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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Transactions of the Korean Society of Mechanical Engineers B
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Journal DOI :
The Korean Society of Mechanical Engineers
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Volume & Issues
Volume 25, Issue 12 - Dec 2001
Volume 25, Issue 11 - Nov 2001
Volume 25, Issue 10 - Oct 2001
Volume 25, Issue 9 - Sep 2001
Volume 25, Issue 8 - Aug 2001
Volume 25, Issue 7 - Jul 2001
Volume 25, Issue 6 - Jun 2001
Volume 25, Issue 5 - May 2001
Volume 25, Issue 4 - Apr 2001
Volume 25, Issue 3 - Mar 2001
Volume 25, Issue 2 - Feb 2001
Volume 25, Issue 1 - Jan 2001
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Experimental Study on the Aerodynamic Characteristics of a Two-Stage and a Counter-Rotating Axial Flow Fan
Cho, Jin-Soo ; Cho, Lee-Sang ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1281~1292
DOI : 10.22634/KSME-B.2001.25.10.1281
Experiments were done for the comparison of performance and flow characteristics between a two -stage axial flow fan and a counter-rotating axial flow fan. Each stage of the two -stage axial flow fan used fur the present study has an eight bladed rotor and thirteen slater blades. The front and the rear rotor of the counter - rotating axial flow fan have eight blades each and are driven by coaxial counter ro latins shafts through a gearbox located between the rear rotor and the electric motor. Both of the two axial fan configurations have identical rotor blades and the same operating condition fur the one -to-one comparison of the two. Performance curves of the two configurations were obtained and compared by varying the blade pitch angles and axial gaps between the blade rows. The fan characteristic curves were obtained following the Korean Standard Testing Methods for Turbo Fans and Blowers (KS B 6311). The fa n flow characteristics were measured using a five-hole probe by a non-nulling method. The velocity profiles between the hub and tip of the fans were measured and analyzed at the particular operating condition s of peak efficiency, minimum and maximum pressure coefficients. The peak efficiency of the counter-rotating axial fan was improved about 2% respectively, compared with the two stage axial fan. At the minimum pressure coefficient point of the two stage axial fan, the fan inlet flow patterns show that axial velocity highly decreased in the vicinity of the blade tip region. Also, the reverse flow took place at the blade tip.
Effect of Diffuser Width on Rotating Stall in Centrifugal with Vaneless Diffuser
Kim, Jin-Hyeong ; Jo, Gang-Rae ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1293~1302
DOI : 10.22634/KSME-B.2001.25.10.1293
It is generally known that radial vane blowers with vaneless diffuser may generate mostly only a rotating stall but backward curved vane blowers may do both an impeller and a diffuser rotating stalls. In this study, it was found from the numerical and experimental results that the diffuser rotating stall does not appear in a radial vane because of the suppression for the diffuser stall appearance by occurring of impeller rotating stall in a large flow rate coefficient. The diffuser rotating stalls occurring when the width of diffuser is broaden fur a backward curved vane blower are classified definitely by the diffuser flow rate coefficient defined by adopting the varying diffuser width.
Modeling of Laminar Burning Velocities for Hydrocarbon and 7ethanol Fuels by Using Detailed Chemical Reaction Mechanisms
Bae, Sang-Su ; Min, Gyeong-Deok ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1303~1310
DOI : 10.22634/KSME-B.2001.25.10.1303
In order to be applicable to the combustion modelling of stratified charged combustion like that of - lean burn and GDI engine, the correlations of laminar burring velocities fur several hydrocarbon fuels and methanol are needed over a wide range of equivalence ratio, pressure and temperature. In this study, these correlations are modeled in the 1311owing form based on the experimental and Muller\`s modeling results for several fuels, where
, ξ, and ξ are functions of pressure and temperature,
)]. By using the results calculated by PREMIX code with Sloane\`s detailed chemical reaction mechanism for propane, it is verified that the coefficients of the abode modeling can be determined by considering laminar burning velocity data only in a range of equivalence ratio less than
. Therefore, Muller\`s modeling results can be adopted leer modeling of the pressure and temperature dependency. Compared with the results of the existing Keck'and Gulder's models, those of the present one showed the good agreement of the recent experimental data, especially in the range of lean and rich sides.s.des.s.
