Assignment : Design and validation of a heat sink

Problem Statement

An isothermal silicon chip of W = A mm and Z = B mm is soldered to a heat sink of equivalent size and

generates heat at a rate of qc = C W (total), as shown in Figure 1. The heat sink needs to be designed so that

the chip’s temperature Tc remains below 80 0C when the ambient temperature is 30 0C.

The heat sink has a base thickness of Lb = D mm and an array of rectangular fins, each of length Lf. Airflow

at T = 30C is maintained through channels formed by the fins and a cover plate, and for a convection

coefficient of h = E W/m2

K, a minimum fin spacing of 3 mm is dictated by limitations on the flow pressure

drop. The solder joint has a thermal contact resistance of R”t,c = F m

2

K/W.

Design constraints

- The maximum height of the fins Lf should not exceed 80 mm.
- The minimum thickness of any fin is 2 mm
- The minimum distance between any two fins is 3 mm
- Material data is given in the table.

Part 1. Two-dimensional heat sink analysis using numerical finite-difference method

Using information provided in the “Problem Statement” section, “Design constraints” section and in

“Parameters” table, determine the following: - Taking advantage of symmetry, discretise the heat sink geometry and write 2-dimensional finitedifference equations for each node.
- Rewrite the equations of (1) in Gauss-Seidel form.
- Determine the 2-dimensional temperature distribution in the heat sink using Gauss-Seidel method.

Continue iterations until the node temperature difference between final iteration and previous iteration is

less than 0.2°C. - Determine the total heat loss per heat sink length.

Part 2. Three-dimensional heat sink analysis using analytical method and ANSYS numerical method

Z

MCE Assignment Brief 2020-21

Page 3 of 5

As an engineer assigned this task and using information provided in the “Problem Statement” section,

“Design constraints” section and in “Parameters” table, determine the following:

Develop at least 3 different designs and evaluate their performances and cost for each design. For material

selection, you can refer to the Table “Material data”. For the final selected design you must investigate how

changes in both the fin length and the convective heat transfer coefficient affect the heat transfer rate in the

heat sink, and which parameter (h or Lf) has a greater effect on performance of the heat sink.

Using analytical method - Include the details of the model and analytical equations you have used to evaluate three different heat

sink designs. Each design must have different fin cross sections. - Any assumptions you have made must be stated.
- Select the final heat sink design and justify why this design was selected.
- For selected final design, perform Parametric Study and investigate the effect of varying convection

coefficient (h) and fin length (Lf) on heat transfer and justify your results.

Using ANSYS numerical method - Construct the CAD models of heat sinks for all three designs with structured hexahedral mesh only and

determine and plot the temperature distribution and heat transfer rate in the sink using ANSYS SteadyState Thermal module. - Compare heat sink analytical results with ANSYS results and provide detail discussions, justifications

and conclusions. You should compare three different cross section shapes (one cross section per design).

Your Part 2 of the assignment must include (as minimum) the following sections:

Problem Statement

Design 1

- Description (including diagrams)
- Analysis
- Discussion of Performance

. . . (repeat the above for each three designs)

Part 3. Combined fluid flow and heat transfer analysis of the heat sink

Using the same configuration of the heat sink shown in Figure 1, and assuming that constant qc enters the

heat sink, and also using information provided in the “Problem Statement” section, “Design constraints”

section and in “Parameters” table, determine the following:

Using analytical method

- Assuming that flow is fully developed, determine Reynolds number and flow velocity.
- Demonstrate whether the flow is laminar or turbulent and determine hydrodynamic and thermal entry

lengths. - Determine the mean outlet temperature of air.

Using ANSYS CFD method - Create 3-D heat sink model with structured hexahedral mesh only.
- Conduct three-dimensional CFD analysis for the heat sink using ANSYS Fluent for the same conditions

as those for analytical method. - Refine your model mesh (double the number of elements) and run mesh sensitivity analysis to

demonstrate that there is no effect of mesh on the results. - Using ANSYS Fluent, demonstrate the effect of fin spacing on flow pressure drop.
- Compare analytical and numerical (CFD) results for temperature, velocity, pressure, heat flux, and

provide detail discussions, justifications, and conclusions. - Plot distributions of velocity, temperature, pressure and heat flux in the heat sink and channels.
- If the air flow velocity increases 30% and heat transfer rate qc increases 20%, redesign the heat sink to

maintain the chip’s temperature Tc ≤ 80 0C at minimum heat sink cost.

Additional instructions to students: IMPORTANT!!! This assignment is an individual work. You have

to use your student ID digits to select input parameters. Zero mark will be given for the results with

input parameters that are not based on your student ID. This assignment should be presented in a

standard engineering report format. You must include the analytical fin, finite-difference and fluid flow

analysis with all relevant equations.

Further Information

Learning outcomes tested in this assessment (from the Module Descriptor):

- Demonstrate a critical understanding of the governing equations and mathematical principles of fluid

mechanics and heat transfer employed in CFD software - Independently plan a CFD project to solve unknown problems involving thermofluids, considering time

and computer resource constraints and demonstrating an awareness of the limitations of CFD

methodologies - Demonstrate a critical awareness of the current and emerging numerical methods in the field of fluid

dynamics and heat transfer - Analyse complex engineering flows systematically using CFD software and make judgements based on

available data - Demonstrate a critical understanding of physical models and their application in CFD software