1 PROBLEM STATEMENT

Give a brief description on usage & advantage of CHT analysis. Choose proper turbulence model & maintain a corresponding y+ values & justify your results. Calculate the wall/surface heat transfer coefficient on internal solid surface. Also plot velocity & temperature profile in appropriate area.

Verify the value of HTC obtained in simulation. Also, discuss the parameter on which HTC depends

2 AIM

Calculate heat transfer coefficient & outlet temperature.

3 INTODUCTION & THEORY

The study of heat transfer problem has a very important role in many fields ranging from material processing to space vehicle design. We can see the application of CHT analysis from micro scale (electronic industry) to macro scale (space vehicle). These industries developed the scope for research in the field of effective heat transfer system for getting optimum cooling.

CHT analysis is important in a situation where multiple subdomains are present in solution field and can’t be solved by using a single governing equation. If we do so, we can’t get accurate result. This problem can be solved by using appropriate governing equation in respective flow domain & later on solution parameter can be conjugated at interface. We have to be very careful while performing the coupling at fluid-solid interface in order to get correct (near to experimental) value. Such type of analysis is known as CONJUGATE HEAT TRANSFER.

We will discuss an example of CHT analysis in order to understand it properly. Let us consider a solid surface & fluid is flowing over the surface. Inside solid surface conduction can take place easily & this mode of heat transfer will carry all heat at outer most surface of solid.

The accumulated heat at solid surface will be carried away by fluid flowing over cylinder. This case can be handled by using parabolic conduction equation inside solid body & fluid domain can be solved by using 3-dimensional continuity, momentum & energy equation. Here we can observe that fluid & solid domain has different governing differential equation so numerical treatment for both subdomains must be different. In order to get accurate results, we need to perform coupling at solid-fluid interface & it should be updated dynamically after each iteration of solution.

Governing equation for both sub domain is not independent. If we choose an equation for solid domain it will help in deciding the solution for fluid domain. 1-Dimensional heat conduction equation for solid domain will result in simple analytical solution. Instead of 1-D, if we consider multi-dimensional heat conduction equation, we have to model the solution domain for finite difference method or finite element method. We can conjugate the domain with the help of 2 model. They are direct approach where complete set of equation can be solved in both models simultaneously & the second method is iterative approach where separate solution is done in all the sub domains & later on conjugated at fluid-solid interface.

4 GEOMETRY

This is cad model of exhaust port. Geometry has 4 inlets & 1 outlets. The cross-sectional area of all inlet & outlet is same. Fluid volume has been extracted for analysis.

Above outermost surface will act as outer convection wall. Fluid will flow inside this port.

4 MESHING

The meshing strategy ensured one to one matching of grid points at the solid–fluid interface. The coupling technique employed for the transfer of heat flux and temperature among fluid and solid domains. We solve the fluid domain & solid domain separately using appropriate governing differential equation. In order to capture effects of coupling, we need to mesh carefully specially at the interface where conduction & convention both takes place simultaneously.

In this study, we created an inflammation layer at interface by controlling total thickness method. Total thickness was 5 mm & we generated 20 layers of inflammation at a growth rate of 1.2

Default size of element was 150 mm of fluid domain & size of outer solid surface was 10mm.Total numbers of nodes & element was 1212576 & 2802618 respectively.

6 SETUP & PHYSICS

K-w SST turbulence model has been adopted for the solution. For this model we have to maintain the value of y+ in between 30 to 300. We have also solved the simulation for energy equation. We have already discussed the importance & application of CHT analysis & this problem will also fall in the same category. We will also implement coupling technique to get better result.

6.1 BOUNDARY CONDITIONS

The inlet velocity of air is constant & equal at all inlet (5m/s) at a temperature of 700k. There is 0 heat flux at adiabatic wall. The heat transfer coefficient was equal to 20 w/m²-K & free stream temperature was 300K at outer convection wall.

Outer convection wall was solved using coupled velocity coupling method for correct CHT analysis. The pressure & momentum equation was solved using second order & second order upwind approximation.

6.2 GOVERNING DIFFERENTIAL EQUATION

For steady or unsteady fluid flows Law:

• Continuity equation -conservation of mass
• Naiver– Stokes equations -conservation of momentum
• Energy Equation-Conservation of energy

Similarly, for steady or unsteady conduction in the solid domain:

• 2-D or 3-D unsteady energy equation
• 2-D or 3-D steady Laplace or Poisson equations
• One dimensional steady or unsteady conduction equation upon considering prevented or negligible heat conduction in other dimensions as in case of heat conduction through thin plates

Next the heat conduction equation was solved in the solid domain with the boundary condition as the input temperature profile from the fluid solver. Solution of heat conduction equation thus offered interface wall temperature as output, which is then passed to fluid solver. Subsequent solution of fluid flow equations in the fluid domain gave heat flux values. These boundary heat flux values are then passed to the solid solver as input to get next level temperature distribution in the solid fluid interface. This iterative procedure has been continued until convergence.

6.3 COUPLING TECHNIQUE

In CHT analysis simultaneous solution of flow field of the fluid and temperature field of solid are carried out. The temperature and heat flux are exchanged at fluid–solid interface at every time steps. Hence real-time prediction of heat transfer rate and wall temperature is possible through such an efficient technique. The key task involved in any CHT solver development is formulation of proper communication strategy between fluid and solid domain. Such a bilateral information exchange is termed as coupling and the strategies followed for the same are known as COUPLING TECHNIQUES.

7 RESULT & DISSCUSION

7.1 RESIDUE-PLOT

Simulation was done for 150 iteration using -w SST turbulence model. Figure below shows the residue plot. The fluctuation in residue is very less.

7.2 TEMPERATURE -PLOT

7.2.1 SOLID BODY

Figure below shows the temperature variation on entire body. We can observe that temperature near the junction for outlet is high (from junction to outlet). The contours of temperature can be seen easily in following plot. The maximum value of temperature is 700.15K.

7.2.2 PLANE-1

Following figure shows temperature plot on plane 1

1.1.1 OUTLET

Following figure shows temperature plot on outlet

7.3 VELOCITY

7.3.1 STREAMLINE & VELOCITY

Figure below shows the streamline coloured by velocity. There is a smaller number of streamlines towards inlet & a greater number of streamlines towards outlet. This distribution of stream line was expected because of greater outlet velocity. This can be seen in velocity plot also.

7.3.2 PLANE-1

Following figure shows velocity plot on plane 1

The highest value of velocity can be observed near the bend. It is so because of presence of maximum number of stream line. It indicates that the maximum heat transfer coefficient will occur near this bend.

7.4 WALL HTC

8 CONCLUSION

Some important parameters to measure for successful design of heat transfer device are

• Temperature
• Heat flux
• Heat transfer coefficient

The presence of heating or cooling environment can be seen to the exposed surface. HTC can be calculated properly by using proper boundary conditions. The fluid domain & solid domain should be coupled properly for getting proper result.

Parameter which effect HTC are

• Temperature gradient at solid fluid interface
• Nusselt number(depends on geometry irrespective of thermal conductivity of gas in forced convection)
• Reynolds number
• Prandtl number

Using following steps we can verify our HTC value

Nu=0.023*Reⁿ*Prⁿ

^Re=ρvl/μ

^{Pr = μc}_p/k

where

^{ρ___ density}

^{μ___Dynamic viscosity}

^{k____ thermal conductivity}

^c_p___ heat capacity