Measurements of Equivalence Ratio in the Spark Plug Gap and Its-Effects on Combustion Under Stratified Mixture Conditions in a Constant Volume Chamber
Bae, Sang-Su ; Lee, Gi-Cheol ; Min, Gyeong-Deok ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1311~1317
DOI : 10.22634/KSME-B.2001.25.10.1311
To investigate only the effects of the stratified mixture distribution on initial flame propagation and combustion characteristics, the instantaneous equivalence ratio in the spark plug gap and combustion pressure were measured simultaneously In a constant volume chamber, To induce the stratified propane-air mixture distribution near the spark plug, counter-flow typed mixture injection system was used under the constant mean equivalence ratio
mean/= 1.0 The instantaneous equivalence ratio was measured by a single-shot Raman scattering with narrow-band KrF excimer laser. The measuring error was within the limit of
3.5% provided that the proposed method was applied to the measured Raman signals. Judging from mass fraction burned derived from the measured pressure, the optimum combustion characteristics were shown under the condition that the local equivalence ratio in the spark plug was near 1.28
0.04, and these characteristics were more remarkable at the initial stage of combustion.
Evaporation Heat Transfer and Pressure Drop Characteristics of Refrigerant R-22 in a P1ate and Shell Heat Exchanger
Seo, Mu-Gyo ; Park, Jae-Hong ; Kim, Yeong-Su ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1318~1326
DOI : 10.22634/KSME-B.2001.25.10.1318
The evaporation heat transfer coefficient and pressure drop for refrigerant R-22 flowing in the plate and shell heat exchanger were investigated experimentally in this study. Two vertical counterflow channels were farmed in the exchanger by three plates of commercial geometry with a corrugated trapezoid shape of a chevron angel of 45 ° Upflow boiling of refrigerant R-22 in one channel receives heat from the hot downf1ow of water in the other channel. The effects of the mean vapor quality, mass flux, heat flux and pressure of R-22 on the evaporation heat transfer and pressure drop were explored. The quality change of R-22 between the inlet and outlet of the refrigerant channel ranges from 0.03 to 0.05. The present data showed that both the evaporation heat transfer coefficient and pressure drop increase with the vapor quality. At a higher mass flux, the evaporation heat transfer coefficient and pressure drop are higher for the entire range of the vapor quality Raising the imposed wall heat flux was found to slightly improve the heat transfer, while at a higher refrigerant pressure, both the heat transfer and pressure drop are slightly lower.
An Experimental Study of Radiated So from Elastic Thin Plate in a Turbulent Boundary Layer
Lee, Seung-Bae ; Gwon, O-Seop ; Lee, Chang-Jun ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1327~1336
DOI : 10.22634/KSME-B.2001.25.10.1327
The structural modes driven by the low wave-number components of smooth elastic wall pressure provide a relatively weak coupling between the flow and the wall motion. If the elastic thin plate has any resonant mode whose wave-number of resonance coincides with
c/, the power will be transmitted to those modes of vibration by the flows. We examine the problem in which the elastic thin plate is subject to pressure fluctuations under turbulent boundary layer. Measurements are presented of the frequency spectra of the near- and far-field pressures and radiated sound contributed by the various wave modes of the thin elastic plate. Dispersion equation for wave motions of elastic plate is used to investigate the effect of bending waves of relatively low wave number on radiated sound. The low wave-number motion of elastic plate is observed to have much less influence on the low-frequency energy of wall pressure fluctuations than that of the rediated sound. High amplitude events of the wall pressure are observed to weakly couple with high-frequency energy of radiated sound for case of low tension applied to the plate. The sound source localization is applied to the measurement of radiated sound by using acoustic mirror system.
