et International Journal on Emerging Technologies 8(1): 54-61(2017)
ISSN No. (Print) : 0975-8364 ISSN No. (Online) : 2249-3255 Heat and Mass Transfer with reference to Aerodynamics Menka Yadav 1 and Santosh Kumar Yadav 2 1Research Scholar, J.J.T. University, Rajasthan, India 2Director (A&R), J.J.T. University, Rajasthan, India (Corresponding author: Menka Yadav) (Received 19 March, 2017 Accepted 28 April, 2017) (Published by Research Trend, Website: www.researchtrend.net) ABSTRACT: Aerodynamic heating produces during passage of high speed aircraft and greatest at high speed and in lower atmosphere, highly dependent on design of vehicle. It plays important role in supersonic and hypersonic so the nose and wing leading edges should be blunt not sharp. Important information regarding heat and mass transfer is provided by the impinging jet. To characterize heat and mass transfer Nusselt number (N u) and Schmidt number (S c) are used. Total aerodynamic heating comprises of convective and radiative heating. To get rid of massive heat accumulation, heat sinks, ablation and radiative cooling is employed. Mass transfer from flat surfaces depends on Reynold and Schmidt number. Keywords: Blunt shape, Impinging jet, Nusselt number, Reynold number, Schmidt number and Slender body. I. INTRODUCTION Practical problems arises in construction of steam turbines, gas turbines, high pressure turbocompressors and Basic unit of heat and mass exchanger are ducts and to in wind tunnel. Flow at high supersonic speed is known as make contacts between gases, solid and liquid, interface is hypersonic flows. The temperature of gas rises very high provided by ducts. Aerodynamic heating is the heating of when a body flies at hypersonic speed. Increase in a solid body produced when it passes through air with temperature takes place due to highly compressed gas in very high speed (or by the passage of air past a test object front of nose and heat produced due to internal friction in a wind tunnel), where its K.E. converted into heat by carried by the body. In hypersonic flow air properties skin friction on the surface of object which in turn changes at high temperature like excitation of internal depends on the viscosity and speed of the air. It is highly degree of freedom, dissociation of gas molecules, related to meteors, reentry vehicles, and the design of high chemical reactions (formation of nitric acid), excitation of speed aircraft. While object passing through air at high electrons and ionization. At lowering the peak speed, K.E. converts into heat through compression and temperature leading edges, heating effects are greatest but friction. At lower speed, if air is cooler, then object lose if it remains at speed then the whole vehicle heats up to a heat to the air. The combined temperature effect of heat stabilized temperature. Turbulent flow is described by from the air and passage through it is called stagnation random fluctuations in quantities like velocity temperature and the actual temperature is called recovery temperature etc. In absence of such fluctuations, flow is temperature. Boundary layer slow down via a non- known as laminar. At transition, Reynold no. laminar flow isentropic process due to viscous dissipative effects to turns into turbulent flow. neighbouring sub layers. Conduction of heat takes place At subsonic speed its effects are minimal but at into the surface material from the higher temperature air. supersonic speeds above M 2.2 it dictates the Consequently, temperature of material increases and a design/materials of the vehicle structure and internal loss of energy from the flow. It is ensured by forced systems. convection that other material replenishes the gases that have cooled to continue the process. As the speed of flow A. Aircraft and Reentry vehicles increases, stagnation and recovery temperature increases. Aerodynamic heating concerns with supersonic and Furthermore, total thermal loading of the object is a hypersonic. The SR-71 used titanium skin panels painted function of recovery temperature and the mass flow rate. black to reduce the temperature and corrugated to Aerodynamic heating is greatest at high speed and in accommodate expansion. Liquid cooling of the leading the lower atmosphere where the density is greater, also edges is also used in some designs for hypersonic missiles increase with the speed of vehicle. Supersonic flow is the (usually the fuel en route to the engine). For Mach 10 fluid motion in which Mach number is greater than unity temp. several design iterations are used, for sprint missile relative to the sonic speed in the same medium. heat shield. Yadav and Yadav 55 To get rid of massive heat accumulation, three approaches applications. Large amount of heat and mass can be are used for thermal protection systems as Heat