2021-03-26T20:34:29.000-0400

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Convective heat transfer is the transfer of energy between a surface and a fluid moving over the surface. This article describes the various heat transfer coefficients in Simcenter STAR-CCM+.

Convective heat transfer is the transfer of energy between a surface and a fluid moving over the surface and is primarily used as a boundary condition when solving solid/fluid heat transfer problems (for example, quenching, electronic device cooling, heat exchangers, and so on). It is governed by Newton’s law of cooling

(1)

where**there is an infinite number of heat transfer coefficient and reference temperature combinations that give the same surface heat flux**.

Historically, heat transfer coefficient data came from experiments, but more recently boundary layer theory (that is, the layer of fluid in the immediate vicinity of a surface where the effects of viscosity and conduction dominate) has given us an analytical means of calculating heat transfer coefficients. So, in Simcenter STAR-CCM+ boundary layer theory is used to calculate surface heat transfer coefficients (that is,*h*), and the conceptual centerpiece of this stems from writing (1) as

(2)

and realizing that one can equate the terms from (1) and (2) and define an*h* in terms of the local flow conditions, where

The Standard Wall Functions (SWFs) are a set of semi-empirical functions used to satisfy the flow physics in the near-wall region (that is, the boundary layer), and they give relationships for T+ and in terms of the laminar and turbulent Prandtl Numbers, the dimensionless near-wall flow velocity, and the turbulent kinetic energy.

### A. Heat Transfer Coefficients

In Simcenter STAR-CCM+ the local surface heat transfer coefficient is always calculated (and used internally) in the code as outlined above using the SWFs and (4) defined below, but there may be times when one wants to view (for example, for comparison to previous work) or export (for example, for use with other applications) heat transfer coefficients defined other ways. In general, this can be accomplished by post-processing the simulation results and defining the one-to-one linear mapping (based on equating the surface heat fluxes)

(3)

In this way one is able to define their own*h* and *Tref* pair, where *h*, *Tc*, and *Ts* are known from the simulation and the user picks *Tref* to match their needs. So, in Simcenter STAR-CCM+ there are three built-in post-processing heat transfer coefficients defined: namely, *specified y+ heat transfer coefficient*, *heat transfer coefficient*, and *virtual local heat transfer coefficient*. The difference between these three heat transfer coefficient postprocessing options is discussed below along with use recommendations in §B.

##### 1. Local Heat Transfer Coefficient

The first heat transfer coefficient option that will be discussed is the one eluded to by (2) and is the one used internally by the code to calculate local surface heat flux. Thus if one equates the terms from (1) and (2),

(4)

are the*Local Heat Transfer Coefficient* and *Local Reference Temperature*, respectively, and we now have the pair (*h1* and *Tref,1*) which can be viewed or exported.

##### 2. Specified y+ Heat Transfer Coefficient

The first built-in post-processing option in Simcenter STAR-CCM+ calculates the heat transfer coefficient as in (4), but at a user specified*y+* value instead of the value associated with the near-wall cell

(5)

Then, using the surface heat flux as calculated in (2), we solve (1) for the reference temperature

(6)

and now have the pair (*h2* and *Tref,2*) which can be viewed or exported. We note that this definition of the reference temperature does not guarantee that *Tref,2 *lies within the temperature range of the local region, so if it does not then either the minimum or maximum temperature will be used in its place and the heat transfer coefficient will be modified accordingly.

##### 3. Heat Transfer Coefficient

The second built-in post-processing option in Simcenter STAR-CCM+ calculates the surface heat flux using (2), and then recasts (1) as

(7)

and calculates the heat transfer coefficient using a user defined reference temperature (*Tref,3*). We now have the pair (*h3* and *Tref,3*) which can be viewed or exported.