The Effects of Thermosolutal Convection on Macrosegregation during Alloy Solidification
Lee, Gyun-Ho ; Mok, Jin-Ho ; Lee, Jin-Ho ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1337~1345
DOI : 10.22634/KSME-B.2001.25.10.1337
Numerical investigation is made to study the effects of thermosolutal convection on the formation of macrosegregation in a Pb-Sn alloy solidification process in a two dimensional confined rectangluar mold. The basic equations are sovled using the Contrinum Model theory with the SIMPE algorithm during the solidification process. In addition, to track the liquid-solid interface with time variations, the moving boundary condition was adopted and moving irregular interface shapes were treated with the time-dependent, boundary-fitted coordinate system. As the temperature reduces from the liquidus to the solidus, the liquid concentration of Sn, the lighter constituent, increases. Then the buoyancy-driven flow due to temperature and liquid composition gradients occurs in the mushy region and forms the complicated macrosegregation maps. belated to this phenomena, effects on the macrosegregation formation depending on the cooling condition and gravity values are examined.
Experimental Study on Heat Transfer Characteristics of Swirling Impinging Jet
Jo, Jeong-Won ; Lee, Sang-Jun ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1346~1354
DOI : 10.22634/KSME-B.2001.25.10.1346
The heat transfer characteristics off swirling air jet impinging on a heated flat plate have been investigated experimentally. The main object is to enhance the heat transfer rate by increasing turbulence intensity of impinging jet with a specially designed swirl generator. The mean velocity and turbulent intensity profiles of swirling jet were measured using a hot-wire anemomety. The temperature distribution on the heated flat surface was measured with thermocouples. As a result the swirl effect on the local heat transfer rate on the impinging plate is confined mainly in the small nozzle-to-plate spacings such as L/D<3 at the stagnation region. For small nozzle-to-plate spacings, the local heat transfer in the stagnation region is enhanced from the increased turbulence intensity due to swirl motion, compared with the conventional axisymmetric impinging jet without swirl. For example, the local Nusselt number of swirling jet with swirl number Sw=0.75 and Sw=1 is about 9.7-76% higher than that of conventional impinging jet at the radial location of R/D=0.5. With the increase of the nozzle-to-plate distance, the stagnation heat transfer rate is decreased due to the diminishing axial momentum of the swirling jet. However, the swirling impinging jet for all nozzle-to-plate spacings tested in this study does not enhance the average heat transfer rate.
Interrelationship Between Topological Structures and Secondary Vortices in the Near Wake of aCircular Cylinder
Seong, Jae-Yong ; Yu, Jeong-Yeol ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1355~1364
DOI : 10.22634/KSME-B.2001.25.10.1355
Characteristics of secondary vortices is topologically investigated in the near-wake region of a circular cylinder, where the Taylor's hypothesis does nut hold. The three-dimensional flow fields in the wake-transition regime were measured by a time-resolved PIV for various planes of view. The convection velocities of the Karman and secondary vortices are evaluated from the trajectory of the vortex center. Then, saddle points are determined by applying the critical point theory. It is shown that the inclination angle of the secondary vortices agrees well with the previous experimental data. The flow fields in a moving frame of reference have several critical points and the mushroom-like structure appears in the streamline patterns of the secondary vortices. Since the distributions of fluctuating Reynolds stresses defined by triple decomposition are closely related with the existence of secondary vortices, the physical meaning of them is explained in conjunction with the vortex center and saddle point trajectories.
A Numerical Study of the Melt Puddle Formation in the Flow Casting,
Kim, Yeong-Min ; Im, Ik-Tae ; Kim, U-Seung ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1365~1372
DOI : 10.22634/KSME-B.2001.25.10.1365
In the planar flow casting(PFC) process, the conditions of the melt puddle between nozzle and rotating wheel affect significantly the quality and dimensional uniformity of the downstream ribbon. For stable puddle formation, the nozzle is placed very close to the quenching wheel, so the surface-tension and wall-adhesion forces have an important effect upon the fluid flow.\`In this study the planar flow casting process has been mode]ed using the VOF method for free surface tracking. The transient puddle formation from the present analysis shows good agreements with the previous experimental results. Furthermore, the variation of melt temperature and the corresponding cooling rate of the melt have been examined. The present results also show how the melt puddle can be farmed on the rotating substrate, how the melt flows within the puddle, and how the changes of the process variables affect the puddle formation and its corresponding fluid flow and heat transfer behavior.
