Heat exchanger design KERN METHOD

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Presentation transcript:

Heat exchanger design KERN METHOD By: Dr. M.R.Shahnazari K.N.Toosi university of technology Heat exchanger design KERN METHOD HEAT EXCANGER DESIGN Lecturer: Dr M.R. Shahnazari K.N.Toosi university of Technology

By: Dr. M.R.Shahnazari

By: Dr. M.R.Shahnazari DOUBLE PIPE HE

By: Dr. M.R.Shahnazari DP EXAMPLE Solution

By: Dr. M.R.Shahnazari DP EXAMPLE…..Solution

By: Dr. M.R.Shahnazari DP EXAMPLE…..Solution

By: Dr. M.R.Shahnazari DP EXAMPLE…..Solution

By: Dr. M.R.Shahnazari SHELL AND TUBE Kern method

Classification of heat exchangers depending on the applications Recuperative Regenerative Rotary regenerator Fixed-matrix regenerator Indirect contact-type Direct Disk type Drum type Tubular Plate Extended surface Double pipe Spiral tube Shell & tube Finned tube Finned plate Gasketed plate Spiral plate Lamella Removable bundle Floating head Fixed tubesheet U-tube Heat Exchanger Heat exchanger may have singe or two phase flow on each side Flow Parallel Counter Cross

LMTD CORRECTION FACTOR By: Dr. M.R.Shahnazari LMTD CORRECTION FACTOR

SAMPLE CORRECTION FACTOR By: Dr. M.R.Shahnazari SAMPLE CORRECTION FACTOR one shell pass; two or more even

TUBE SIZE: : Birmingham Wire Gage By: Dr. M.R.Shahnazari TUBE SIZE: : Birmingham Wire Gage

By: Dr. M.R.Shahnazari TUBE PATTERN

By: Dr. M.R.Shahnazari TUBE PITCH

Why a Shell and Tube Heat Exchanger? By: Dr. M.R.Shahnazari Why a Shell and Tube Heat Exchanger? Shell and tube heat exchangers are the most widespread and commonly used basic heat exchanger configuration in the process industries. The reasons for this general acceptance are several. The shell and tube heat exchanger provides a comparatively large ratio of heat transfer area to volume and weight. It provides this surface in a form which is relatively easy to construct in a wide range of sizes.

By: Dr. M.R.Shahnazari Better Concurrence…. It is mechanically rugged enough to withstand normal shop fabrication stresses, shipping and field erection stresses, and normal operating conditions. The shell and tube exchanger can be reasonably easily cleaned, and those components most subject to failure - gaskets and tubes – can be easily replaced. Shop facilities for the successful design and construction of shell and tube exchangers are available throughout the world.

Simple Shell & Tube Heat Exchanger By: Dr. M.R.Shahnazari Simple Shell & Tube Heat Exchanger

By: Dr. M.R.Shahnazari Inner Details of S&T HX

Components of STHEs By: Dr. M.R.Shahnazari It is essential for the designer to have a good working knowledge of the mechanical features of STHEs and how they influence thermal design. The principal components of an STHE are: shell; shell cover; tubes; tubesheet; baffles; and nozzles. Other components include tie-rods and spacers, pass partition plates, impingement plate, longitudinal baffle, sealing strips, supports, and foundation.

Types of Shells By: Dr. M.R.Shahnazari

By: Dr. M.R.Shahnazari Fixed tube sheet

By: Dr. M.R.Shahnazari U-Tube STHE

Floating Head STHE TEMA S By: Dr. M.R.Shahnazari Floating Head STHE TEMA S

Floating Head STHE TEMA T By: Dr. M.R.Shahnazari Floating Head STHE TEMA T

Cross Baffles Baffles serve two purposes: By: Dr. M.R.Shahnazari Baffles serve two purposes: Divert (direct) the flow across the bundle to obtain a higher heat transfer coefficient. Support the tubes for structural rigidity, preventing tube vibration and sagging. When the tube bundle employs baffles, the heat transfer coefficient is higher than the coefficient for undisturbed flow around tubes without baffles. For a baffled heat exchanger the higher heat transfer coefficients result from the increased turbulence. the velocity of fluid fluctuates because of the constricted area between adjacent tubes across the bundle.

Types of Baffle Plates : Segmental Cut Baffles By: Dr. M.R.Shahnazari Types of Baffle Plates : Segmental Cut Baffles The single and double segmental baffles are most frequently used. They divert the flow most effectively across the tubes. The baffle spacing must be chosen with care. Optimal baffle spacing is somewhere between 40% - 60% of the shell diameter. Baffle cut of 25%-35% is usually recommended.