sinks, transferred in an effective way if flow released against a Ablation, Radiative cooling. surface. Heat transfer process used in heating of optical Heat sinks are extramaterial used to absorbs the heat by surfaces, cooling of electronic components, turbine lowering the peak temperature can be lowered by components and critical machinery structures and in increasing the volume of material. Carbon and ceramics aeronautical, chemical, civil, electrical, metallic and have very high latent heat of fusion. During vaporaization, metallurgic engineering. Drying and removal of small these materials soaks up large amount of heat energy. If surface particulate are applications of typical mass the Vehicle's surface is coated with these material, then transfer. In practical applications, if order of magnitude of vehicle can be protected. The melting process can be Reynold number is greater than boundary layer thickness termed as ablation. Radiative cooling is the process of 1 in stagnation zone becomes of nozzle diameter. Jet reducing equilibrium temp., by emitting heat energy 100 th before absorbing the vehicle's structure. has finite breadth and it exchanges momentum with Immense heat is created by very high reentry speeds surrounding, then accelerated stagnation flow converts (greater than Mach 20) and it is sufficient to destroy into decelerated wall jet flow. In stagnation zone, vehicle so special techniques are used. To produce a boundary layer becomes laminar due to stabilizing effect stand-off bow shock blunt shape is given such as used on of acceleration. In comparison to other heat and mass Mercury, Gemini and Apollo. It results, most of heat transfer arrangements, which do not involve phase dissipation transfer to surrounding air without transferring change, efficient use of fluid and high transfer rates are the vehicle structure. Moreover, at high temp., these offered by jet impingent device. Due to very thin vehicle's ablative material sublimate into gas. During impingement boundary layer heat transfer coefficients are sublimation process, thermal energy is absorbed from the three times higher at a given maximum flow speed than aerodynamic heating and material is eroded as opposed to conventional convection cooling by confined flow parallel heating the capsule. The surface of the heat shilf for the to the cooled surface. Multiple jets can be used for more Mercury spacecraft had a coating of aluminium with glass uniform coverage over large surfaces. It also offers a fiber in many layers. As the temperature increases upto compact hardware arrangements. 1100 °C (1400 K), layer would evaporate and take the heat To characterize heat transfer at the target surface, with it. The spece craft get heated but not harmfully, so on Nusselt number (N ) and the mass transfer from the lower surface of space shuttle insulating tiles are used to u surface with a Schmidt number (S c) are used. For device absorb and radiate heat vehicle preventing conduction to performance assessment and design efficiency, these the alumium airframe. values are tracked vs. jet flow per unit area or vs. the Cooling fin is also used to transfer heat from a solid to power required to supply the flow. an ambient fluid for cooling purpose often exhibit slender geometries. Their dimension in the conductive heat C. Impinging Jet Regions transfer are larger than in directions transverse to it (fins The flow of a submerged impinging jet passes through or needles). Thermal energy balance is allowed by different regions as shown in Fig. 1. The jet comes out geometrical property of the fin to be formulated in a quasi from a nozzle with a velocity and temperature profile, and one-dimensional form, where coordinates of conductive the turbulence characteristics depends upon the upstream heat transport are geometrical properties of fin and flow. For a tube nozzle, the flow develops into the temperature. Improving design tools with respect to flight parabolic velocity profile. A round jet with an experiment could be helpful in the development of axisymmetric flow profile or a slot jet, a long thin jet aerodynamics. with a two-dimensional flow profile is used in typical jet Aerodynamic heating becomes severe at hypersonic nozzles. It behaves as a free submerged jet when it passes speed so the nose and leading edges should be blunt not far from impingement surface. At the edges of jet velocity sharp, otherwise vehicle can destroyed by aerodynamic gradient create a shearing at the edges, which allows the heating. The unfortunate example of this type of transfer of momentum laterally outward and raises the jet destruction occurred during liftoff of the space shuttle mass flow. During this process energy is lost by jet and Columbia on February 1, 2003. During launch many the velocity profile becomes wide in spatial