##### 4. Virtual Local Heat Transfer Coefficient

The third and final built-in post-processing option in Simcenter STAR-CCM+ does not need to solve the energy equation in the fluid, but instead uses the*Local Heat Transfer Coefficient* (4) which is calculated using only flow field information, but because we are not solving the energy equation in the fluid, the user must choose a reference temperature (*Tref,4*) in order to calculate the surface heat flux. This chosen reference temperature does not need to be assigned in the sim file, but should be chosen appropriately based on the problem definition (bulk fluid temperature, inlet temperature, etc), and kept in mind when using the corresponding heat transfer coefficient. We now have the pair (*h1* and *Tref,4*) which can be viewed or exported.

### B. Use Recommendations

In this section we discuss our recommendations for accurate use of the SWFs and the above described built-in post-processing heat transfer coefficients, but reiterate that the code always uses (2) to obtain the local surface heat flux when solving for fluid temperatures (and/or solid temperatures in CHT applications). The important boundary layer physics is embodied in this expression and it is important that the user follow recommendations to ensure its proper application. The heat transfer coefficients are Simcenter STAR-CCM+ post-processing results which can be used for comparing to other solutions, visualization, or exporting to other applications such as ABAQUS, Nastran, and so on. In general, standard wall functions give reasonable accuracy for a majority of high-Reynolds-number, wall-bounded flows but reach their limitation when the flow conditions differ too much from the ideal conditions used to define the functions. The cases in which this limit might be reached are:

Thus to get good results when using the SWFs, the problem should not contain any of the above outlined physics conditions, and the y+ of the near-wall cell should be either in the viscous sub-layer (y+ < 5) or the inertial sub-layer (30 < y+ < 150), and temperature dependent fluid properties should be used to ensure maximum accuracy. If the near-wall cell lies in the buffer layer (5 < y+ < 30) between the viscous and inertial sub-layers, the ”All y+” option (default) should be used which smoothly connects the viscous and inertial sub-layers.

Lastly, the particular choice of HTC will not affect the simulation results if the user is solving for both the fluid and solid temperatures within Simcenter STAR-CCM+, but if Simcenter STAR-CCM+ is being**two-way-coupled** to another application which solves for the temperature in the solid, then in this case the choice of HTC is important, and will of course impact the results in that application. So, it is very important to choose the correct option. Our suggested boundary conditions to be used when explicitly coupling (that is, **two-way-coupled**) fluid & solid simulations are:
##### 1. Local Heat Transfer Coefficient

##### 2. Specified y+ Heat Transfer Coefficient

##### 3. Heat Transfer Coefficient

##### 4. Virtual Local Heat Transfer Coefficient

Why are the values of the Heat Transfer Coefficient (HTC) so different from those of the Local Heat Transfer Coefficient?

Convection and Radiation Boundary Modeling through Heat Transfer Coefficient

How to apply your own Heat Transfer Coefficients

Simcenter STAR-CCM+ User Guide sections:

Simulating Physics > Heat Transfer > Convective Heat Transfer Coefficients

Interacting with CAE Software > File-Based Coupling > Exchanging Heat Transfer Coefficients > What Methods Are Available for Exchanging Heat Transfer Coefficients?

(1)

where

- q”s is the local surface heat flux (that is, power per unit area),
- h is the local convective heat transfer coefficient,
- Ts is the surface temperature, and
- Tref is a characteristic temperature of the fluid moving over the surface.

Historically, heat transfer coefficient data came from experiments, but more recently boundary layer theory (that is, the layer of fluid in the immediate vicinity of a surface where the effects of viscosity and conduction dominate) has given us an analytical means of calculating heat transfer coefficients. So, in Simcenter STAR-CCM+ boundary layer theory is used to calculate surface heat transfer coefficients (that is,

(2)

and realizing that one can equate the terms from (1) and (2) and define an

*Cp,f*is the fluid specific heat capacity,- is a velocity scale based on the wall shear stress,
*T+*is the dimensionless temperature,- is a Reynolds number, and
- yc and Tc are the normal distance and temperature of the near-wall cell, respectively.

