Sinusoidal Wall Research Articles

Effects of Asymmetric Channel on the Convective Heat Transfer: A Computational Study

In the fields of engineering, especially in the heat transfer area, the contribution of the fluid flows through different channels is remarkable. Among the different available shapes in the channel, the sinusoidal wavy channels are considered more efficient in the heat transfer areas such as cooling of electronic devices, boilers, biomedical applications, etc., due to their increased recirculation capability of mixing the flowing fluids - which increases the heat transfer performance, consequently. The optimization of channel design and modelling has been an engineering problem in recent years. In this research, flat, symmetric sinusoidal, and asymmetric sinusoidal channels were designed - using ANSYS 2020 - to investigate the effects of channel shape, amplitude, and aspect ratio of sinusoidal wavy walls on the overall heat transfer performance. Several designs have been considered in the present study at different Reynolds numbers and different aspect ratios, keeping the wall temperature as constant. The results of this study exhibit that at an aspect ratio of 0.4, the asymmetric channel shows the highest heat transfer effect due to increased recirculation tendency.

Analysis of the Melting Time of Phase Change Material in a Heat Exchanger with Sinusoidal Inner Duct

Three-dimensional computational analysis has been performed to investigate the melting time of the phase change material (PCM) in a sinusoidal pipe inserted into another pipe. The other pipe is filled with PCM and the system is heated from the inner sinusoidal pipe at different temperatures. The main aim of the study is to control the melting time. The finite volume method (FVM) is used to solve time-dependent governing equations. Four different cases are chosen for the sinusoidal wall to see the effects of geometry on melting. After the analysis, it is observed that melting time can be controlled via an adjustment of the geometrical parameter, namely a passive technique, without spending extra energy.

Çok Sayıda Flebolitle İzlenen Oral Hemanjiyom

Hemangioma is a rare, non-reactive, benign vascular tumor, characterized by endothelial cell proliferations and results from vascular malformation. Hemangioma mostly occurs on head and neck skin and regresses spontaneously within 5-10 years in 50-90% of cases. However, oral lesions show less regression than skin lesions. The most commonly affected area is tongue and palatal mucosa, and rarely observed in jaw bones. Diagnosis is based on anamnesis and clinical features. Blanching of the hemangioma under pressure is characteristic clinical finding. Phlebolith is calcified thrombus in veins, venules and sinusoidal walls of hemangiomas. Head and neck phleboliths almost always indicate the soft tissue hemangioma. Phleboliths observed with hemangioma in head and neck region have distinctive appearance on panoramic radiographs. Cone-beam computed tomography provides useful information about location and distribution of phleboliths. In this case report, clinical and radiological features of oral hemangioma and many associated phleboliths are presented.

Evaluation of SPH and FVM Models of Kinematically Prescribed Peristalsis-like Flow in a Tube

Peristaltic flow is important in many biological processes, including digestion, and forms an important component of any in silico model of the stomach. There is a clear need to verify the simulations of such flows. An analytical solution was identified that can be used for model verification, which gives an equation for the net volumetric flow over a cycle for an applied sinusoidal wall motion. Both a smooth particle hydrodynamics (SPH) code (from the CSIRO), which is being used to develop a stomach model that includes wall motion, buoyancy, acid secretion and food breakdown, and the Ansys Fluent Finite Volume Method (FVM) solver, that is widely used in industry for complex engineering flows, are used in this exercise. Both give excellent agreement with the analytic solution for the net flow over a cycle for a range of occlusion ratios of 0.1–0.6. Very similar velocity fields are obtained with the two methods. The impact of parameters affecting solution stability and accuracy are described and investigated. Having validated the moving wall capability of the SPH model it can be used with confidence in stomach simulations that include wall motion.

Changing the physical behavior of phase change material by means of numerical technique

Numerical simulation was offered for scrutinizing the freezing of water within the complex container. The container has elliptic left adiabatic wall while the right wall is sinusoidal wall and maintained at cold temperature. The drawback of water has been removed by adding alumina nanoparticles. For this modeling, different ranges of volume and shape factor of nanoparticles have been scrutinized by incorporating FEM. The configuration of grid alters with change of time and verification test has been presented which proved good accuracy. As bigger shape factor has been selected, the time of process decline less than 4% for cylinder shape and this percentage augments around 78.22% for blade shape. As nanoparticle fraction increases, the required time declines around 26.84%. The impact of blade shape in view of adding nanoparticles is 25.74% greater than that of cylinder shape.

