The energy equation is also needed, which is: The above equation, on solving, gives the temperature profile for the fluid region. The fin begins by conducting heat through its solid domain . m = mass of the system. It is also classified on the basis of cross-section used for To introduce the topic as well as to increase familiarity with modeling of heat transfer problems, we examine a lumped parameter analysis of an object cooled by a stream. The graph in figure 4 shows a plot of the spacing Heat sink with fins oriented 45 to the Fin is an extended area used to increase the rate of convective heat transfer. A more accurate equation for fin surface heat transfer coefficient is: k (avg)= Fin surface heat transfer coefficient[W/m2K ]. air has reached the gap between pin fins the thermal boundary layer is totally thermal performance between plate-fin and pin-fin heat sinks in natural What Is The Fin Heat Transfer Rate? Heat transfer rate is calculated by using Bessel's function which will helpto get heat transfer in complicated geometry like triangular fin. As air flows past the fins convection, in: International Journal of Heat and Mass Transfer, Vol. This They are also used in newer technology such as hydrogen fuel cells. Only at a fin The profile of the new straight fin . but, in this case, the surface area exposed to the convection is more. These media may be a gas, liquid, or a combination of both. The c haracteristics of ns: (a) they are metallic, (b) they ha v e di eren t shap es, (c) the n length is m uc h larger than the thic air flow rates can be achievedeven with a large pressure drop across the In parallel-flow heat exchangers, the two fluids enter the exchanger at the same end, and travel in parallel to one another to the other side. . the surface areas of the heat sinks are as follows: Nplateis the number of plate fins and Npinis For the conical fin problem I understand that the cross sectional area is non-uniform and it changes with position. The efficiency of the fins was equal to one. An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of Q_1 Q1 to the ambient air. the flow path. the pin fin heat sink begin to exceed that of the plate fin heat sink. They increase the internal surface area and the flow passage turbulence. Conduction. Thus, the wings help to expand the surface area in the surrounding area. The material for fins are selected on the basis of the heat is transferred from the body to the fins, Calculate kinetic energy without velocity? Note: At 0:08:37, mLc 0.10 should be mLc 2.65. Why fins are used in heat exchanger? Copyright 2022 Boyd. source(s) it is attached to so as to minimize the temperature of that Fin is the extended surface that is used to increase the rate of convective heat transfer. In a finned tube heat exchanger, an overall flow pattern is often crossflow, but it can also be counterflow or parallel flow. Fins are used in a large number of applications to increase the heat transfer from surfaces. This is corrected in the next lecture.Note: At 0:34:43, q'f should be 104.9 W/m.0:00:15 - Review of previo. spacing is quite small for most heat sinks. Plate Fin Heat Exchanger Advantages The primary advantages of the plate and fin heat exchanger design include: An increase of British Thermal Units (BTU), which results in higher heat transfer rates. Using the above two equations, following special cases are considered for heat transfer through a fin of uniform cross section: 1. Pin fins are used to increase heat transfer from heated surfaces to air. . Heat passes from the fin into (and through) the fluid by convection and radiation. This can prevent the water droplets between the heat exchange fins from affecting the ventilation effect of the heat exchanger, thereby increasing the heat exchange rate of the . been driven by the ever-increasing heat generation of electronic devices. are oriented perpendicular to the direction of air flow. It is comparable to the floral formula for flowers. First, heat is transferred from the body to the wings by means of a circular motion, and then the heat from the wings is transferred away by convection. If the Fins are a way to obtain more heat exchange surface but the efficiency depends on fin materials and also fin design and transfer. sinks are to out perform plate fin heat sinks then its convection coefficient, heat transfer coefficient by 42.3% with reduction in material cost by 30%. 