extent and thermal protection tiles near the leading edge of the left decreases in magnitude along jet sides. Due to momentum wing get damaged by debris. It permitted the penetration transfer shearing layer remains unaffected. If nozzle is at of hot gases into surface and damage the internal wing two diameters (2D) from the target, then free jet region structure. may not exist. Region of core decay forms when shearing layer B. Impinging Jet Heat Transfer expands inside the center of jet prior to reaching the Imping jets provides information regarding transfer of target. heat and mass in an efficient way in many industrial Yadav and Yadav 56 The axial position at which centraline flow dynamic ∂T −K pressure attains 95% of its original value, known as the c ∂ n end of one region. h = T− T In the decay jet, the radial velocity profile resembles to ojet wall Gaussian curve and axial velocity component decreases in ∂T where provides the temperature gradient central part. In stagnation region or declaration region, as ∂ n the flow approaches the wall, it loses axial velocity. The component normal to the wall. Nusselt number is higher static pressure on and above the wall is created by independent of target characteristics. T is the jet the flow. In the deceleration region, high normal and ojet temperature for adiabatic wall temperature of the shear stresses is experienced by the non-uniform turning deceleration jet flow, a factor of vital importance at flow by which local transport properties are affected to a increasing Mach numbers. Amount of K.E. is transferred great extent. For round jets stagnation region extends 1.2 into and retained in thermal form as the jet slows down, nozzle diameters above the wall. After the flow turns the known as non-dimensional recovery factor. core of the wall jet may accelerate due to conservation of T− T momentum. wall ojet recovery factor = 2 Ujet/ 2 C p Experiments shows that the temperature recovery factor varies from 70% to 100% of the full theoretical recovery with lowered recoveries in the stagnation region of a low H/ D jet ( H / D = 2) and 100% elevated stagnation region recoveries for jet with H/D = 6 and higher. Rate of mass transfer can be evaluated by non- dimensional Sherwood number as
Sh= Ki D/ D i ∂C ∂n ki= D i [Cobj− C wall ] ∂C where provides the mass concentration gradient ∂n component normal to the wall. Spatial distribution of concentration forms similar pattern as the temperature with sufficiently low mass concentration. Heat and mass transfer can be related via equation given below 0.4 Pr Nu / Sh = Sc The non-dimensional parameters which describe the impnging jet heat transfer problem comprises properties such as Prandtl number P r (ratio of fluid thermal diffusivity to viscosity) and the following: Fig. 1. The flow regions of an impinging jet. H/D : Nozzle height to nozzle diameter ratio r/D : Non-dimensional radial position from the center Non dimensional Heat and Mass Transfer of the jet. Coefficients: Z/D : non-dimensional vertical position measured from
Nusselt (N u) no. is a major parameter to evaluate heat the wall. transfer coefficient Tu : non-dimensional turbulence intensity generally evaluated at the nozzle. Nu= hD n/ K c where h is the convective heat transfer coefficient and Re 0 : Reynolds number U 0D/ ν; can be defined as M : Mach number (flow of speed / speed of sound in the fluid). Pjet /D : Jet center to center spacing (pitch) to diameter ratio, for multiple jets. Af : Free area Yadav and Yadav 57 f : relative nozzle area As H decreases, value of N u increases, so designer Flow exist at the nozzle is considered as the reference prefer to select smallest tolerable H value, effects of location while evaluating the fluid properties. Using existing flow, physical constraints, manufacturing position characteristics we can calculate fluid temperature capabilities and then selects nozzle size. average flow speed, viscosity and length scale D. Jet diameters ranges from 5-30 mm for large scale Diameter D can be replaced by the slot width B in slot jet. industrial applications and from 0.2 to 2 mm for small- Nature of the target and the field source are the two scale turbomachinery application. parameters necessary for geometry and flow conditions in At low Mach number modelling of turbulent flow is impinging jet. When pressure drop associated with defined by the mass, momentum and energy conservation delivering and exhausting the flow is very-2 small, then equation : the design goal is to extract cooling from a given air mass ∂u i = 0 flow. The jet emerges at a high Mach number at high ∂x pressure ratios. If the flow exists the nozzle as an under i expanded supersonic jet, then jet forms complex ∂u∂u j ∂ p ∂σ ij ∂ τ ij ρi + ρ u =−+ + interacting shock patterns and a recirculation "bubble" i ∂t ∂ xj ∂∂∂ xxx i j j directly below the jet, which can decreases heat transfer. Moreover, overall device performance is affected by the ∂u∂uj ∂p ∂ ∂ u ∂ u j ∂ ρρi +u =−+ µi ++− ρ u u impingement device design. i ()i j ∂t ∂ xj ∂∂ xx ij ∂∂∂ xxx ji i (Alternate form) ∂Τ ∂T ∂u ∂ µC∂ T ρC+ ρ C u =+ σ i p + p pj ij ∂t ∂ xj ∂∂∂ xxPx j jrj ∂ ∂u′∂u′ ∂ u ′ −ρC u′ T ′ + µ i + j i ()p j ∂xj ∂∂∂ xxx jij ∂u ∂u σ= µ i + j ij ∂xj ∂ x i