Effect of frequency of the wavy wall on turbulent wall jet heat transfer characteristics

The thermal and hydraulic characteristics of a sinusoidal wavy wall are studied numerically to increase the heat transfer rate of the turbulent wall jet. To do so, the sinusoidal profile (y=A∗sin(ωNx)) is used for the wavy wall, where ωN=2πN/L is the frequency with suffix N denoting the number of cycles for the given length L and A is the amplitude. The amplitude “A” is varied from 0 to 0.8a and ωN is changed from ω4 to ω12, to find out the optimum amplitude and frequency for which the heat transfer rate is maximum. The low Reynolds number two equations RNG k−ϵ model is used for the detailed study and to understand the impact of a re-circulation zone on the heat transfer rate. The inlet velocity is uniform and equals to 10.95 m/s for all the cases to achieve the inlet Reynolds number 15000 for a 20 mm nozzle height. At the inlet, jet is heated to a temperature of 330 K and the wavy wall on which the jet flows is provided an isothermal condition with 300 K temperature. With these conditions, the results for streamwise maximum velocity decay, skin friction coefficient, re-circulation area and local Nusselt number have been compared for different amplitudes and frequencies of the wavy wall. From the results, it has been observed that with the increasing amplitude and frequency the Umax increases, the area of re-circulation zone increases and the thermal potential core decreases. For the wavy wall amplitude A = 0.8 and frequency ω12, the peak of Umax is 170% more than the plane wall jet, the area covered by re-circulation zone is 58.2% of the total area and the thermal potential core reduces to X=3.7 which is about 50% of the plane wall jet. The local Nusselt number also increases with the increasing amplitude and frequency in the near field, but in the far field it starts decreasing as the re-circulation effect dominates there. For the wavy wall, the maximum increase in heat transfer rate is 23.23% with respect to the plane wall case.

Exact moment analysis of transient/asymptotic dispersion properties in periodic media with adsorbing/desorbing walls

The paper develops a robust and computationally efficient homogenization approach, grounded on exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of solute particles in periodic media possessing absorbing/desorbing walls. Adsorption onto and desorption from active walls allow linear and reversible mass transfer between the solid surface and the fluid phase. The transient analysis reveals some important features of the dispersion process that cannot be captured by asymptotic approaches aimed at determining exclusively the long-range/large-distance dispersion properties. Two case studies are considered: the dispersion of an analyte in a sinusoidal channel with adsorbing/desorbing walls and the retentive pillar array column for liquid chromatography. For both systems, the transient analysis shows how the tortuous fluid motion induced by the sinusoidal walls or by the presence of pillars induces wide and persistent temporal oscillations of the effective velocity and dispersion coefficient even for a steady (non-pulsating) Stokes flow. The adsorption/desorption process strongly amplifies the phenomenon of the overshoot for the effective dispersion coefficient that, on short/intermediate time scales, reaches values significantly larger than the asymptotic one. Moreover, the method proposed allows a detailed analysis of the temporal evolution of the skewness of the marginal distribution of the analyte along the main stream direction. It clearly shows that the time scale for achieving the macro-transport regime, which implies a Gaussian (symmetric) marginal pdf, is largely underestimated if one bases the analysis on the attainment of constant asymptotic values for the effective velocity and for the dispersion coefficient.

Generation & characterization of expandable human liver sinusoidal endothelial cells and their application to assess hepatotoxicity in an advanced in vitro liver model