Types of Baffle Plates Double Segmental Baffles By: Dr. M.R.Shahnazari Double Segmental Baffles Triple Segmental Baffles The triple segmental baffles are used for low pressure applications.

By: Dr. M.R.Shahnazari Types of Baffle Plates

Types of Baffle Plates By: Dr. M.R.Shahnazari Disc and ring baffles are composed of alternating outer rings and inner discs, which direct the flow radially across the tube field. § The potential bundle-to-shell bypass stream is eliminated § This baffle type is very effective in pressure drop to heat transfer conversion

Therm-Hydraulic Analysis of Heat Exchanger By: Dr. M.R.Shahnazari Therm-Hydraulic Analysis of Heat Exchanger Initial Decisions. Tube side Thermal Analysis. Thermal analysis for Shell side. Overall Heat Transfer coefficient. Hydraulic Analysis of Tube side. Hydraulic Analysis of Shell side.

Fluid Allocation : Tube Side By: Dr. M.R.Shahnazari Tube side is preferred under these circumstances: The higher velocities will reduce buildup Mechanical cleaning is also much more practical for tubes than for shells. Corrosive fluids are usually best in tubes Tubes are cheaper to fabricate from exotic materials This is also true for very high temperature fluids requiring alloy construction Toxic fluids to increase containment Streams with low flow rates to obtain increased velocities and turbulence High pressure streams since tubes are less expensive to build strong. Streams with a low allowable pressure drop

Fluid Allocation : Shell Side By: Dr. M.R.Shahnazari Fluid Allocation : Shell Side Shell side is preferred under these circumstances: Viscous fluids go on the shell side, since this will usually improve the rate of heat transfer. On the other hand, placing them on the tube side will usually lead to lower pressure drops. Judgment is needed. Low heat transfer coefficient: Stream which has an inherently low heat transfer coefficient (such as low pressure gases or viscous liquids), this stream is preferentially put on the shell-side so that extended surface may be used to reduce the total cost of the heat exchanger.

General design consideration By: Dr. M.R.Shahnazari General design consideration Factor Tube-side Shell-side Corrosion More corrosive fluid Less corrosive fluids Fouling Fluids with high fouling and scaling Low fouling and scaling Fluid temperature High temperature Low temperature Operating pressure Fluids with low pressure drop Fluids with high pressure drop Viscosity Less viscous fluid More viscous fluid Stream flow rate High flow rate Low flow rate

Flow Past Tube Bundles : Outside Film Coefficient By: Dr. M.R.Shahnazari Flow Past Tube Bundles : Outside Film Coefficient

Major Steps in Design Initial Decisions. Tube side Thermal Analysis. By: Dr. M.R.Shahnazari Major Steps in Design Initial Decisions. Tube side Thermal Analysis. Thermal analysis for Shell side flow. Overall Heat Transfer coefficient. Hydraulic Analysis of Tube side. Hydraulic Analysis of Shell side.

Initial Decisions Spatial allocation of fluid. By: Dr. M.R.Shahnazari Initial Decisions Spatial allocation of fluid. Determination of flow velocity. Initial guess for number of tubes. Correction for standard tube diameter. Effect of number of tubes on tube length….

By: Dr. M.R.Shahnazari Avoid Developed Flow

Thermal Analysis of Heat Exchanger By: Dr. M.R.Shahnazari Thermal Analysis of Heat Exchanger Known as heat exchanger specification problems and their solutions. These are ‘rating’, ‘design’, and ‘selection’.

By: Dr. M.R.Shahnazari Rating Analysis The rating problem is evaluating the thermo-hydraulic performance of a fully specified exchanger. The rating program determines: the heat transfer rate and the fluid outlet temperatures for prescribed fluid flow rates, inlet temperatures, and the pressure drop for an existing heat exchanger; therefore the heat transfer surface area and the flow passage dimensions are available.

By: Dr. M.R.Shahnazari The Rating Analysis

The Design (Sizing) Analysis By: Dr. M.R.Shahnazari ‘Design’ is the process of determining all essential constructional dimensions of an exchanger that must perform a given heat duty and respect limitations on shell-side and tube-side pressure drop. In the Design (sizing) Analysis, An appropriate heat exchanger type is selected. The size to meet the specified hot and cold fluid inlet and outlet temperatures, flow rates, and pressure drop requirements, is determined. Constraints: Minimum or maximum flow velocities, Size and/or weight limitations, Ease of cleaning and maintenance, erosion, tube vibration, and thermal expansion. Each design problem has a number of potential solutions, but only one will have the best combination of characteristics and cost.

