow of a viscoelastic fluid around cylinders. The results reveal that the reason for failure of the search for steady numerical solutions at relatively high Deborah numbers is that the two-dimensional flow separates and eventually becomes unsteady. For a lower extensibility parameter, L² = 100, a similar recirculation is formed given rise to a small standing eddy behind the cylinder which becomes unsteady and pulsates in time for Deborah numbers larger than De ≈ 4.0–4.5.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.     

Effects of the jet-to-crossflow momentum ratio on a sonic jet into a supersonic crossflow

Numerical investigation of a transverse sonic jet injected into a supersonic crossflow was carried out using large-eddy simulation for a free-stream Mach number M = 1.6 and a Reynolds number Re = 1.38 × 10⁵ based on the jet diameter. Effects of the jet-to-crossflow momentum ratio on various fundamental mechanisms dictating the intricate flow phenomena, including flow structures, turbulent characters and frequency behaviors, have been studied. The complex flow structures and the relevant flow features are discussed to exhibit the evolution of shock structures, vortical structures and jet shear layers. The strength of the bow shock increases and the sizes of the barrel shock and Mach disk also increase with increasing momentum ratio. Turbulent characters are clarified to be closely related to the flow structures. The jet penetration increases with the increase of the momentum ratio. Moreover, the dominant frequencies of the flow structures are obtained using spectral analysis. The results obtained in this letter provide physical insight in understanding the mechanisms relevant to this complex flow.     

Conjugate turbulent heat transfer in a square cavity with a solar control coating deposited to a vertical semitransparent wall

This paper presents a numerical study of the conjugate heat transfer (natural convection, surface thermal radiation and conduction) in a square cavity with turbulent flow. The cavity has one vertical isothermal wall, two horizontal adiabatic walls and one vertical semitransparent wall with a selective coating applied to the inner side to control the solar radiation transmission. Later on the semitransparent wall is replaced with another one without the selective coating. The mathematical model for the turbulent flow in the cavity was solved using the finite volume method. The system had the following conditions: the uniform temperature in the isothermal wall was 21 °C, the external ambient temperature was fixed at 35 °C and on the semitransparent wall the direct normal solar irradiation of 750 W/m² was considered constant. The Rayleigh number was varied in the range of 10⁹ ? Ra ? 10¹² by changing the lengths of the cavity from 0.70 m to 6.98 m, respectively. The results show that, even though the air temperature of the cavity with the solar control film coating semitransparent wall (case A) is higher compared with the one without solar film coating (case B), the total amount of heat going through the cavity is lower compared to the one going through the cavity without solar control film. The total amount of energy transferred to the air in cavity for the case A was 41.98% less than for the case B. A set of correlations for the Nusselt number was obtained for both cases considering the conjugate heat transfer.