Liver sinusoidal endothelial cells (LSECs) are highly specialized endothelial cells forming the hepatic sinusoidal wall. Besides their high endocytic potential, LSECs have been demonstrated to markedly contribute to liver homeostasis and immunity, and may partially explain unexpected hepatotoxicity of drug candidates. However, their use for in vitro investigations is compromised by poor cell yields and a limited proliferation capacity. Here, we report the transient expansion of primary human LSECs from three donors by lentiviral transduction. Transduced (“upcyte®”) LSECs were able to undergo at least 25 additional population doublings (PDs) before growth arrest due to senescence. Expanded upcyte® LSECs maintained several characteristics of primary LSECs, including expression of surface markers such as MMR and LYVE-1 as well as rapid uptake of acetylated LDL and ovalbumin. We further investigated the suitability of expanded upcyte® LSECs and proliferating upcyte® hepatocytes for detecting acetaminophen toxicity at millimolar concentrations (0, 0.5, 1, 2, 5, 10 mM) in static 2D cultures and a microphysiological 3D model. upcyte® LSECs exhibited a higher sensitivity to acetaminophen-induced toxicity compared to upcyte® hepatocytes in 2D culture, however, culturing upcyte® LSECs together with upcyte® hepatocytes in a co-culture reduced APAP-induced toxicity compared to 2D monocultures. A perfused Dynamic42 3D model was more sensitive to acetaminophen than the 2D co-culture model. Cytotoxicity in the 3D model was evident by decreased cellular viability, elevated LDH release, reduced nuclei counts and impaired cell morphology. Taken together, our data demonstrate that transient expansion of LSECs represents a suitable method for generation of large quantities of cells while maintaining many characteristics of primary cells and responsiveness to acetaminophen.

Physical treatment of paraffin in existence of nanoparticles using computational simulation

Development of numerical code for evaluating the solidification of water has been scrutinized in this work. The container has two circular and sinusoidal cold walls at bottom and top surfaces. Galerkin-based code has been employed to model this phenomenon. To elevate the conductivity of phase change material (PCM), alumina particles with nanosized were utilized with incorporating different shapes. The conductivity of nanoencapsulated phase change material (NEPCM) is a function of concentration and shapes of nanoparticles. The freezing process is mainly dominated by conduction and selecting curved shaped and adding nanoparticles can affect this mechanism. Verification test reveals the good accommodation and applying adaptive grids leads to higher accuracy. As shape coefficient increases, the period of process declines around 10.65% owing to stronger conduction. Also, mixing water with alumina nanopowders with blade shape causes decrement in needed time around 32.51%. Besides, outputs reveal that utilizing blade shape of powders has more effect on required time than that of cylindrical shape.

Influence of nanoparticles on freezing inside container equipped with fins

With loading of different shapes of nanoparticles, the solidification speed can be changed which was scrutinized in current work. Although the nanoparticles dispersion can decline the heat capacity, the conduction mode can be improved with such technique and changing the styles of nano-powders can alter the strength of conduction. The velocity terms were neglected in freezing, thus, the main equations include two equations with unsteady form for scalars of solid fraction and temperature. Grid adaption with position of ice front has been considered in simulations utilizing FEM. The upper sinusoidal and inner rectangular walls maintain cold temperature and freezing starts from these regions. Adding nanomaterial can expedite the process around 15.75% (for m = 4.8) and 29.8% (for m = 8.6). Also, utilizing particles with shapes of blade form can augment the freezing rate around 16.69%. The efficacy of m on freezing process rises around 4% with elevate of concentration of nanoparticles.

Impact of a hot constructal tree-shaped fin on the convection flow of single wall carbon nanotube water nanofluid inside a sinusoidal enclosure

Heat transfer due to natural convection in different types of fins embedded closed enclosures are widely used in various fields including petrochemicals, solar collectors, heat exchangers, gas turbines, semiconductor devices, automobile radiators, etc. Herein, the natural convection flow of a water-based single-wall carbon nanotube (SWCNT) nanofluid inside a novel sinusoidal closed geometry is investigated. The horizontal bottom and top boundaries of the enclosure are presumed to be hot and thermally adiabatic, respectively. The left and right vertical sinusoidal boundaries are assumed to be cold. A hot constructal tree-shaped fin is placed at the center of the hot bottom wall. The impact of the simple constructal heated tree-shaped fin on steady, two-dimensional, laminar, and incompressible flow of the water-based SWCNT nanofluid inside the sinusoidal enclosure is analyzed. The mathematical formulation of water-based SWCNT nanofluid flow inside the enclosure is formulated using the Navier–Stokes equations under the Boussinesq approximation. A modified effective thermal conductivity model of carbon nanotubes including the radius of water molecules and carbon nanotubes is employed. Galerkin finite element simulations are conducted to study the flow and heat transfer characteristics via stream function, isotherms, local Nusselt number, and averaged Nusselt number graphs. The combined effect of the amplitude of the sinusoidal wall (A = 0.1, 0.15, and 0.2) with the Rayleigh number (Ra = 104–106), nanotube volume fraction (φ = 0.01–0.05), and the thickness of the tree-shaped fin (B = 0.02–0.06) are comprehensively studied. The temperature gradient decreases with increasing nanotube volume fraction and the sinusoidal wall amplitude, while it increases above the fin with the thickness of the tree-shaped fin. Moreover, the averaged Nusselt number increases with the thickness of the tree-shaped fin by 14.72%, 16.74%, and 19.6% for A = 0.1, 0.15, and 0.2 along the fin, respectively. The averaged Nusselt number along the fin is an increasing function of the Rayleigh number, nanotube volume fraction, thickness of the tree-shaped fin, and amplitude of waviness. Additionally, a novel correlation for the averaged Nusselt number along the fin is derived.

