## Conjugate Heat Transfer Analysis of Exhaust Port

Conjugate Heat Transfer:

Conjugate heat transfer is a process in which heat transfer takes place at an interface of fluid and solid areas. It is a combination of conductive heat transfer in solids and convective heat transfer in liquids.  In solids, conduction dominates in the solids where as in fluids, convection usually dominates.

If there is a solid and liquid interface exist, there we can observe the thermal heat exchange. Then in such heat exchange processes we can apply the conjugate heat transfer analysis in order to find the surface temperatures at the interface.

Typical examples/places/components where CHT analysis is done:

Heat exchangers, Inter combustion engine, Boilers, Heat pipes, Tanks, Turbochargers, Graphic cards.

CHT analysis is used mainly for:

• Measurement of heat transfer due to conduction in solids and heat transfer by convection in the fluid.
• Determining the heat exchange capabilities of heat exchangers, boilers, turbochargers etc.
• Optimising the design in order to improve the heat transfer capability of the component.
• Determining the heat concentration zones over the component.
• Measuring the cooling capabilities of the fluids by varying the velocity of the flow.
• Determining the surface temperatures of the component during the heat exchanging process.

CHT analysis of Exhaust Manifold

During the CHT analysis velocity, temperature and heat transfer coefficient of Exhaust Manifold are determined and compared for two simulation of baseline mesh and another refined mesh.

Geometry Setup:

• Fluid volume is extracted from the model using ‘Volume extract’ tool in spaceclaim.

Mesh Setup:

• Inlet, outlet and outer convective wall have been specified in the model
• The solid volume and liquid volume are combined together using the ‘Share Tolopology’.
• A baseline is meshed is created for the first simulation and another finer mesh is created.
• In finer mesh, total of 5 inflation layers are created with the growth rate of 1.2

Solver set up:

The solver is taken as ‘Pressure based’

Velocity formation is taken as ‘Absolute’

Stead state simulation is taken into consideration.

Energy equation is also taken into the consideration.

Viscous model is considered as ‘k-epsilon’.

Material of the exhaust manifold is taken as ‘Aluminium’ and working fluid as ‘Air’.

Boundary Conditions:

Velocity of air coming from all the four inlets is taken as 5 m/s and temperature is taken as 700k.

Outlet is taken as ‘pressure-outlet’ and gauge pressure maintained is 0 pascals.

Convective heat transfer coefficient on the wall surface is taken as 20 W/m^2 k

Case 1: Analysis of Exhaust Manifold using Baseline Mesh

The number of nodes are 27484

Residual Plots:

Temperature distribution:

Streamline Distribution:

Velocity profile at the throat:

Wall Heat Transfer Coefficient

Case 2: Analysis of Exhaust Manifold using Refined Mesh

The number of nodes are 410246

Inflation Layers:

Residual Plots:

Temperature distribution:

Streamline Distribution:

Velocity profile at the throat:

Wall Heat Transfer Coefficient:

Observations and Conclusions:

• We can observe that after 140 iterations in both baseline mesh and refined mesh cases we attain steady state simulation.
• From the temperature profiles, we can observe lower temperatures at the inlets and higher temperature at the outlet port. This is because the fluid from all the four inlets combine and flow into the outlet. This process makes all the inertial forces of the inlet fluids to combine and the velocity is increased very much when compared to the inlet. As the inertial forces increases, Reynolds number also increase. Increase in Reynolds number increases the convective heat transfer coefficient.
• From the velocity contours, we can conclude that velocity at the throat area is higher when compared to the inlets since fluid from all the inlets gets combined and flow into the throat area. This is also because at the bend section, we find drop in the pressure, this decrease in pressure leads to the increase in the fluid velocity at the throat section.
• Since temperature is higher at the throat area, we can say that wall heat transfer coefficient is also higher.
 Case 1-Baseline mesh Case 2-Refined mesh Max Wall Temperature (K) 700 700 Max Velocity (m/s) 29.17 30.93 Wall Heat Transfer Co-efficient (W*m2/K) 94.76 115.1

Conclusions by comparing the baseline mesh and refined mesh:

• Results of the refined model are more accurate than the baseline meshed model since accuracy is higher for dense mesh.
• From the above table we can conclude that the max wall temperature is almost same for both meshes but by comparing the temperature contours of the two, we can say that there is change in the minimum temperatures observed during the simulation.
• Since the max velocity of the fluid in the refined mesh simulation is higher, we can observe that wall heat transfer co-efficient is much higher in the refined mesh as compared to the baseline mesh.

Verifying the Heat Transfer Co-efficient prediction:

Heat transfer co-efficient at the surface level of any solid is calculated by the help of Nusselt number. So to verify the predicted HTC, we need to calculate the Nusselt number.

The Nusselt number is the ratio of convective to conductive heat transfer across a boundary. The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow in the simple case. It is a dimensionless number, closely related to the fluid's Rayleigh number.

A Nusselt number of value one represents heat transfer by pure conduction. A value between one and 10 is characteristic of slug flow or laminar flow. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range

Since the flow of the gases in the exhaust manifold can be considered as turbulent flow inside a circular pipe, Nusselt number for such condition is calculated using the below formula

By knowing the Nusselt number, we can calculate the HTC by the help of below formula:

h =(N_u*k)/L

where

h is the convective heat transfer coefficient of the flow,

L is the characteristic length,

k is the thermal conductivity of the fluid.

Factors Affecting the accuracy of the HTC prediction:

• Grid shape and size: Finer the mesh, higher the accuracy.
• Material specifications and properties loaded to the fluent has be same as the actual material.
• Selection of the solution type and methodology needs to be correct.
• Inflation layer: By incorporating the inflation layer, quality of the mesh around the boundaries becomes finer and helps in giving accurate results.

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