Fig. 2. Supersonic jet flow pattern. τij= − ρ u ij′ u ′ Turbulence Generation and Effects where an overbar above a single letter represents a Jet behaviour is described by its Reynold no. R = time-average term and prime symbol represent fluctuating e values and a large overbar represent a correlation. The U0D/ ν where U 0 is initial flow speed, ν is viscosity and D is nozzle exist diameter. Laminar flow properties are time variant momentum equation gives the conservative transport equation for Reynolds stresses for an shown by flow field at R < 100 but at R > 3000, flow field e e incompressible field. shows turbulent properties. Transition region lies in between 1000 < R e< 3000 Turbulence affects greatly the ∂∂τij τ ij ∂u j∂u p′ ∂∂ u′ jj u ′ +u =−τ − τ i + ++ heat and mass transfer rates. For e.g., an isolated round jet k ik jk ∂∂txk ∂ x k ∂ x k ρ ∂∂ xx ji at R e = 2000, Pr = 0.7, H/D = 6 delivers an average Nu of 19 over a circular target spanning six jet diameters, but at Re = 100,000 the average Nu on the same target spacing ∂ p′ ∂u′ ∂u′ ∂ 2τ uuuuu′′′ ′ ′ 2 i j v ij value of N u lies in the range of 2 −20. In the relation of −−ijk{} ijkδ + jik δ +− ν + ∂x jk ρ ∂∂xxkk ∂∂ xx kk Nusselt number and Reynold number N∝ R b , the u e exponent b ranges b = 0.5 for low-speed flows with a low- ∂τij ∂ τ ij turbulence wall jet, upto b = 0.85 for high Re flows with a + uk represent convective transport of Reynold turbulence-dominated wall jet. ∂t ∂ x k For a underexpanded supersonic jet at stress 6 ∂u Re =(1.028) × 10 local N u values may be as high as 1700. j ∂ui τik+ τ jk Reynold number varies from 4000 to 80,000 in case of ∂xk ∂ x k gas jet installations and H/D can vary from 2 to 12.
Yadav and Yadav 58 measures turbulent production of Reynold stresses. u′ p′ ∂ui′ ∂ j + measures the contribution of the pressure- ρ ∂xj ∂ x i strain rate correlation to Reynold stresses. ∂ p′ The term −uuuijk′′′ −{} u ′ jjkδ + u ′ jjk δ gives the ∂xk ρ effect of the gradient of turbulent diffusion. ∂u′ ∂ u ′ −2v i j represent the effects of turbulent ∂xt ∂ x k dissipation. ∂2T v ij represent the effects of molecular diffusion. Fig. 3. Convective and radiative heating rates of a blunt ∂xk ∂ x k reentry vehicle as a function of flight velocity. Intensity of turbulent flow field is given by the specific Aerodynamic heating in hypersonic flow: turbulent K.E. k. Downstream flow and heat transfer Heat transfer coefficient (Stanton number) can be characteristics are affected by the steady time-averaged defined as nozzle-velocity profile and fluctuations in the velocity qɺw over time. Turbulent fluctuations helps to understand the CH = (7) performance of impinging jets. ρeeu( h aw− h w )
Aerodynamic heating depends on the design of vehicle where qɺw represents heat transfer rate per unit area on also. Laminar flow produces less heating than turbulent body surface at a given point flow so to minimize it, focus is to maintain the boundary ρ = local density at the edge of boundary layer flow on the vehicle's surface. At the beginning e reentry vehicle posses large amount of P.E. due to its high ue = local velocity at the edge of boundary altitude and large amount of K.E. due to high velocity. hw = enthalpy of the gas at wall. But when the vehicle lift off to earth, it has no K.E. & haw = adiabatic wall enthalpy P.E. This shows that the huge amount of energy is At zero angle of attack consider the hypersonic flow imparted to heating the body and the airflow around the ignoring viscous interaction effect where ρ= ρ and body. If a major portion of energy is transferred to the air, e w then less amount of energy will be transferred in vehicle ue = u ∞ . heating. Heat transfer rate to the airflow can be increased Taw is nearly 12 percent less than the total temperature by creating a stronger shock wave at the nose which is in free stream at high Mach number laminar flow over a turn can be achieved using blunt nose body. Through flat plate. If T≈ T then from equation (1) mode of conduction energy is transferred from the hot aw 0 shock layer to the surfaces. haw≈ h a (2) Convective heating is given by, where h 0 represents the total enthalpy of the freestream, ∂T which can be expressed as qc = − k 2 ∂n V∞ h0 = h ∞ + (3) ∂T 2 where represents temperature gradient and it is V is very large at hypersonic speed. ∂n ∞ property of flow field. Air is comparatively cool at far ahead of the vehicle.
