Professor! For what purposes is CFD analysis of heat exchangers performed? Are manual calculation methods like the NTU or LMTD methods insufficient?

Manual calculation methods (LMTD, ε-NTU) are effective for estimating overall performance. However, local phenomena such as maldistribution in tube bundles, dead zones around baffles, and non-uniform temperature distributions cannot be evaluated without CFD.

Could you explain the fundamental equations for heat exchanger CFD?

It involves solving for flow and heat transfer in a coupled manner. The core equations are the Navier-Stokes equations plus the energy equation. $$ \rho c_p \left(\frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T\right) = \nabla \cdot (k \nabla T) + \Phi $$

What are the key points to pay attention to in heat exchanger CFD?

Temperature dependence of fluid properties (viscosity is significantly affected by temperature). Wall heat transfer and conjugate heat transfer between fluid and solid. Modeling of leakage gaps in baffles (the clearance between tubes and baffle holes). Inlet effects in tube bundles (higher heat transfer coefficients in the first few rows).

Heat Exchanger CFD Analysis

Category: 流体解析（CFD） | Integrated 2026-04-06

CAE visualization for heat exchanger cfd theory - technical simulation diagram

熱交換器のCFD解析

Theory and Physics

Overview

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Teacher! What is the purpose of performing CFD analysis on heat exchangers? Are manual calculation methods like the NTU method or LMTD method insufficient?

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Manual calculation methods (LMTD, ε-NTU) are effective for estimating overall performance, but local phenomena such as flow maldistribution in tube bundles, dead zones around baffles, and temperature distribution non-uniformity cannot be evaluated without CFD.

Governing Equations

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Please tell me the fundamental equations for heat exchanger CFD.

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Solve flow and heat transfer in a coupled manner. It's Navier-Stokes + the energy equation.

$$ \rho c_p \left(\frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T\right) = \nabla \cdot (k \nabla T) + \Phi $$

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The fundamental equations for overall performance evaluation are the LMTD method and the ε-NTU method.

$$ Q = U A \Delta T_{lm} $$

$$ \Delta T_{lm} = \frac{(T_{h,in} - T_{c,out}) - (T_{h,out} - T_{c,in})}{\ln\frac{T_{h,in} - T_{c,out}}{T_{h,out} - T_{c,in}}} $$

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$U$ is the overall heat transfer coefficient, and $A$ is the heat transfer area, right? In CFD, do we back-calculate these from the simulation results?

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Yes. Calculate $Q$ from the inlet/outlet temperatures obtained by CFD, then back-calculate $U$ from that and compare it with the design value.

$$ \varepsilon = \frac{Q}{Q_{max}} = \frac{Q}{C_{min}(T_{h,in} - T_{c,in})} $$

Heat Exchanger Type-Specific Modeling

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Does the analysis method differ between shell & tube and plate type?

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They differ significantly. For shell & tube, the flow outside the tubes is complex and the influence of baffles is large. For plate type, the flow and heat transfer inside the channels are dominant.

Type	CFD Model	Main Evaluation Items
Shell & Tube	Tube Bank + Baffle	Shell-side flow maldistribution, dead zones
Plate Type	Periodic model of one channel	Heat transfer enhancement effect of corrugated plates
Fin-tube (Air Conditioning)	Periodic model of one row	Fin Efficiency, Condensation
Double Pipe	Full 3D	Flow pattern (counterflow/parallel flow)

Shell & Tube Porous Media Approach

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Modeling every single tube in a shell & tube type is tough, right?

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Meshing hundreds to thousands of tubes individually is unrealistic. In practice, the tube bundle is modeled as a porous media + distributed resistance.

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The pressure drop in a tube bank is expressed by correlation formulas corresponding to the tube arrangement. For in-line arrangement:

$$ \Delta p = N_r \chi f \frac{\rho V_{max}^2}{2} $$

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$N_r$ is the number of tube rows, $\chi$ is the arrangement correction factor, and $f$ is the friction coefficient, right? $V_{max}$ is the velocity at the minimum cross-section.

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The correlation by Zukauskas (1972) is widely used. This is converted into porous media resistance parameters and input into the CFD.

Practical Considerations

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What should I be especially careful about in heat exchanger CFD?