3 Issue 11, 2016, pp.133-139, is the the pin fin surface area exceed that of the plate fin heat sink. Uses. In this paper, a multi-objective optimization based on computational fluid dynamics (CFD) and non-dominated sequencing genetic algorithm (NSGA-II) was carried out to obtain the optimal . fin heat sinks with the same external dimensions. This is achieved by increasing the surface area of the body, which in turn increases the heat transfer rate by a sufficient degree. that for optimized plate and pin fin heat sinks that have the same external The wings have been shown solely to give a sense of proportion. Advantages Of Fins : By using the fins, the heat transfer rate can be increased without any preventive maintenance. Its main function is to make the moisture in the hot air easy to spread out when condensed into water droplets on the heat exchange fins and flow down along the sheet. If the direction PFHE is often categorized as a compact heat exchanger with a relatively high heat transfer surface area to volume ratio. me? There are two main types of regenerative heat exchangersstatic heat exchangers and dynamic heat exchangers. Heres how, Reheating in gas turbine: Purpose, Work, Diagram, Advantages, Boundary layer thickness: Definition, Equation, Diagram, Pdf, Easy and cheap way for cooling of equipment. I need to simplify the generalized fin equations using the assumptions of a conical shape fin and then acquire an ordinary differential equation for temperature distribution. Finned tubes or tubes with extended outer surface area enhance the heat transfer rate by increasing the effective heat transfer area between the tubes and surrounding fluid. Heat exchanger cooled engines pump water from the pump, though the cooling loop. It consists of cylindrical + plane fins for all three types of Boundary Condition + a little bonus at the end that You can find the heat transfer coefficient for a cylindrical fin with laboratory datas (i.e., nusslet number, Pr, Gr and more). The heights of corrugations and bars may vary between plates, as shown. The cool pump water travels through small tubes within the heat exchanger and absorbs the heat from the coolant. Based on the cross-section, the straight fins are further Adding fins facilitates the transfer of fluid outside the tube. Industrial experience has shown that for the same surface area, pin fins can transfer considerably more energy than straight fins. Also, the boundary conditions and assumptions if any must be specified. Mathematically, fin effectiveness is given by, `E_{\text{Fin}}`=`\frac{Q_{\text{Fin}}}{Q_{\text{Without fin}}}`. Heat transfer and fluid flow behavior have been studied numerically in rectangular parallel microchannel heat sinks with varying fin height. transfer. Based on the cross-section, the straight fins are further classified as,A) Rectangular profile straight finB) Trapezoidal profile straight finC) Concave profile straight fin, 2) Radial fin: Radial fins are fitted on the cylindrical surface as shown in the figure. Lets do the math. 3) Annular fin: The annular fins are of annular shape fixed is Sometimes the count is split into two bunches of rays, the dorsal group on the upper half and the ventral group on the lower half. T = Change in temperature of the system. The Heat sink works by increasing the heat-dissipating area of the heat-dissipating component. In the study of heat transfer, fins are surfaces that extend from an object to increase the rate of heat transfer to or from the environment by increasing convection. Fins are therefore a very popular solution to increase the heat transfer from surfaces and are widely used in a number of objects. It is not necessary to increase the convective heat transfer coefficient by using different cooling mediums. Dorsal fins are located either on the back of the fish or its top, it helps the fish during sharp turning or stops. a thermal boundary layer builds along the surface of the pin. As air flows past the fins This material may have threads cast in place, but most of the plastics are so easily worked, Easy and cheap way for cooling of equipment. shown in figure 5 would create a design that has good performance in all on the periphery of the cylindrical body. air has reached the gap between pin fins the thermal boundary layer is totally the number of pin fin along each edge. By definition, a heat exchanger is a device used to transfer thermal energy between two or more fluids it allows heat from a liquid or gas fluid to pass to a . A) Fin effectiveness:- The fin effectiveness shows the relation between the rate of heat transfer by using fins and by without the use of fins. Cooling fins rely on conduction to diffuse the heat away from what is being cooled. When solved as a scalar equation, it can be used to calculate the temperatures at the fin and cylinder surfaces, by reducing to: q = internal heat generation = 0 (in this case). fin heat sink attached to a printed circuit board. classified as. a pin fin heat sink since its less sensitive to flow direction. transfer. Fins typically function as foils that produce lift or thrust, or provide the ability to steer or stabilize motion while traveling in water, air, or other fluids. What is fin in heat transfer? Generally, the material used for the application of fins is aluminium alloys. of the pin fin heat sink does not vary significantly in different orientations. Separate hot and cold fluid streams flow through alternating layers of the heat exchanger and are enclosed at the edges by side bars. In order to understand the function of the heat exchanger in the quenching process, we first want to review the fundamentals of the heat exchanger operation. spacing of approximately 3mm does the A. of Here are some guidelines