It is important mode of heat transfer for reentry Therefore h∞= Cp T ∞ is small. So at high speeds, from velocities. At high temp., mode of heat transfer is equation (3). radiation. Total aerodynamic heating can be expressed as 2 V q= q + q where q and q are convective heating and h ≈ ∞ (4) c r c r 0 2 radiative heating respectively.
Yadav and Yadav 59 At high Mach number surface temperature of the plate is where m represents mass of vehicle and minus sign smaller than the total temperature. Hence we made represents deceleration of vehicle: approximation that h0 >> h w (5) From above equation, We can write from the above mentioned equations, dV∞ D 1 2 =− =− ρ∞V ∞ SC D (14) V 2 dt m2 m h− h ≈ hh − ≈ h ≈ ∞ (6) aw w0 w 0 2 dQ where C D denotes vehicle's drag coefficient and So for a flat plate, equation can be written as – dt qɺw C = dQ dV ∞ H can be written as ρ∞V ∞ ( haw− h w ) dV∞ dt Using equation (6) Then qɺw dQ dQ 1 2 CH ≈ 2 = − ρ∞V ∞ SC D (15) ρ∞V ∞( V ∞ / 2) dt dV∞ 2 m 1 3 From (12) and (15) or qɺw≈ ρ∞ V ∞ C H (7) 2 dQ 12 1 3 It shows that aerodynamic heating depends on the cube −ρ∞∞V SCD = ρ ∞∞ V SC f dV2 m 4 of velocity but aerodyanmic drag varies with square of ∞ velocity. It shows that aerodynamic heating becomes a dQ 1 C f or = − mV dominant aspect of hypersonic vehicle design at very high ∞ dV∞ 2 V D velocities. It connects the aerodynamic heating with 1 C dV 2 hypersonic flow. dQ= − m f ∞ (16) 2C 2 Quantitative Explanation of blunt vs. Slender bodies in D Hypersonic flow Integrating from beginning of entry to the end, we have Q total Stanton number C for total heat transfer to the H Qtotal 0 2 1 C f V vehicle per unit time is ∫dQ= − ∫ d ∞ 2CD 2 dQ/ dt 0 VE C = (8) H C ρ∞V ∞ ( h0 − hSw ) 1f 1 2 or Qtotal= mV E (17) where S represents reference area and making use of 2CD 2 approximation equation (7) can be written as Equation (17) gives the total heat input and two major
dQ 1 2 conclusions can be drawn from it. = δ∞V ∞ SC n (9) dt 2 1 2 (i) Total input heat Q total varies directly with mV (K.E. For laminar flow Reynold's analogy can be expressed 2 E as, of vehicle) C 1 H −2/3 C f = Pr (10) (ii) It is also directly proportional to where C and C 2 f f CD P where C f denotes local skin friction coefficient and r CD represents skin friction drag and total drag denotes Prandtl number. respectively. If P r = 1, then Reynold analogy can be written as (iii) Aerodynamic drag on a vehicle is, C= C + C D Dp f CH 1 = (11) where CD is pressure drag coefficient C 2 p f and C is skin friction coefficient. Substituting equation (11) into (10) we get, f To minimize total aerodynamic heating in equation (17), dQ 1 3 = ρ∞V ∞ SC f (12) it is necessary to minimize, dt 4 C In case of hypersonic vehicle entry at very high Mach f C+ C number in space, aerodynamic drag slows down the DP f vehicle. Now consider the aerodynamic configuration as shown According to Newton's second law, in fig given below, dV C F= D = − m ∞ (13) f ≈ 1for slender body dt CD Yadav and Yadav 60 concentration may vary in time and space, even in an Cf << 1for slunt body insothermal system. Convective mass flux may arise due C D to inertial impaction, body force actions such as gravity, Reason being large skin friction for slender body and electrical and magnetic forces, lift force, particle inertia large pressure drag for blunt body. interaction and fluid turbulance field in homogeneity. In convective mass transfer product of conductance and driving force is known as total mass flux. In Tuurbulent boundary layer convective mass transfer product of boundary layer, flux of small particles can be obtained by integrating the modified Fick's law of diffusion, dc J= −() DB + D f dy