Basic Design Procedure By: Dr. M.R.Shahnazari Basic Design Procedure K.N.Toosi university of Technology

Basic Design Procedure By: Dr. M.R.Shahnazari Basic Design Procedure Heat exchanger must satisfy the Heat transfer requirements (design or process needs) Allowable pressure drop (pumping capacity and cost) Steps in designing a heat exchanger can be listed as: Identify the problem Select an heat exchanger type Calculate/Select initial design parameters Rate the initial design Calculate thermal performance and pressure drops for shell and tube side. Evaluate the design. Is performance and cost acceptable?

The Selection Analysis By: Dr. M.R.Shahnazari The Selection Analysis ‘Selection’ means choosing a heat exchanger from among a number of units already existing. Typically, these are standard units listed in catalogs of various manufacturers. Sufficient manufacturer’s data usually exist to allow one to select comfortably oversized exchanger with respect to both area and pressure drop.

Thermal Analysis for Shell-Side By: Dr. M.R.Shahnazari Thermal Analysis for Shell-Side Conventional Methods are based on Non-dimensional Analysis… Convection Heat Transfer demands Definition of Nusselt Number – Output Reynolds Number – Input Prandtl Number -- Input

Shell Side Fluid Flow By: Dr. M.R.Shahnazari

Shell-Side Reynolds Number By: Dr. M.R.Shahnazari Shell-Side Reynolds Number Reynolds number for the shell-side is defined based on the equivalent diameter and the velocity based on a reference flow:

Simplified Classification of Shell Side Flow By: Dr. M.R.Shahnazari

Fluid dynamic Similarity of Counter & Cross Flow Heat Transfer ?!?!?! By: Dr. M.R.Shahnazari

Tube Layout & Flow Structure By: Dr. M.R.Shahnazari A Real Use of Wetted Perimeter !

Tube Layout By: Dr. M.R.Shahnazari Tube layout is characterized by the included angle between tubes. Two standard types of tube layouts are the square and the equilateral triangle. Triangular pitch (30o layout) is better for heat transfer and surface area per unit length (greatest tube density.) Square pitch (45 & 90 layouts) is needed for mechanical cleaning. Note that the 30°,45° and 60° are staggered, and 90° is in line. For the identical tube pitch and flow rates, the tube layouts in decreasing order of shell-side heat transfer coefficient and pressure drop are: 30°,45°,60°, 90°. The 90° layout will have the lowest heat transfer coefficient and the lowest pressure drop.

In that case, a minimum cleaning lane of ¼ in. (6.35 mm) is provided. By: Dr. M.R.Shahnazari The square pitch (90° or 45°) is used when jet or mechanical cleaning is necessary on the shell side. In that case, a minimum cleaning lane of ¼ in. (6.35 mm) is provided. The square pitch is generally not used in the fixed header sheet design because cleaning is not feasible. The triangular pitch provides a more compact arrangement, usually resulting in smaller shell, and the strongest header sheet for a specified shell-side flow area. It is preferred when the operating pressure difference between the two fluids is large.

Tube Pitch The selection of tube pitch is a compromise between a By: Dr. M.R.Shahnazari Tube Pitch The selection of tube pitch is a compromise between a Close pitch (small values of PT/do) for increased shell-side heat transfer and surface compactness, and an Open pitch (large values of PT/ do) for decreased shell-side plugging and ease in shell-side cleaning. Tube pitch Pt is chosen so that the pitch ratio is 1.25 < PT/do < 1.5. When the tubes are to close to each other (PT/do less than 1.25), the header plate (tube sheet) becomes to weak for proper rolling of the tubes and cause leaky joints. Tube layout and tube locations are standardized for industrial heat exchangers. However, these are general rules of thumb and can be “violated” for custom heat exchanger designs.