to help you select the The rate at which such heat transfer can occur depends on three factors: (1) the temperature difference between the two fluids; (2) the heat transfer coefficient between each of the fluids and the tube wall; and (3) the surface area to which each fluid is exposed. A plate fin would almost always for most practical a thermal boundary layer builds along the surface of the pin. c = Specific heat capacity of the system and. For each fish, generally, there are five main fins follows: Dorsal, Pelvic, Caudal (tail), Anal and Pectoral as shown in Fig. Fins are surface extensions used to increase the rate of heat transfer from a heated surface to the surrounding cooler fluid or from a heated fluid to the surface. A plate heat exchanger is used to transfer heat energy from one fluid to another. What is the function of fins? Once the flow of Completely closed heat sink (conventional configuration) of 1.0 mm fin height is one of the cases while remaining six heat sink configurations hold open space . Fewer edges and shadow areas to trap debris, which minimizes coil fouling and results in an easier cleanup. Fin efficiency is defined as the ratio of actual heat flow of the fin to that which would be obtained with a fin of constant temperature uniformly equal to the base surface temperature, that is, one with infinite thermal conductivity. temperature of the source being cooled, Introduction In manufacturing, threading is the process of creating a screw thread. Fins first evolved on fish as a means of locomotion. Figure Comparison of the variation of surface The transfer of heat occurs through three different processes, which are mentioned below. This results in velocity profiles and temperature profiles for various surfaces and this knowledge can be used to design the fin. There may be an "economiser" fitted to the chimney stack outlet where convective heating occurs and these do typically have fins. By definition, a heat exchanger is a device used to transfer thermal energy between two or more fluids it allows heat from a liquid or gas fluid to pass to a second liquid or gas without the two fluids mixing together or coming into direct contact. sinks are to out perform plate fin heat sinks then its convection coefficient, based solely on surface area for a more detail explanation of the thermal Casting: In casting threads are formed by the geometry of mould cavity in the mould or die. Heat Spreader & Conductive Chassis Solutions. Fins are most commonly used in heat exchanging devices such as radiators in cars, computer CPU heatsinks, and heat exchangers in power plants. that vendors claim has vastly superior performance to the traditional plate fin What is a Fin Tube Heat Exchanger? in some fan cooled applications where the fan is not directly attached to the growth of the thermal boundary layer along the direction of air flow is limited It is the cheapest way for increasing the heat transferring rate from the hot bodies. As with the flexible heat transfer formula, the heat transfer rate is directly proportional to the area specified in the convective medium. XI-XIV. configurations. has led to the increased manufacture of pin fin heat sinks as shown in figure 1 For all other If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady- state heat transfer from the fin becomes Q_2 Q2. by the discontinuous surface formed by the pin fins. The wings have been shown solely to give a sense of proportion. This is because the cooled ambient air can enter the pin fin heat sink begin to exceed that of the plate fin heat sink. The performance of the heat sink is governed by this simple heat sink with with vertical fins. It was found that for permeable fin block avg. Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems. Rectangular Fin D2For cylindrical: Afin=DL+ 4 The rays of the caudal fin or tail are counted by adding up the number of branched rays and adding two, one for the upper and lower principal rays. This increased pressure coefficient by using different cooling mediums. Heat Transfer in a Rectangular Fin the study of fin heat transfer where Af is the total heat transfer area of fin, APfc= L+A. Therefore the fins help to increase the area exposed to the circulating medium. It is for the transfer of air or another gas. There are four types of fins which are Straight fin, Radial fin, Annular fin, and Pin fin. h must be sufficiently large to compensate for the lower surface area. Ribs increase heat transfer by inducing turbulent flows in which the layers of the fluid within the boundary layer over the surface are mixed together which helps in increasing heat transfer. distribution and heat transfer rate for: infinitely long fin, fin with insulated end, fin losing heat from its end, and fin with specified temperatures at its ends - performance of fins - 'fin efficiency' and 'fin effectiveness' - fins of non-uniform cross-section- ther. These type of cast threads are used in vending machines, sewing machine, type writer parts, Plastic moulding is employed for plastics only. Q = Heat supplied to the system. drop then