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Temperature dependence of fluid properties (viscosity is greatly affected by temperature)
Wall heat transfer and conjugate heat transfer between fluid and solid
Modeling of leakage gaps in baffles (gap between tube and baffle hole)
Entry effects in tube bundles (heat transfer coefficient is high in the first few rows)

Coffee Break Yomoyama Talk

Establishment of Heat Exchanger Theory—The Birth of LMTD and ε-NTU Methods (1940s)

The "LMTD (Logarithmic Mean Temperature Difference) method" and "ε-NTU (Effectiveness-Number of Transfer Units) method," still used today as thermal design theories for heat exchangers, were systematized in the 1940s by Mason (1954) and Kays & London (1964), among others. In particular, Kays & London's classic book "Compact Heat Exchangers" compiled experimental data for St (Stanton number) and f (friction factor) for hundreds of types of heat sink/fin geometries, becoming the bible for compact heat exchanger design. These experimental correlations are still used today, 50 years later, to check the validity of CFD results. If the Nu and f calculated by CFD deviate by more than 20% from the Kays-London correlations, it's a sign that there is a problem with the mesh or boundary conditions.

Physical Meaning of Each Term

Temporal Term $\partial(\rho\phi)/\partial t$: Imagine the moment you turn on a faucet. At first, water comes out in an unstable, splashing manner, but after a while, it becomes a steady flow, right? This "state of change" is described by the temporal term. The pulsation of blood flow from a heartbeat, or the flow fluctuation each time an engine valve opens and closes—all are unsteady phenomena. So what is steady-state analysis? It looks only at "after sufficient time has passed and the flow has settled down"—meaning this term is set to zero. Since computational cost is significantly reduced, solving first with a steady-state approach is a basic CFD strategy.
Convection Term $\nabla \cdot (\rho \mathbf{u} \phi)$: What happens if you drop a leaf into a river? It gets carried downstream by the flow, right? This is "convection"—the effect where fluid motion transports things. Warm air from a heater reaching the far end of a room is also because the "carrier," air, transports heat via convection. Here's the interesting part—this term contains "velocity × velocity," making it nonlinear. That is, as the flow becomes faster, this term rapidly strengthens, making control difficult. This is the root cause of turbulence. A common misconception: "Convection and conduction are similar" → They are completely different! Convection is carried by flow, conduction is transmitted by molecules. There is an order of magnitude difference in efficiency.
Diffusion Term $\nabla \cdot (\Gamma \nabla \phi)$: Have you ever put milk in coffee and left it? Even without stirring, after a while it naturally mixes, right? That's molecular diffusion. Now a question—honey and water, which flows more easily? Obviously water, right? Honey has high viscosity ($\mu$), so it flows poorly. When viscosity is high, the diffusion term becomes strong, and the fluid moves in a "thick" manner. In low Reynolds number flow (slow, viscous), diffusion is dominant. Conversely, in high Re number flow, convection overwhelmingly dominates, and diffusion plays a supporting role.
Pressure Term $-\nabla p$: When you push the plunger of a syringe, liquid shoots out forcefully from the needle tip, right? Why? The piston side is high pressure, the needle tip is low pressure—this pressure difference provides the force that pushes the fluid. Dam discharge works on the same principle. On a weather map, where isobars are tightly packed? That's right, strong winds blow. "Where there is a pressure difference, flow is generated"—this is the physical meaning of the pressure term in the Navier-Stokes equations. A common point of confusion here: "Pressure" in CFD is often gauge pressure, not absolute pressure. If results become strange immediately after switching to a compressible analysis, it might be due to confusion between absolute/gauge pressure.
Source Term $S_\phi$: Heated air rises—why? Because it becomes lighter (lower density) than its surroundings, so it is pushed up by buoyancy. This buoyancy is added to the equation as a source term. Other examples: chemical reaction heat generated by a gas stove flame, Lorentz force acting on molten metal in a factory's electromagnetic pump... These are all actions that "inject energy or force into the fluid from the outside," expressed by source terms. What happens if you forget the source term? In a natural convection analysis, if you forget to include buoyancy, the fluid doesn't move at all—you get a physically impossible result, like warm air not rising in a room with the heater on in winter.