Desulfurization Characteristics of Domestic Anthracite by Limes at Bench Scale Pressurized Fluidized Bed Combustor .
Han, Geun-Hui ; Ryu, Jeong-In ; Jin, Gyeong-Tae ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1373~1383
DOI : 10.22634/KSME-B.2001.25.10.1373
The desulfurization characteristics of anthracite in a bench scale pressurized fluidized bed combustor are investigated. The coal used in the experiment is domestic anthracite from Kangwon Taeback area. The desulphurization experiment is performed with limestone from Chungbuk Danyang. The pressure of the combustor is maintained at 6 atm, and the combustion temperatures are 850, 900, and 950
. The superficial gas velocities are 0.9, 1.1, and 1.3 m/s. The excess air ratio is varied from 5 to 35%. The Ca/S mole ratios are 0.5, 1.5, 2.5 and 4.5 mole. All experiments are executed at 2m bed height. Consequently, SO
concentration in the flue gas is increased with incresing bed temperature and superficial gas velocity. However SO
concentration is decreased with incresing excess air ratio and Ca/S mole ratio.
Numerical Calculation of Three-Dimensional F1ow through A Transonic Compressor Rotor
Lee, Yong-Gap ; Kim, Gwang-Yong ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1384~1391
DOI : 10.22634/KSME-B.2001.25.10.1384
Three-dimensional flow analysis is implemented to investigate the flow through transonic axial-flow compressor rotor(NASA R67) and to evaluate the performances of Abid's low-Reynolds-number k-
and Baldwin-Lomax turbulence models. A finite volume method is used fur spatial discretization. The equations are solved implicitly in time by the use of approximate factorization. The upwind difference scheme is used for inviscid terms and viscous terms are approximated with central difference. The flux-difference-splitting method of Roe is used to obtain fluxes at the cell faces. Numerical analysis is performed near peak efficiency and near stall. The results are compared with the experimental data for NASA R67 rotor. Blade-to-Blade Mach number distributions are compared to confirm the accuracy of the code. From the results, it is concluded that Abid'k-
model is better for the calculation of flow rate and efficiency than Baldwin-Lomax model. But, the predictions for Mach number and shock structure are almost the same.
Flow Control Inside a Molten Zn Pot for Improving Surface Quality of Zinc Plated Strips
Choe, Jae-Ho ; Go, Min-Seok ; Kim, Seok ; Lee, Sang-Jun ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1392~1399
DOI : 10.22634/KSME-B.2001.25.10.1392
The flow fields inside a molten Zn pot of continuous hot-chip galvanizing process were investigated experimentally. With varying several parameters including the strip speed Vs, flow rate Q of induction heater. scrapper location and baffle configuration, instantaneous velocity fields were measured using a PIV velocity field measurement technique. Inside the strip region, counter-clockwise rotating flow is dominant. The general flow pattern inside the strip region is nearly not influenced by the strip speed Vs, flow rate Q and the scrapper location. In the exit region, the flow separated from the moving strip due to the existence of a stabilizing roll ascends to the free surface, for the cases of no scrapper and scrapper detached form the roll. On the other hand, the ascending flow to the free surface is decreased, as the flow rate Q of induction heater increases. By installing a baffle around the uprising strip, the flow moving up to the stabilizing roll decreases. In addition, B-type baffle is better than A-type baffle in reducing speed of flow around the stabilizing rolls. However, the flow ascended to the free surface is largely influenced by changing the flow rate Q, and the scrapper location, irrespective of the baffle type.