Identification of (Pseudo) Velocity Scale By: Dr. M.R.Shahnazari Identification of (Pseudo) Velocity Scale

Shell Side Pseudo Flow Area By: Dr. M.R.Shahnazari The number of tubes at the centerline of the shell is calculated by where is Asthe bundle cross flow area, Dsis the inner diameter of the shell, C is the clearance between adjacent tubes, and B is the baffle spacing

Pseudo Shell side Mass Velocity By: Dr. M.R.Shahnazari Pseudo Shell side Mass Velocity The shell-side mass velocity is found with

Selection of Shell Diameter By: Dr. M.R.Shahnazari

By: Dr. M.R.Shahnazari Shell Diameter The number of tubes is calculated by taking the shell circle and dividing it by the projected area of the tube layout. That is where Apro-tube is the projected area of the tube layout expressed as area corresponding to one tube, Ds is the shell inside diameter, and CTP is the tube count calculation constant that accounts for the incomplete coverage of the shell diameter by the tubes, due to necessary clearances between the shell and the outer tube circle and tube omissions due to tube pass lanes for multitude pass design.

Projected area of Tube Layout By: Dr. M.R.Shahnazari Projected area of Tube Layout Where PT is the tube pitch and CL is the tube layout constant.

Coverage of Shell Area By: Dr. M.R.Shahnazari

The CTP values for different tube passes are given below: By: Dr. M.R.Shahnazari The CTP values for different tube passes are given below:

Pseudo Shell side Mass Velocity By: Dr. M.R.Shahnazari Pseudo Shell side Mass Velocity The shell-side mass velocity is found with

Shell side Equivalent (Hydraulic) Diameter By: Dr. M.R.Shahnazari Shell side Equivalent (Hydraulic) Diameter Equivalent diameter employed by Kern for correlating shell side heat transfer/flow is not a true equivalent diameter. The direction of shell side flow is partly along the tube length and partly at right angles to tube length or heat exchanger axis. The flow area at right angles is harmonically varying. This cannot be distinguished based on tube layout. Kern’s experimental study showed that flow area along the axis showed excellent correlation wrt Tube layout, tube pitch etc….

Equivalent Counter Flow : Hydraulic or Equivalent Diameter By: Dr. M.R.Shahnazari Equivalent Counter Flow : Hydraulic or Equivalent Diameter The equivalent diameter is calculated along (instead of across) the long axes of the shell and therefore is taken as four times the net flow area as layout on the tube sheet (for any pitch layout) divided by the wetted perimeter.

Process (thermal) design procedure of Heat Exchanger [Kern method ]  

 

 

If the tube-side pressure drop exceeds the allowable pressure drop for the process system, decrease the number of tube passes or increase number of tubes per pass. Go back to step #6 and repeat the calculations steps.   If the shell-side pressure drop exceeds the allowable pressure drop, go back to step #7 and repeat the calculations steps. Step #15. Upon fulfillment of pressure drop criteria, go mechanical design.

Selection of Fluids for Tube and Shell Side Routing of the shell side and tube side fluids has considerable effects on the heat exchanger design. Some general guidelines for positioning the fluids are given in Table These guidelines are not ironclad rules and the optimal fluid placement depends on many factors that are service specific Tube-side fluid Shell-side fluid Corrosive fluid Condensing vapor (unless corrosive) Cooling water Fluid with large temperature difference (>40°C) Fouling fluid   Less viscous fluid High-pressure steam Hotter fluid

Effect of Temperature Differences on Design of Shell and Tube Heat Exchanger Countercurrent flow Cocurrent flow Cross Approach   1-1 exchanger flow 1-2 exchanger flow

Pseudo Shell side Mass Velocity: Perpendicular Flow By: Dr. M.R.Shahnazari Pseudo Shell side Mass Velocity: Perpendicular Flow The shell-side mass velocity is found with

Hydraulic or Equivalent Diameter : Axial Flow By: Dr. M.R.Shahnazari Hydraulic or Equivalent Diameter : Axial Flow A Hydraulic radius based on cross flow cannot recognize the importance of tube layout. The equivalent diameter is calculated along (instead of across) the long axes of the shell and therefore is taken as four times the net flow area as layout on the tube sheet (for any pitch layout) divided by the wetted perimeter.