The Standard Wall Functions (SWFs) are a set of semi-empirical functions used to satisfy the flow physics in the near-wall region (that is, the boundary layer), and they give relationships for T+ and in terms of the laminar and turbulent Prandtl Numbers, the dimensionless near-wall flow velocity, and the turbulent kinetic energy.

In Simcenter STAR-CCM+ the local surface heat transfer coefficient is always calculated (and used internally) in the code as outlined above using the SWFs and (4) defined below, but there may be times when one wants to view (for example, for comparison to previous work) or export (for example, for use with other applications) heat transfer coefficients defined other ways. In general, this can be accomplished by post-processing the simulation results and defining the one-to-one linear mapping (based on equating the surface heat fluxes)

(3)

In this way one is able to define their own

The first heat transfer coefficient option that will be discussed is the one eluded to by (2) and is the one used internally by the code to calculate local surface heat flux. Thus if one equates the terms from (1) and (2),

(4)

are the

The first built-in post-processing option in Simcenter STAR-CCM+ calculates the heat transfer coefficient as in (4), but at a user specified

(5)

Then, using the surface heat flux as calculated in (2), we solve (1) for the reference temperature

(6)

and now have the pair (

The second built-in post-processing option in Simcenter STAR-CCM+ calculates the surface heat flux using (2), and then recasts (1) as

(7)

and calculates the heat transfer coefficient using a user defined reference temperature (

The third and final built-in post-processing option in Simcenter STAR-CCM+ does not need to solve the energy equation in the fluid, but instead uses the

- Pervasive low-Reynolds-number or near-wall effects (that is, flow through a small gap or highly viscous low-velocity fluid flow).
- Massive transpiration through the wall (for example, blowing/suction).
- Severe pressure gradients leading to boundary layer separation.
- Strong body forces (for example, flow near rotating disks or buoyancy-driven flows).
- High three-dimensionality in the near-wall region (for example, Ekman spiral flow or strongly skewed 3D boundary layers).

Thus to get good results when using the SWFs, the problem should not contain any of the above outlined physics conditions, and the y+ of the near-wall cell should be either in the viscous sub-layer (y+ < 5) or the inertial sub-layer (30 < y+ < 150), and temperature dependent fluid properties should be used to ensure maximum accuracy. If the near-wall cell lies in the buffer layer (5 < y+ < 30) between the viscous and inertial sub-layers, the ”All y+” option (default) should be used which smoothly connects the viscous and inertial sub-layers.

Lastly, the particular choice of HTC will not affect the simulation results if the user is solving for both the fluid and solid temperatures within Simcenter STAR-CCM+, but if Simcenter STAR-CCM+ is being

- The solid only simulation should pass the wall temperature to the fluid only simulation.
- The fluid only simulation should pass the Heat Transfer Coefficient and its corresponding Reference Temperature to the solid only simulation.
- Single thermal physics: fluid flow with no phase-change or radiative transport
- Use the Specified Y+ Heat Transfer Coefficient and Specified Y+ Heat Transfer Reference Temperature, starting with a y+ = 100, but if needed for better convergence, one may try a different y+ value.

- Multiple thermal physics: fluid flow + radiative transport + phase-change + and so on
- Use the Local Heat Transfer Coefficient and Local Heat Transfer Reference Temperature, and if needed, one may linearly transform this pair to another pair having better convergence behavior.

- Single thermal physics: fluid flow with no phase-change or radiative transport

- It is recommended that temperature dependent fluid properties be used to ensure maximum accuracy, and that if temperature dependent fluid properties are used, all fluid properties should be temperature dependent and not just some (for example, to get the Prandtl Number correct you need to account for temperature dependence in both the momentum and thermal diffusivity).
- Because y+ of the near-wall cell can lie in the viscous sub-layer, the inertial sub-layer, or anywhere in between, this option may not give heat transfer coefficients anywhere near values found in classic textbooks.
- This option is not recommended for coupled use with other applications unless the user can not use
*Specified y+ Heat Transfer Coefficient*for some reason.