Heat storage modeling for air ventilation usage considering freezing of paraffin through a sinusoidal duct

In this article, sinusoidal layers of PCM through air ventilation were employed. Current unsteady process with neglecting gravity impact is simulated by Finite volume method. Temperature of all zones is 303.15 K at t = 0 and PCM zones contain liquid RT28. Six cases were tested and three of them have various configurations for air gap arguments. Dispersing CuO nanoparticles (φ = 0.05) makes the required time for freezing to decrease about 5.55 %. With changing the shape of PCM zone to wavy duct, full solidification time decreases about 23.52 %. With insertion of air gaps, adding CuO nanoparticles (φ = 0.05) and considering sinusoidal duct, the needed time reduces about 44.44 %. The highest case in view of freezing time is first case. With increase of time, temperature of PCM reduces with heat releasing to air. With insertion of air gaps and sinusoidal wall, the outlet temperature decreases about 0.379 % at the end of discharging.

Liver in guinea pig: Scanning and transmission electron microscopic studies

The liver performs many functions, which support metabolism, immunity, digestion, detoxification, vitamin storage, and so on. The liver is the storage organ for fat-soluble vitamins, iron and copper. Six adult healthy guinea pigs of 16-32 weeks of age (Irrespective of sex) were procured from the Department of Laboratory Animal Medicine, TANUVAS as per ethical committee approval. Animals were dissected as per CPCSEA norms and liver pieces were utilized for scanning electron microscopy (SEM) and transmission electron microscopy (TEM) study. The study was performed to document the ultrastructural details of liver of guinea pigs by SEM and TEM. By SEM, the liver parenchyma appeared as lobular with anastomosed one cell thick hepatic cell plates, which appeared as continuous sheets with small to large holes representing sinusoids. The sinusoidal lumen was lined by two types of cells namely endothelial cells and Kupffer cells. Endothelial cells had numerous large and small cytoplasmic fenestrations. Presence of Kupffer cells along with Ito cells were observed in the sinusoids. By TEM, hepatocytes had angular shape with sinusoidal face and bile canalicular face. Hepatocytes had oval nucleus with peripheral heterochromatin and central electron lucent granules and a prominent nucleolus. Bile canaliculi were formed by two adjacent hepatocytes. Fenestrated endothelial cells with flat and elongated shape were found to be in the formation of hepatic sinusoidal wall. A narrow space of Disse was found between the sinusoidal endothelium and hepatocytes. Kupffer cells and pit cells were found within the sinusoidal lumen. Ito cells were found in the space of Disse. RESEARCH HIGHLIGHTS: By scanning electron microscopy, the liver parenchyma appeared as lobular with anastomosed one cell thick hepatic cell plates, which appeared as continuous sheets with small to large holes representing sinusoids. By transmission electron microscopy, hepatocytes had angular shape with sinusoidal face and bile canalicular face. Hepatocytes had oval nucleus with peripheral heterochromatin and central electron lucent granules and a prominent nucleolus.