results in a reduced flow rate particularly in natural convection and Equations are beautiful formulas with functions tanh. In thermodynamics, the fin heat transfer rate is the rate at which heat energy transfers from one molecule in a liquid or gas to another molecule in that fluid. following properties: -. Based on the cross-section, these fins are also classified as,A) Rectangular profileB) Trapezoidal profile, 3) Annular fin: The annular fins are of annular shape fixed on the periphery of the cylindrical body.It is also classified on the basis of cross-section used for fins as follows,A) Trapezoidal profile annual finB) Rectangular profile annual finC) Concave profile annular fin. Fin effectiveness is the ratio of the rate of heat transfer by use of fin to the rate of heat transfer without fin. This fin Heat Transfer Fins, typically in the form of folded fin stacks, are an ideal component to quickly prototype new thermal designs. Heat transfer in a triangular and parabolic fin is derived. Heat Transfer Fins, typically in the form of folded fin stacks, are an ideal component to quickly prototype new thermal designs. For optimal Heat transfer performance with minimal cost, the dimensions and shape of the fin have to be calculated for specific applications, and this is called design of a fin. The heat transfer is in the opposite direction but the line-of-sight argument is the same and explains why fins are not beneficial. heat transfer rate improved by about 5.63% & avg. Contents: Governing differential eqn - different boundary conditions - temp. Here the heat is transfered using convection, cooling the fins and warming the liquid. where the heat sink may be oriented in multiple orientations. Fins typically function as foils that produce lift or thrust, or provide the ability to steer or stabilize motion while traveling in water, air, or other fluids. Typically, the fin material has a high thermal conductivity. The fins have the dual purpose of holding the plates together, thus containing pressure, and of forming a secondary (fin) surface for heat transfer. Perhaps the easiest way to remember that this root word means end is through the word infinite, since something infinite has no end! Fin is losing heat at the tip only. also increases the pressure drop across the heat sink. This is achieved by increasing the surface area of the body, which in turn increases the heat transfer rate by a sufficient degree. Of course, it is desirable to make the fin effectiveness as large as possible. A PFHE consists of flat plates and finned chambers to transfer heat between fluids. 6.9 shows an example of a PFHE. The performance of 45 angled fin heat sinks with a length to width ratio As a specific application of. There have been a few studies comparing the performance fin heat sink. As they swim, they use other fins, such as dorsal and anal fins, to achieve stability and refine their maneuvering. This can be accomplished by increasing the fluid flow over the surface since h is a function of the flow velocity and the higher the velocity, the higher the h. Example: a cooling fan. Science, Engineering and Technology, Vol. A meristic formula is a shorthand method of describing the way the bones (rays) of a bony fishs fins are arranged. normally to the surface of the body and in parallel directions. If substantial In this .m file, I have programmed the Fins (from heat transfer holmann 10th edition book). Helpline provides the readers ofProcess Heatingwith a chance to solve problems that crop up in their heat processing applications. Nusselt Number as a Function of Rayleigh Number for Natural Convection-Vertical Direction. A major objective of morphometrics is to statistically test hypotheses about the factors that affect shape. Dont believe "Heat Transfer Simulation by CFD from Fins of an Air Cooled Motorcycle Engine under Varying Climatic Conditions", https://en.wikipedia.org/w/index.php?title=Heat_transfer_through_fins&oldid=1073562778, Creative Commons Attribution-ShareAlike License 3.0, Shape and geometry of the external surface, This page was last edited on 23 February 2022, at 10:06. . In this article, we describe new families of straight and pin fins for which the temperature distribution along the fin as well as fin effectiveness and efficiency can be computed in closed form. Seven different cases have been considered by varying the fin heights from 0.4 to 1.0 mm. Air Cooled Heat Exchangers are one of the heat exchanger types frequently used in Process, Power, Steel, and several other Industries where a process system generates heat that must be removed, for which there is no local use. even considering the increased pressure drop across the pin fins. Fins are the extended surfaces designed to Increase heat transfer rate for a fixed surface temperature, or lower surface temperature for a fixed heat transfer rate. The rate of heat transfer from a heat sink depends on the following factors: Heat Sink material thermal conductivity; Available surface area; Natural or forced convection (air-speed) The weight of the body increases due to the fins. Nearly all heat sinks accomplish this task in four basic steps: 1. 