Measurement of Size Distributions of Submicron Electrosprays Using a Freezing Method and an Image Processing Technique
Gu, Bon-Gi ; Kim, Sang-Su ; Kim, Yu-Dong ; Lee, Sang-Yong ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1400~1407
DOI : 10.22634/KSME-B.2001.25.10.1400
The size distributions of electrospray droplets from the Taylor cone in cone-jet mode are directly measured by using a freezing method and a transmission electron microscope (TEM) image processing technique. These results are compared with the data obtained by an aerodynamic size spectrometer (TSI Aerosizer DSP). The use of glycerol seeded with NaI and a freezing method make it possible to sample droplets with their original sizes preserved. Since pictures of droplets are taken with TEM with very low vapor pressure of the solution, evaporation is suppressed by freezing. For liquid flow rates below 1 nl/sec, the measured droplet diameters by the TEM image processing technique and the aerosizer are in the range of 0.25 to 0.32 m add 0.3B to 0.40m, respectively. Comparing the TEM data with the aerosizer measurements, it has been revealed that the TEM image processing technique can afford more accurate values of droplet size distributions in the submicron range of 0.1 to 0.4m.
A Study on the Near Wake of a Square Cylinder Using Particle Image Velocimetry ( I )- Mean Flow Field -
Lee, Man-Bok ; Kim, Gyeong-Cheon ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1408~1416
DOI : 10.22634/KSME-B.2001.25.10.1408
Mean flow fields in the near wake of a square cylinder have been studied experimentally using a Particle Image Velocimetry (PIV). Ensemble-averaged velocity fields are successfully measured fur the square cylinder wake including the reverse flow region which arises many difficulties in accurate measurement by using conventional techniques, Experiments are performed at two free stream velocities of U
/ = 1.27m/s and 3.03m/s. The corresponding Reynolds numbers based on the free-stream velocity and cylinder diameter are 1600 and 3900, respectively. The intensity of free-stream turbulence is less than 1%, the blockage ratio (D/H) is 6.6% and the aspect ratio (W/D) is 40. The effect of Reynolds number on the near wake of a square cylinder has been investigated by the global mean velocity and instantaneous velocity fields. The most striking feature is that the length of the recirculating region increases with increasing Reynolds number, which turns out totally reverse trend compared with those observed in the circular cylinder wake at the same range of Reynolds number. Fer the case of higher Reynolds number, the mean velocity data agree well with those of relevant existing data obtained at much higher Reynolds numbers, which reflects the general aspect of sharp-edged bluff body wake.
A Study on the Near Wake of a Square Cylinder Using Particle Image Velocimetry (II)- Turbulence Characteristics -
Lee, Man-Bok ; Kim, Gyeong-Cheon ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1417~1426
DOI : 10.22634/KSME-B.2001.25.10.1417
Turbulent flow characteristics in the near wake of a square cylinder have been studied experimentally by using a Digital PIV method. Experiments are performed at the Reynolds numbers of 1600 and 3900 based on the free-stream velocity and the square height. The ensemble averaged turbulence statistics are acquired from 2030 realizations of instantaneous fluctuating velocity field after the conventional Reynolds decomposition. The differences in turbulent intensity and Reynolds shear stress profiles fur both oases indicate that the effect of Reynolds number seems to be descernible mainly due to the occurrence of transition in the separated shear layer. Because of the periodic nature of vortex shedding process, transverse velocity fluctuations contribute dominantly , to turbulent kinetic energy distribution. A comparison with previous LDV data obtained at much higher Reynolds number shows a fairly good agreement each other. It turns out that the effect of Reynolds number diminishes as increasing Reynolds number, which is a well-known feature of a sharp-edged bluff body wake. The streamwise variation of turbulence intensities are compared with those from a circular cylinder along the centerline at the same Reynolds number. The overall magnitudes and the decay rates of turbulence intensities are quite similar, but some differences are noticeble especially in the transverse intensity variation.