Free Flow Area for Square Layout: By: Dr. M.R.Shahnazari Free Flow Area for Square Layout: Free Flow Area for Triangular Layout:

Perimeter for square Layout: By: Dr. M.R.Shahnazari Perimeter for square Layout: Perimeter for triangular Layout: Equivalent diameter for square layout: Equivalent diameter for Triangular layout:

Shell-Side Reynolds Number By: Dr. M.R.Shahnazari Reynolds number for the shell-side is based on the equivalent diameter (based on axial flow) and the velocity on the cross flow area at the diameter of the shell:

Correlation for Shell side Heat Transfer Coefficient By: Dr. M.R.Shahnazari Correlation for Shell side Heat Transfer Coefficient

Overall Heat Transfer Coefficient for the Heat Exchanger By: Dr. M.R.Shahnazari Overall Heat Transfer Coefficient for the Heat Exchanger The overall heat transfer coefficient for clean surface (Uc) is given by Considering the total fouling resistance, the heat transfer coefficient for fouled surface (Uf) can be calculated from the following expression:

Outlet Temperature Calculation and Length of the Heat Exchanger By: Dr. M.R.Shahnazari Outlet Temperature Calculation and Length of the Heat Exchanger The outlet temperature for the fluid flowing through the tube is The surface area of the heat exchanger for the fouled condition is :

and for the clean condition By: Dr. M.R.Shahnazari and for the clean condition where the LMTD is always for the counter flow. The over surface design (OS) can be calculated from :

The length of the heat exchanger is calculated by By: Dr. M.R.Shahnazari The length of the heat exchanger is calculated by

Hydraulic Analysis for Tube-Side By: Dr. M.R.Shahnazari Hydraulic Analysis for Tube-Side The pressure drop encountered by the fluid making Np passes through the heat exchanger is a multiple of the kinetic energy of the flow. Therefore, the tube-side pressure drop is calculated by The second term in above equation is the additional pressure drop introduced by the change of direction in the passes. The tube fluid experiences sudden expansions and contractions during a return that is accounted for allowing four velocity heads per pass.

Hydraulic Analysis for Shell-Side By: Dr. M.R.Shahnazari Hydraulic Analysis for Shell-Side The shell-side fluid experiences a pressure drop as it passes through the exchanger, over the tubes, and around the baffles. If the shell fluid nozzles (inlet and outlet ports) are on the same side of the heat exchanger, then the shell-side fluid makes an even number of the tube bundle crossings, but if they are on opposite sides, then it makes an odd number of the bundle crossings. The number of bundle crossings therefore influences the pressure drop.

By: Dr. M.R.Shahnazari Based on experiments, the pressure drop experienced by the shell-side fluid is calculated by Where,

The wall temperature can be calculated as follows: By: Dr. M.R.Shahnazari μb is the viscosity of the shell-side fluid at bulk temperature, and μw is the viscosity of the tube-side fluid at wall temperature. The wall temperature can be calculated as follows: OR:

Evaluation & Fine tuning of Design By: Dr. M.R.Shahnazari Evaluation & Fine tuning of Design Insufficient Thermal Rating Insufficient Pressure Drop Rating

Insufficient Thermal Rating By: Dr. M.R.Shahnazari Insufficient Thermal Rating If the output of the rating analysis is not acceptable, a geometrical modification should be made If the required amount of heat cannot be transferred to satisfy specific outlet temperature, one should find a way to increase the heat transfer coefficient or increase exchanger surface area One can increase the tube side heat transfer coefficient by increasing the fluid velocity - Increase number of tube passes One can increase the shell side heat transfer coefficient by decreasing baffle spacing and/or baffle cut One can increase the surface area by Increasing the heat exchanger length Increasing the shell diameter Multiple shells in series

Insufficient Pressure Drop Rating By: Dr. M.R.Shahnazari Insufficient Pressure Drop Rating If the pressure drop on the tube side is greater than the allowable pressure drop, then the number of tube passes can be decreased or the tube diameter can be increased which may result to decrease the tube length – (Same surface area) increase the shell diameter and the number of tubes If the shell side pressure drop is greater than the allowable pressure drop then baffle spacing, tube pitch, and baffle cut can be increased or one can change the baffle type. THERE IS ALWAYS A TRADE-OFF BETWEEN THERMAL & PRESSURE DROP RATINGS!

The Trade-Off Between Thermal Balance & Flow Loss By: Dr. M.R.Shahnazari The Trade-Off Between Thermal Balance & Flow Loss Heat transfer and fluid friction losses tend to compete with one another. The total energy loss can be minimized by adjusting the size of one irreversibility against the other . These adjustments can be made by properly selecting physical dimensions of the solid parts (fins, ducts, heat exchanger surface). It must be understood, however, that the result is at best a thermodynamic optimum. Constraints such as cost, size, and reliability enter into the determination of truly optimal designs.

