Heat transfer- determine heat of chip using convection

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Discussion Overview

The discussion revolves around a homework problem involving heat transfer from a silicon chip embedded in a ceramic substrate. Participants explore the relationship between electrical power input, heat transfer coefficients, and surface temperature of the chip, focusing on convection as the primary mode of heat loss.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states the problem involves a silicon chip with specific dimensions and power input, seeking to determine the surface temperature under steady-state conditions.
  • Another participant clarifies that since conduction is negligible, all power input must be lost through convection.
  • There is a discussion about the units of power and energy, with participants confirming that watts are equivalent to joules per second.
  • Participants discuss the equation for heat transfer, Q = h(c)A(ΔT), and the need to equate power input to heat loss.
  • One participant proposes a specific equation setup to solve for the surface temperature, incorporating the coolant temperature.
  • Concerns are raised about unit consistency, particularly regarding the use of millimeters in calculations involving the heat transfer coefficient.
  • A participant expresses difficulty in rearranging equations and seeks guidance on the best approach to isolate the temperature variable.
  • Another participant provides a general formula for rearranging equations, emphasizing the importance of understanding such manipulations for future scientific studies.

Areas of Agreement / Disagreement

Participants generally agree on the principles of heat transfer and the need to equate power input to heat loss. However, there is no consensus on the specific steps to rearrange the equation for temperature, as some participants express uncertainty.

Contextual Notes

Participants note the importance of unit consistency in calculations, particularly when converting dimensions from millimeters to meters for use in the heat transfer equation.

Who May Find This Useful

This discussion may be useful for students studying heat transfer, thermodynamics, or related engineering fields, particularly those working on homework problems involving steady-state heat transfer scenarios.

andyb1990
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Homework Statement



A silicon chip measuring 5mm by 6mm and of thickness 1mm is embedded in a ceramic substrate. At a steady state, the chip has an electrical power input of 0.3W. The top surface of the chip is exposed to a coolant whose temperature is 20°C. The heat transfer coefficient for convection between the chip and the coolant is 150W/(m^2.k). If the heat transfer by conduction between the chip and the substrate is negligible, determine the surface temperature of the chip



Homework Equations





The Attempt at a Solution



my attempt at this question is using the formula:

Q= h(c)A (ΔT)

where h(c) is the heat transfer coefficient

I am unsure what to do with the electrical power that has been put in the question?
 
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The unit of power is the watt. A watt has the unit of work/second. What are the units of work and how do these units compare with Q in your equation above?

Since there is negligible heat being conducted to the substrate, all must leave by convection.
 
work = joules?
 
Yes, work is joules which is also a unit of energy. Power is work/second or energy/second. So, electrically, you are inputting energy per second into the wafer. Since the problem indicates the situation is steady state, all that comes in MUST leave. So what does this tell you to do?
 
would you divide the heat transfer coefficient by the power input?
 
No you would not do that.

What are the units of Q? What does Q represent?
 
Q represents the amount of heat loss?

and units are watts?
 
Yes, that is correct. So you have a steady state situation here. All the power that comes into the chip via electricity must leave via heat transfer. Equate them.

Q= h(c)A (ΔT)

You have Q, you have h, you have A, and you have the coolant temperature. The only part of the above equation you don't have is the surface temperature. That is what you solve for.
 
so would it be

0.3= 150*(5mm*6mm)(T-293)
 
  • #10
and also what is the best/easiest way to re arrange for T?
 
  • #11
Whenever you use an equation you must insure that the units match. Look at the film coefficient of 150 watts/m^2-K. But you are plugging millimeters into the equation.

You can use the 20 C directly because 1 degree change in C is 1 degree change in K.
 
  • #12
What class are you taking?
 
  • #13
Thank you, and also what is the best/easiest way to re arrange for T? I always struggle trying to figure this out!
 
  • #14
You have

A = B*(C*D)*(X - E) where A,B,C,D, and E are constants.

X = A/(B*C*D) + E

You should know this. If you plan to continue in the sciences, you will certainly see much more of this and other equations that are considerably more complicated. This is trivial.
 

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