Linearised Reynolds-averaged predictions of secondary currents in turbulent channels with topographic heterogeneity

A rapid predictive tool based on the linearised Reynolds-averaged Navier–Stokes equations is proposed in this work to investigate secondary currents generated by streamwise-independent surface topography modulations in turbulent channel flow. The tool is derived by coupling the Reynolds-averaged momentum equation to the Spalart–Allmaras transport equation for the turbulent eddy viscosity, using a nonlinear constitutive relation for the Reynolds stresses to capture correctly secondary motions. Linearised equations, describing the steady flow response to arbitrary surface modulations, are derived by assuming that surface modulations are shallow. Since the equations are linear, the superposition principle holds and the flow response induced by an arbitrary modulation can be obtained by combining appropriately the elementary responses obtained over sinusoidal modulations at multiple spanwise length scales. The tool permits a rapid exploration of large parameter spaces characterising structured surface topographies previously examined in the literature. Here, channels with sinusoidal walls and with longitudinal rectangular ridges are considered. For sinusoidal walls, a large response is observed at two spanwise wavelengths scaling in inner and outer units respectively, mirroring the amplification mechanisms in turbulent shear flows observed from transient growth analysis. For longitudinal rectangular ridges, the model suggests that the analysis of the response and the interpretation of the topology of secondary structures is facilitated when the ridge width and the gap between ridges are used instead of other combinations proposed in the literature.

Two-phase mixture numerical and soft computing-based simulation of forced convection of biologically prepared water-silver nanofluid inside a double-pipe heat exchanger with converging sinusoidal wall: Hydrothermal performance and entropy generation analysis

The cooling performance of biological water-silver nanofluid (NF) in three double-pipe heat exchangers with converging sinusoidal inner wall (SCDHX), converging inner wall (CDHX), and plain inner wall (PDHX) was examined numerically using the first and second laws of thermodynamics. The two-phase mixture model is employed to conduct the simulations. Based on the results, the sinusoidal wall increases the flow mixing, and thereby the convective heat transfer coefficient in SCDHX enhances by 50% and 18% over the PDHX type for Res of 500 and 2000, respectively. Moreover, the highest NF frictional entropy generation rate (S˙f,m,c) was obtained for SCDHX; 67% and 80% higher than those for CDHX and PDHX, respectively. The efficiency criteria ratio (η) of SCDHX was obtained as roughly 1.1 for Res of 500 and 1000, which is 27.27% higher than that for CDHX type. Also, the efficiency criteria ratio of SCDHX over the CDHX was in the range of 1.21-1.41. Besides, a robust soft computing, namely the Gaussian process regression (GPR) approach, was proposed to accurately estimate the total entropy of cold NF, the total entropy of hot NF, and the performance ratio based on the nanoparticle concentration and Reynolds number.

Heat transfer in a square cavity filled by nanofluid with sinusoidal wavy walls at different wavelengths and amplitudes

This study's main purpose is to investigate the wavy wall effect with a sinusoidal function on two-dimensional natural convection in a cavity with Cu-Water nanofluid. The SIMPLE algorithm is used to solve the FVM discretized governing Equations of velocity field and heat transfer. The effect of wall wavelength, amplitude, and volume fraction (VF) of nanoparticles, is investigated at a Rayleigh number of 10000 to find the optimal heat transfer mode. The amplitude varied from 0 to 0.15, the wavelength from 0.25 to 1, and the concentration of nanoparticles is changed from 0 to 0.04. The effect of all three parameters is determined separately by statistical analysis using the signal-to-noise ratio. According to the results, the most important parameter that can affect heat transfer is VF. As the VF increases from 0 to 0.04, the average Nusselt number (Num) increases by about 2.5 times. For example, at amplitude A = 0.05, wavelength B = 0.25, with increasing VF from 0 to 0.04, the null number increases from 35.30086 to 90.4793. In contrast, wall wavelength has the least effect on it. Three steps of −1, 0, and +1 are defined for further investigation of heat transfer. The wavy wall's Num increases with increasing VF and wavelength from step −1 to +1. The surface heat transfer coefficient also shows an increasing trend.

Performance improvement of rectangular microchannel heat sinks using nanofluids and wavy channels