where DB denotes Brownian diffusivity. dc and D denotes turbulent diffusivity and is Slender body Blunt body f dy largeC f large C Df concentration gradient Small C small C Dp f Mass Transfer from flat Surface C≈ C C≈ C Consider a flat plate in fluid flow parallel to its surface D f D D p and assumes that material properties are independent of large friction drag large pressure drag composition take constant pressure and density
throughout the flow field. Furthermore velocity field v is Fig. 4. Comparison of blunt and slender bodies. divergence free and no chemical reactions there. In steady laminar flow, Sherwood number for forced Due to this reason all successful entry vehicles utilize convective mass transfer across a flat plate is given by rounded nose and rounded leading edge. For e.g. Sh= 0.332 R S 1/ 3 intercontinental ballistic missiles (ICBMs), Apollo lunar ex c return capsule, space shuttle etc. where R=U x / ν Aerodynamic heating for blunt shape can be calculated ex ∞ at the stagnation point. In hypersonic, maximum heat and symbols have their usual meanings. transfer takes place at this point. Relation between Value of ratio of thicknesses of the dynamic to stagnation point and nose radius is given by concentration boundary layers is determined by Sc . 1 Small value of Sc represents thicker concentration qɺw ∝ R boundary layer at a given position x along the plate. where R represent nose radius at stagnation. Consequently flow velocity is assumed constant, velocity It is clear that to reduce heating we must increase nose ratio along a flat plate is determined by the Blasius radius. Shock waves associated with blunt vehicles are solution of boundary layer problem. detached and spread the heat of re-entry over a relatively Concentration profile is given by large volume. At the surface of blunt vehicles, air flow ηr ɶ2 ɶ tends to inhibit convective heat transfer, which lowers the ∫ exp(−Scηr /4) d η r heating rate for blunt vehicles. Streamlined vehicles have ρi− ρ iw 0 = ∞ attached shock waves due to it temperature becomes very ρi,∞ − ρ i , w 2 Sc →0 exp(−Scη /4) d η high at sharp tip, which is sufficient to melt most of the ∫ r r materials. 0 In laminar field flow, non-dimensional concentration
Mass Transfer profile along flat plate for small Sc is given by Mass transfer can be affected by Brownian in a flowing ξ ρ− ρ 2 2 fluid and surface gradient in temperature arise diffusive i i, w = ∫ e−ξ . d ξɶ ρ− ρ π mass flux. If mass is transported by equimolar diffusion, i,∞ i , w Sc →0 0 then different mixture components are transported into S η two directions across a steady balance surface in space erf c r = with equal rate of moles. Therefore no. of moles in 2 mixture do not change during transport process. Therefore where erf represents error function. mixture concentration is constant on two sides of the surface. In Non-Equimolar diffusion mixture Yadav and Yadav 61 The corresponding Sherwood no. is [5]. S.S Bhat and R.N. Govardhan, “Stall flutter of naca 0012 airfoil at low reynoldnumbers, “ Journal of Fluids and ∂ρ* U x d ρ * Sh =i = ∞ j Structures, May, 2013. Sc →0 y* νd η [6]. B. Sunden et. al , Heat and Mass Transfer, 2014. ∂ y* =0 r ηr =0 [7]. B. Sunden et. al , Heat and Mass Transfer , 2014. U x S [8]. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., Transport = ∞ c Phenomena 2nd edition, Wiley, 2004. ν π [9]. C.P. Kothandaraman, Fundamentals of Heat and Mass It can be further written as Transfer , 2006. Sh= 0.5642 R x Sc 1/.2 [10]. Carslow, H.S., Jaeger, J.C.: Conduction of Heat in Solids , Sc →0 x 2nd edn. Oxford Science Publications, Oxford (2005) The above equation shows how Sherwood number [11]. Clarencol, Johnson, Haggie Smith, Kelly : More than my depends on the Schmidt number. share of it all. Washington, D.C. Smithsoniau Institution, Press, Large Schmidt number means thinner concentration p. 141 ISBN 0874744911, 1985. boundary layer than dynamic boundary layer. At large [12]. D.Y. Shang, Theory of Heat Transfer with Forced Schmidt number (S ), sherwood number is given by Convection Film Flows , Springer Heidelberg, Dordrecht c London, New York, 2011. Sh= 0.3387 R x S 1/ 3 S →0 x c [13]. D’ Ambrosio D., “ A study on shock Wave – Boundary c th This relation shows dependency of Sherwood number on Layer Interactions in High Speed Flows “4 European Symposium on Aerothermodynamics for Space Vehicles, Reynold and Schmidt number. October 2011. Fluid particles may assume surface shapes it different [14]. Davis J.P., Sturtevant, B., “ Separation Length in High - from spherical equations derived for (Nussellt and) Enthalpy Shock/ Boundary Layer Interaction ”, “ Physics of Sherwood numbers of diffusive (heat and) mass transfer Fluids , Vol. 12 , No. 10, 2000. across the surfaces are useful for transport process. [15]. De Filippis F., Caristia S., Del Vecchio A., Purpura C., Results developed by Frössling are useful for correlations “The Scirocco PWT Facility Calibration Activities ”, 3rd of the Nusselt and Sherwood numbers. Correlations international Symposium Atmospheric Re- entry Vechile and comprises of diffusive and corrective part and heat and Systems, Arcachon , France, March, 2003. mass transfer are analogous at low rates of mass transfer. [16]. Dhirendra Kumar Dixit, Heat and Mass Transfer, 2016. [17]. Dhirendra Kumar Dixit, Heat and Mass Transfer , 2016. According to Frössling, Sherwood no. is given by [18]. Di Clemente M., Marini M., Schettino a, “ Shock Wave 1/2 1/3 Sh=2 + 0.552 Re S c Boundary Layer Interactions in SCIROCCO Plasma Wind Constant 2 represents purely diffusive transfer from the Tunnel, East –West High Speed Flows Conference , Pechino, spherical particle oscilltion of gas bubble in liquid exhibit October 2005 [19]. Di Clemente M., MARINI M., Schettino A, “ Shock Wave spheroidal equilibrium shapes. Boundary Layer Interaction in EXPERT Flight Conditions and th II. CONCLUSION Scirocco PWT ” , 13 AIAA/ CIRA International Space planes conference Capua , may 2005. In Aerodynamics, transfer of heat and mass gives insight [20]. E.L Cussler, Diffusion Mass Transfer in Fluid systems, of fluid flow with high speed objects. Blunt shape body 2013. helps to reduce heating and heat sinks, ablation and [21]. Ethirajan Rathakrishan Theoretical Aerodynamics, First radiative cooling can be used for thermal protection. Edition, 2013, John Wiley & Sons Singapor Pvt. Ltd. Minimization of pressure drag coefficient and skin [22]. F. Moukalled et.al, The finite volume method in friction coefficient reduces aerodynamic heating. Rate of computational fluid dynamics, 2016. [23]. Gunter Brenn, Analytical Solution for Transport Process, mass transfer can be evaluated by non-dimensional 2017. Sherwood number. Nature of target and field source are [24]. H.S. Carslow, J.C. Jaeger, Conduction of Heat in Solids, important parameter in impinging jet. 2nd e dn. Oxford Science Publications, Oxford, 2005. REFERENCE [25]. Incropera, F.P., De Witt, D.P., Bergman, T.L., Lavine, A.S.: Principles of Heat and Mass Transfer 7thedn. Wiley, New [1]. A. Bhandarker et. al, A Novel CFD method to estimate heat York (2013). transfer coefficient for high speed flow 2016. [26]. IzzetSachin and Adem Acir, Numerical and experimental [2]. A. Bhandarker et.al, A Novel CFD method to estimate heat investigations of Lift and Drag Performances of NACA 0015 transfer coefficient for high speed flow 2016. Wind Turbine Airfoil, 2015. [3]. A.D. Kraus, A. Aziz, and J.R Welty, Extended Surface Heat [27]. Kurt C. Rolle, Heat and Mass Transfer, 2016. Transfer , John Wiley & sons, New York, NY, USA, 2001 [28]. Labs Bell, 1974, 9-17. [4]. Andrea de Lieto Vollaro et. al, CFD Analysis of Convective [29]. R. Ben, Rich, Leo, Janes, Skunk works: A personal memoir Heat Transfer Coefficient on External Surfaces of Buildings, of my year at lockheedd. Warner Books p. 218. ISBN 2015. 0751515035, 1994.