Assumptions and Applicability Limits

Continuum Assumption: Valid for Knudsen number Kn < 0.01 (mean free path ≪ characteristic length)
Newtonian Fluid Assumption: Shear stress and strain rate have a linear relationship (viscosity model required for non-Newtonian fluids)
Incompressible Assumption (for Ma < 0.3): Treat density as constant. For Mach number > 0.3, consider compressibility effects
Boussinesq Approximation (Natural Convection): Consider density variation only in the buoyancy term, use constant density in other terms
Non-applicable Cases: Rarefied gas (Kn > 0.1), supersonic/hypersonic flow (shock capturing required), free surface flow (VOF/Level Set, etc. required)

Dimensional Analysis and Unit Systems

Variable	SI Unit	Notes / Conversion Memo
Velocity $u$	m/s	When converting from volumetric flow rate for inlet conditions, pay attention to cross-sectional area units
Pressure $p$	Pa	Distinguish between gauge and absolute pressure. Use absolute pressure for compressible analysis
Density $\rho$	kg/m³	Air: approx. 1.225 kg/m³ @20°C, Water: approx. 998 kg/m³ @20°C
Viscosity Coefficient $\mu$	Pa·s	Be careful not to confuse with kinematic viscosity $\nu = \mu/\rho$ [m²/s]
Reynolds Number $Re$	Dimensionless	$Re = \rho u L / \mu$. Indicator for laminar/turbulent transition
CFL Number	Dimensionless	$CFL = u \Delta t / \Delta x$. Directly related to time step stability

Numerical Methods and Implementation

Details of Numerical Methods

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Please tell me the specific setup methods for heat exchanger CFD.

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Let me explain the settings according to the modeling approach.

Approach 1: Full Geometry (Small Scale / Detailed Evaluation)

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The approach of meshing each tube individually, right?

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For double pipe or small heat exchangers with 20 tubes or less, full geometry is possible. Mesh the tube wall as a solid domain and couple the fluid and solid using Conjugate Heat Transfer (CHT).

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Setup Procedure:

1. Define fluid domains (inside tube, outside tube) and solid domain (tube wall) separately

2. Set Coupled Wall condition at fluid-solid interfaces

3. Turbulence Model: Realizable k-ε + Enhanced Wall Treatment (outside tube)

4. Energy Equation: ON

5. Property Values: Temperature dependent (especially viscosity)

Parameter	Tube Side	Shell Side
Turbulence Model	Realizable k-ε	SST k-ω (if there is flow separation at baffles)
y+	≈ 1	≈ 1 to 30
Mesh	O-grid + prism layers	Tetrahedral + prism layers

Approach 2: Porous Media Model (Large Scale / Overall Evaluation)

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The method of treating the tube bundle as a porous body, right?

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Use Fluent's Heat Exchanger Model (Macro Model). Treat the shell side as a porous media, and calculate tube bundle resistance and heat transfer with a sub-model.

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Required Input Data:

Tube outer diameter, tube pitch, tube arrangement pattern (in-line, staggered)
Tube-side flow rate and inlet temperature
Shell-side heat transfer correlation (Zukauskas, Kern, Bell-Delaware, etc.)
Number of baffles, spacing, cut ratio

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Can we directly input the Bell-Delaware method parameters?

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Fluent's Heat Exchanger Model internally calculates correction factors based on the Bell-Delaware method. The user only needs to specify the baffle geometry.

Conjugate Heat Transfer (CHT) Settings

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What should I be careful about in CHT calculations?

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Match the mesh at fluid-solid interfaces (non-conformal is possible but accuracy decreases)
At least 3 layers of mesh in the solid (in the tube wall thickness direction)
For high thermal conductivity materials like copper or aluminum, temperature gradients within the solid are small, so a coarse solid mesh is acceptable
For stainless steel, wall temperature distribution is important, so use a finer solid mesh

Material	Thermal Conductivity [W/(m K)]	Solid Mesh
Copper	385	Coarse is acceptable (3 layers)
Aluminum	205	Coarse is acceptable (3 layers)
Stainless Steel	16	Somewhat fine (5-8 layers)
Titanium	22	Somewhat fine (5-8 layers)

Convergence Criterion

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What should I look at for convergence criteria in heat exchanger CFD?

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In addition to residuals, confirm that the following physical quantity monitors have reached a steady state.

Outlet temperatures for tube side and shell side
Heat exchange rate Q (inlet enthalpy - outlet enthalpy)
Difference between tube-side and shell-side Q within 1% (energy balance)

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If the Q for the tube side and shell side don't match, it means energy isn't conserved, right?

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Exactly. Energy balan...