- It is recommended that the user follow all recommendations for getting accurate results using the SWFs.
- The user specified value of y+ should be less than about 150: a value of 100 has been shown to work well.
- It is recommended that temperature dependent fluid properties be used to ensure maximum accuracy, and that if temperature dependent fluid properties are used, all fluid properties should be temperature dependent and not just some (for example, to get the Prandtl Number correct you need to account for temperature dependence in both the momentum and thermal diffusivity).
- This is the recommended heat transfer coefficient and reference temperature pair to be used when coupling Simcenter STAR-CCM+ to other applications because it is less dependent on the mesh than the
*Local Heat Transfer Coefficient*, gives better conditioned systems at solve time, and for a given number of coupling-iterations (that is, one coupling-iteration involves solving for the flow field given the initial solid wall temperature and then solving for the solid temperature field given h and Tc from the flow field computation) this heat transfer coefficient and reference temperature pair will give the fastest convergence; so even one coupling-iteration may give good results (although at least two coupling/iterations is recommended). It is not recommended that alternative techniques (for example, the fluid code passes the local heat flux to the solid code and the solid code passes the local wall temperature to the fluid code) of exchanging boundary conditions between the Simcenter STAR-CCM+ and other applications be used for accuracy and numerical stability reasons. - May have implications for cycle averaging and mapping.

- It is recommended that the user follow all recommendations for getting accurate results using the SWFs.
- This option is primarily used for comparison of heat transfer coefficients to experimental data or other previous work.
- For external flows where there is a well defined free-stream temperature outside the thermal boundary layer, the usual practice is to use this temperature as the reference temperature. For internal flows without axial re-circulation, it is often the practice to define the reference temperature as the local bulk temperature obtained by solving the one-dimensional (stream-wise) energy equation, although if the bulk temperature varies little relative to the overall fluid-wall temperature difference, the reference temperature can be set to the inlet temperature.
- It is recommended that temperature dependent fluid properties be used to ensure maximum accuracy, and that if temperature dependent fluid properties are used, all fluid properties should be temperature dependent and not just some (for example, to get the Prandtl Number correct you need to account for temperature dependence in both the momentum and thermal diffusivity).
- Poor choice of reference temperature can lead to a negative heat transfer coefficient.
- This option is not recommended for coupled use with other applications.

- It is recommended that the user follow all recommendations for getting accurate results using the SWFs.
- This option is useful when you are not interested in the temperature distribution in the fluid and it is easy to define a reasonable global reference temperature, for example, in an external/internal flow where the temperature of the fluid is not expected to change much due to surface heat flux. For external flows where there is a well defined freestream temperature outside the thermal boundary layer, the usual practice is to use this temperature as the reference temperature. For internal flows without axial re-circulation, it is often the practice to define the reference temperature as the local bulk temperature obtained by solving the one-dimensional (stream-wise) energy equation, although if the bulk temperature varies little relative to the overall fluid-wall temperature difference, the reference temperature can be set to the inlet temperature.
- The y+ of the near-wall cell should be in the inertial sub-layer (30 < y+ < 150) because it is more likely that the user specified reference temperature is close to what is used in the SWFs to calculate h.
- This option should not be used for laminar flows because calculating the surface heat flux accurately requires the near-wall cell to lie in the viscous sub-layer, but as mentioned above, this is not recommended.
- This option is not recommended for coupled use with other applications.

Why are the values of the Heat Transfer Coefficient (HTC) so different from those of the Local Heat Transfer Coefficient?

Convection and Radiation Boundary Modeling through Heat Transfer Coefficient

How to apply your own Heat Transfer Coefficients

Simcenter STAR-CCM+ User Guide sections:

Simulating Physics > Heat Transfer > Convective Heat Transfer Coefficients

Interacting with CAE Software > File-Based Coupling > Exchanging Heat Transfer Coefficients > What Methods Are Available for Exchanging Heat Transfer Coefficients?