Improvement of Natural Ventilation in a Factory Building Using a Velocity Field Measurement Technique
Im, Hui-Chang ; Kim, Hyeong-Beom ; Lee, Sang-Jun ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1427~1435
DOI : 10.22634/KSME-B.2001.25.10.1427
Air movement in wokplaces, whether resulting from a forced ventilation system or naturally occurring airflow, has a significant impact on occupational health. In a huge shipbuilding factory building, typical harmful factors such as fume or vaporized gas from welding and cutting of steel plates, and dusts from grinding give unpleasant feeling. From field data survey, the yearly dominant, wind directions for the shipbuilding factory building tested were northwest, northeast and southeast Among the three wind directions, the ventilation improvement was the worst for the northeastern wind. This study was focused on location of the opening vents in order to utilize the natural ventilation effectively. Instantaneous velocity fields inside the 1/1000 scale-down factory building model were measured using a 2-frame PIV system. The factory building model was embedded in an atmospheric boundary layer simulated in a wind tunnel. The modified vents improve the internal Ventilation flow with increasing the flow speed more than two times, compared with that of present vents.
Experimental Study on Stall Inception in a High-Speed Centrifugal Compressor (I) - inception Type -
Gang, Jeong-Sik ; Gang, Sin-Hyeong ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1436~1444
DOI : 10.22634/KSME-B.2001.25.10.1436
Stall inception in a high-speed centrifugal compressor has been examined. The main objective was to find stall precursor and to develop a reliable stall warning method. Eight equally spaced fast-response pressure transducers in the inducer detected the spatial structure of small amplitude perturbations, via spatial Fourier transform, as stall is approached. Near the stall inception point, the phase of spatial courier coefficients increased linearly with the speed of impeller relation for several impeller revolutions at all test speeds, and the spectrum at impeller frequency increased as stall is approached. These are the clear evidences that the impeller frequency participates in the stalling process.
Experimental Study on Stall Inception in a High-Speed Centrifugal Compressor ( II )- Stall Warning Method -
Gang, Jeong-Sik ; Gang, Sin-Hyeong ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1445~1450
DOI : 10.22634/KSME-B.2001.25.10.1445
Stall inception in a high-speed centrifugal compressor has been examined. The main objective was to find stall precursor and to develop a reliable stall warning method. For stall warning, a method which uses the spectrum at impeller frequency is suggested. The use of the spectrum at impeller frequency as a stall warning method showed a warning time of about two hundreds impeller revolutions. This method uses only one sensor that it has made the stall warning method more useful. And the well-known traveling wave energy method proved to be a good method for stall warning also in a high-speed centrifugal compressor. The warning time was about one hundred impeller revolutions at lower speeds, and about one thousand impeller revolutions at higher speeds. The stall warning methods used here were found to be robust and reliable. Therefore, it seems to be promising to set up a reliable stall avoidance control based on this analysis.
Effects of a Specularly Reflecting Wall in an Infinite Square Duct on Conductive-Radiative Heat Transfer
Byeon, Gi-Hong ; Han, Dong-Cheon ;
Transactions of the Korean Society of Mechanical Engineers B, volume 25, issue 10, 2001, Pages 1451~1458
DOI : 10.22634/KSME-B.2001.25.10.1451
The effects of a specularly reflecting surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The walls are opaque, and black or gray. The walls emit diffusely but reflect diffusely or speculary. Heat is transferred by the combined effect of conduction and radiation. The radiative heat transfer is analyzed using direct discrete-ordinates method. The parameters under study are conduction, to radiation parameter, optical depth, wall emissivity, and reflection characteristics. The specular reflection and diffuse reflection show sizeable differences when the conduction to radiation parameter is less than around 0.01. The differences appear only either on the side wall heat flux or on the medium temperature profiles for the range of this study. The differences on the side wall heat flux are observed for optical thickness less than around 0.1 However the differences on the medium temperate profiles are found for optical thickness greater than around 1. The difference increase with increasing reflectance. The specular reflection increases the well heat flux gradient along the side wall.