Roadmap To Increase Heat Transfer By: Dr. M.R.Shahnazari Increase heat transfer coefficent Tube Side Increase number of tubes Decrease tube outside diameter Shell Side Decrease the baffle spacing Decrease baffle cut Increase surface area Increase tube length Increase shell diameter à increased number of tubes Employ multiple shells in series or parallel Increase LMTD correction factor and heat exchanger effectiveness Use counterflow configuration Use multiple shell configuration

Roadmap To Reduce Pressure Drop By: Dr. M.R.Shahnazari Roadmap To Reduce Pressure Drop Tube side Decrease number of tube passes Increase tube diameter Decrease tube length and increase shell diameter and number of tubes Shell side Increase the baffle cut Increase the baffle spacing Increase tube pitch Use double or triple segmental baffles

By: Dr. M.R.Shahnazari Kern’s Method

By: Dr. M.R.Shahnazari SHELL SIDE CROSSFLOW

By: Dr. M.R.Shahnazari KERN METHOD

By: Dr. M.R.Shahnazari KERN METHOD…con.

By: Dr. M.R.Shahnazari KERN METHOD…con.

By: Dr. M.R.Shahnazari KERN METHOD…con.

Fluid Allocation: Shell or Tubes? Corrosion Fouling Fluid temperatures Operating pressures Pressure drop Viscosity Stream flow rates

Shell and Tube Fluid Velocities High velocities give high heat-transfer coefficients but also high pressure drop. Velocity must be high enough to prevent settling of solids, but not so high as to cause erosion. High velocities will reduce fouling For liquids, the velocities should be as follows: Tube side: Process liquid 1-2m/s Maximum 4m/s if required to reduce fouling Water 1.5 – 2.5 m/s Shell side: 0.3 – 1 m/s

Pressure Drop As the process fluids move through the heat exchanger there is associated pressure drop. For liquids: viscosity < 1mNs/m2 35kN/m2 Viscosity 1 – 10 mNs/m2 50-70kN/m2

Tube-side Heat Transfer Coefficient For turbulent flow inside conduits of uniform cross-section, Sieder-Tate equation is applicable: C=0.021 for gases =0.023 for low viscosity liquids =0.027 for viscous liquids μ= fluid viscosity at bulk fluid temperature μw=fluid viscosity at the wall

Tube-side Heat Transfer Coefficient Butterworth equation: For laminar flow (Re<2000): If Nu given by above equation is less than 3.5, it should be taken as 3.5

Heat Transfer Factor, jh “j” factor similar to friction factor used for pressure drop: This equation is valid for both laminar and turbulent flows.

Tube Side Heat Transfer Factor

Heat Transfer Coefficients for Water Many equations for hi have developed specifically for water. One such equation is: where hi is the inside coefficient (W/m2 0C) t is the water temperature (0C) ut is water velocity (m/s) dt is tube inside diameter (mm)

Tube-side Pressure Drop where ΔP is tube-side pressure drop (N/m2) Np is number of tube-side passes ut is tube-side velocity (m/s) L is the length of one tube m is 0.25 for laminar and 0.14 for turbulent jf is dimensionless friction factor for heat exchanger tubes

Tube Side Friction Factor

Shell-side Heat Transfer and Pressure Drop Kern’s method

Procedure for Kern’s Method Calculate area for cross-flow As for the hypothetical row of tubes in the shell equator. pt is the tube pitch d0 is the tube outside diameter Ds is the shell inside diameter lB is the baffle spacing, m. Calculate shell-side mass velocity Gs and linear velocity, us. where Ws is the fluid mass flow rate in the shell in kg/s

Procedure for Kern’s Method Calculate the shell side equivalent diameter (hydraulic diameter). For a square pitch arrangement: For a triangular pitch arrangement

Shell-side Reynolds Number The shell-side Reynolds number is given by: The coefficient hs is given by: where jh is given by the following chart

Shell Side Heat Transfer Factor

Shell-side Pressure Drop The shell-side pressure drop is given by: where jf is the friction factor given by following chart.

Shell Side Friction Factor

(Figure 8 in notes)

(Table 3 in notes) (Figure 10 in notes)

(Figure 12 in notes)

By: Dr. M.R.Shahnazari KERN METHOD…con.

By: Dr. M.R.Shahnazari KERN METHOD…example

By: Dr. M.R.Shahnazari KERN METHOD…example

By: Dr. M.R.Shahnazari KERN METHOD…example

By: Dr. M.R.Shahnazari KERN METHOD…example

By: Dr. M.R.Shahnazari KERN METHOD…example

By: Dr. M.R.Shahnazari KERN METHOD…example