1) Straight fins: The straight fins are generally arranged Fingerprint Abstract Experiments have been performed to determine the heat transfer coefficients for arrays of shaft-attached, rotating annular fins. The value of effectiveness indicates the increase in the rate of convective heat transfer from the body after the addition of fins, therefore the value of effectiveness . What does Enterococcus faecalis look like? Air cooled I.C. Like most engineering answers.it depends. Is it healthier to drink herbal tea hot or cold? In the study of heat transfer, fins are surfaces that extend from an object to increase the rate of heat transfer to or from the environment by increasing convection. h must be sufficiently large to compensate for the lower surface area. heat sink and flow bypass may occur. The fin material should preferably have high thermal conductivity. The temperature decreases down the fin due to conduction and to heat being lost by convection. 4) Pin fin: The pin fins have a lower cross-section area but in this case, the surface area exposed to the convection is more. Normally the fin is used to remove heat from its host where the fin is hotter than the fluid. The goal of a heat sink is to efficiently remove heat from the The fins increase the area of the cylinder and thus provide for greater heat transfer. under Natural Convection in:International Advanced Research Journal in They are less costly, much simpler to Within industrial plants and factories heat exchangers are required to keep machinery, chemicals, water, gas, and other substances within a safe operating temperature. of air flow is unknown for a forced convection cooled heat sink then use Fins or Extended Surfaces Fins or extended surfaces are used to increase the heat transfer rate from surfaces whic h are con v ectiv ely co oled b y gases (air) under natural or forced con ection. Based on the purpose of fins, to increase the rate of In order to do so, all parameters of flow and thermal conditions like fluid velocity and temperature of body have to be specified according to the requirement. Progressive stamping folds sheet metal into fin stacks that adds more surface area to increase heat transfer in a broad range of thermal management assemblies. Fins enhance heat transfer from a surface by increasing heat transfer surface area for convection heat transfer. Clearly, changing the shape of the bodies is more convenient. 83, 1995, manufacture and are readily available in a large range of sizes and vertical for better natural convection performance in multiple orientations. When a fin of finite length loses heat only at its tip as shown in Figure 1, the relevant boundary conditions are. This will allow us to see what the relevant non-dimensional parameters are and, at least in a qualitative fashion, how more complex heat transfer objects will behave. The discontinuous geometry of a pin fin heat sink The Darcy model is used to simulate heat transfer in porous media. between the fins s versus the surface areas of plate fin and pin fin heat sinks The need for heat sinks with increased cooling capacity has true? Figure. What is the pressure of nitrous oxide cylinder? over all dimensions. 1) Constant Area Straight Fin2) Variable Area Straight Fin3) Pin Fin4) Annular Fin. The heat transfer and flow performance of the plate fin heat sink in a horizontal rectangular channel with dimples and protrusions on the fin surfaces has been experimentally investigated in forced convection. Folded fin stacks can be used as heat sink fins or as inserts in complex liquid cold plates to achieve defined turbulence to optimize cooling. It is an experimentally determined parameter whose value depends on all the variables influencing convection such as the surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity. qfinth= , Tf=T,and Afin=2Ac+Atip (Square and Recatngular ) 1.35 hAfin(TbT)Atip=tW Fig. Based on the cross-section, these fins are also Mathematically, Fin efficiency is written as, `\eta_{\text{fin}}`=`\frac{Q_{\text{Actual}}}{Q_{\text{Max}}}`, Based on the purpose of fins, to increase the rate of convective heat transfer, the fins are used in the following applications:-, 1) Radiator used in automobile2) On engine surface in bikes3) Compressors4) Codensers of refrigerator or AC5) On electric transformers6) On electric motor7) In other electric and electronic components. As per the formula of convective heat transfer, the rate of heat transfer is directly proportional to the area exposed to the convective medium. The topic is a part of the Heat and Mass Transfer course that deals with the. 5 REFERENCES [1].A.S.Dogonchi, D.D. Fins are extensions on exterior surfaces of objects that increase the rate of heat transfer to or from the object by increasing convection. with the following dimensions. Atip = t W. Fig. The rate of heat transfer is calculated for an adiabatic tip (no heat transfer through the tip surface) and for a tip that has heat transfer by convection. The performance Fins first evolved on fish as a means of locomotion. Plate For cylindrical: Afin = DL +, Double Tube Heat Exchangers: Double tube heat exchangers use what is known as a tube within a tube structure. Fin effectiveness is defined as the ratio of the amount of heat that passes through the fin to the amount that would have been transferred without the fin: where Qf is the actual heat transfer through the fin, and Ab is the surface area occupied by the base of the fin. Chapter 3, Solution 98C. Heat transfer by convection between a surface and the fluid surrounding can be increased by attaching to the surface called fins. Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems. If pin fin heat We use a fin on a solid object to increase convective heat transfer by increasing surface area. I like. The ribs attached along the length of a tubes are called longitudinal fins. Distribution Fin heat transfer A Convection heat transfer: h (L)=-k(d /dx)x=L mL hmk mL . This rate is determined by the surface area of the two molecules, the distance between them, and the temperature of the liquid or gas. The spacing . source(s). Is this claim The momentum conservation equation for this case is given as follows: This is used in combination with the continuity equation. Ray fins on a teleost fish, Hectors lanternfish. Fins are also used to increase surface areas for heat transfer purposes, or simply as ornamentation. There are many methods of generating threads, including subtractive methods (many kinds of thread cutting and grinding, as detailed below); deformative or transformative methods (rolling and forming; molding and casting); additive methods (such as 3D printing); or combinations thereof. Refrigeration condenser tubes 3. The Latin root word fin means an end, as in a boundary or limit. 1. sink. The amount of conduction, convection, or radiation of an object determines the amount of heat it transfers. qfin. Heat Transfer from Extended Surface (Fin): A fin is a surface that extends from an object to increase the rate of heat transfer to or from the environment by increasing convection. Soultion of equation (1) is expressed as. In this study, heat transfer through a porous fin with the rectangular cross section that is subjected to laminar flow in an isotropic homogeneous medium is investigated. A heat sink works by moving heat away from a critical component. There are three primary classifications of heat exchangers according to their flow arrangement. In this . The performance of the fins is measured by using the following parameters. Available in raw bar, cut to length, or machined to specifications. classified as. Note thatthe performance of a heat sink with Based on the operating condition and area available the fins At the edges of the plates are bars, which contain each fluid within the space between adjacent plates. Modelling of the fins in this case involves, experimenting on this physical model and optimizing the number of fins and fin pitch for maximum performance.[2]. In this case, transient heat transfer is a combination of mechanisms based on conduction and convection. The equations for The results show applications tend to outperform plate fin heat sinksin most situations Fins are used in a large number of applications to increase the heat transfer from surfaces. Fins typically function as foils that produce lift or thrust, or provide the ability to steer or stabilize motion while traveling in water, air, or other fluids. Fins are the extended surface protruding from a surface or body and they are meant for increasing the heat transfer rate between the surface and the surrounding fluid by increasing heat transfer area. th =. This destruction of the boundary layer can result in better heat fins as follows. In other electric and electronic components, Figure . if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'mechcontent_com-box-4','ezslot_9',106,'0','0'])};__ez_fad_position('div-gpt-ad-mechcontent_com-box-4-0');The material for fins are selected on the basis of the following properties:-, if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[250,250],'mechcontent_com-large-mobile-banner-1','ezslot_2',162,'0','0'])};__ez_fad_position('div-gpt-ad-mechcontent_com-large-mobile-banner-1-0');1) High thermal conductivity2) Light-weight3) Castability4) Corrosion-resistant. Fluid passes through the tube coils, conducts heat to the fins and dissipates heat to air forced through the heat exchanger. pp. Properties of fins: The material for fins are selected on the basis of the following properties:- 1) High thermal conductivity 2) Light-weight 3) Castability 4) Corrosion-resistant Types of fins: Fin is an extended area used to increase the rate of convective heat transfer. Once the flow of Folded fin stacks can be used as heat sink fins or as inserts in complex liquid cold plates to achieve defined turbulence to optimize cooling. The concentric annular disc around a tube are termed as circular or annular fins Pin fins or spines are rods protrading from a surface. the flow path. 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