In this article, the effect of two different methods of cooling enhancement, including the use of nanofluid as the coolant and sinusoidal wavy walls, on the performance of rectangular microchannel heat sinks (MCHSs) has been numerically investigated. Three-dimensional simulations based on the finite-volume approach are carried out using three different wave amplitudes (50, 100, and 200 µm) and wavelengths (1.3, 2, and 4 mm). Water-based nanofluid containing Al2O3 nanoparticles with volume fraction of 1% is employed as the coolant, and its influence on the hydraulic and thermal performance of the MCHS is compared with the water. The simulation of nanofluid flow is performed by both the single-phase method and the two-phase mixture method. Comparison between predicted results and experimental data from literature is carried out, which indicates the two-phase method is more precise than the single-phase method. Results showed that the enhanced microchannels with higher wave amplitudes and lower wavelengths performed better in terms of heat transfer, and among the investigated geometries, the wavelength of 1.3 mm and the amplitude of the 200 µm show the highest cooling performance. Using these optimal geometrical values in the wavy-walled microchannel heat sink (WMCHS), the amount of heat absorbed by the water-Al2O3 with volume fraction of 1% increases by 43% compared with the water flow in the straight-walled microchannel heat sink (SMCHS) at Reynolds number of 500. In addition, in a given geometry with fixed length and cross section area, employing wavy walls has a greater effect on heat transfer enhancement than using nanofluid instead of water. Employing optimal wavy walls in the MCHS, the amount of absorbed heat increases by 30% when the coolant is pure water and by 21% when the coolant is nanofluid. Whereas if nanofluid is used instead of water, the heat absorbed increases by 18% in SMCHS and 10% in WMCHS. Although both methods of cooling enhancement increase the pressure drop as well, the negative effect of the increase in pressure drop is less than the positive effect of increasing heat transfer in both methods.

Mathematical computations for the physiological flow of Casson fluid in a vertical elliptic duct with ciliated heated wavy walls

This mathematical investigation discloses the peristaltic flow of non-Newtonian fluid in a vertical duct with an elliptic cross-section and ciliated walls. The Casson fluid’s non-Newtonian model is utilized for an elliptic duct with heated ciliated walls. The physical aspects of cilia-driven metachronal wave combined with sinusoidal wavy wall movement are highlighted. A set of dimensionless partial differential equations with relevant boundary conditions is obtained after simplifying the dimensional form of governing equations using appropriate transformations. A complete mathematical method is conveyed to get exact solutions for this convection heat transfer problem. The final solutions are further analyzed through graphical results. The increase in the value of changes the mechanism from non-Newtonian to a Newtonian flow. Moreover, if is increased to infinity, then it becomes a complete Newtonian fluid flow problem. Moreover, the velocity increases with an increasing value of .

Melting process of various phase change materials in presence of auxiliary fluid with sinusoidal wall temperature

This paper presents a numerical simulation approach to investigate the water effect as an auxiliary fluid in direct contact with various phase change materials (PCMs). The technique is defined as a hybrid method due to the using of an external intermediary for melting process improvement. Oleic acid (OA), coconut oil (CO), hexadecane, and heptadecane are selected as PCMs due to immiscibility in water and differences in density, melting point, and enthalpy of fusion. An auxiliary fluid is embedded above PCM in an enclosure subjected to sinusoidal wall temperature for melting rate increase through density differences improving heat transfer rate due to materials displacement during process. Based on water accessibility and price, this approach would be preferable to costly enhancement methods such as nanoparticles addition or utilizing extending heat transfer surfaces. Each PCM melting process in the hybrid system with a volume ratio of 50% PCM - 50% water is simulated and compared with a pure (100% PCM) reference melting process. A 23%, 30%, 62%, and 98% increase in energy storage capacity can be attributed to hybrid systems with OA, CO, hexadecane, and heptadecane, respectively. Also, stored heat rate computation shows that using water increases 177% stored heat rate per PCM kg in the system. Meanwhile, it accelerates PCM melting process. Higher density differences cause a dynamic flow field and faster melting process, increasing stored heat rate about twice, which is a significant result for system design and optimization.

Simulation for discharging of phase change material within a porous duct utilizing multi layers

Effect of nanoparticles on solidification within a duct with multi air layer was scrutinized in current research. Impose of wavy canal and nanoparticles can augment the solidification rate and these factor were checked in current unsteady modeling. Exergy drop and solid fraction distributions were analyzed. As mass of liquid reduces, exergy drop declines and impose of sinusoidal wall can augment the exergy drop. Cold air make the liquid PCM convert to solid and its temperature augments. With use of sinusoidal wall, better exchange of heat occurs and solidification occurs in lower time. Air temperature reduces as mass of liquid decreases and same behavior was reported for temperature of NEPCM. At t = 1.4hr, Tair of two cases were the same and after this time, temperature of flat plate is greater than another case. After full solidification, temperatures of air for two cases become equal. Solidification time reduces about 26.6% with utilizing wavy surface.