Heat Transfer - Viscosity questions

[weeman203]

Homework Statement

I do not need to solve this problem, see below.
EXAMPLE 7.1
Air at a pressure of 6kN/m2 and a temperature of 300C flows with a velocity of 10m/s over a flat plate 0.5m long. Estimate the cooling rate per unit width of the plate needed to maintain it at a surface temperature of 27C.

Homework Equations

Kinematic viscosity

The Attempt at a Solution

My question is about the very first/second step, I have attached pictures showing the example problem and the table A4 from the back of the book.
1. How did they decide on the temperature 437K to use in the table.
2. And why is the viscosity 10^-6? Not 10^6?
3. I see that the description mentions something about the inverse viscosity, can anyone elaborate a little about that?
4.Last question is on the 3rd image it shows the Reynolds number is ~9000, isn't that a turbulent flow, but they say its laminar? According to wikipedia laminar flow is less than 2000 correct?

Thanks for any help, I just want to understand the concepts going on. No need to solve the problem.

 

[Chestermiller]

Homework Statement

I do not need to solve this problem, see below.
EXAMPLE 7.1
Air at a pressure of 6kN/m2 and a temperature of 300C flows with a velocity of 10m/s over a flat plate 0.5m long. Estimate the cooling rate per unit width of the plate needed to maintain it at a surface temperature of 27C.

Homework Equations

Kinematic viscosity

The Attempt at a Solution

My question is about the very first/second step, I have attached pictures showing the example problem and the table A4 from the back of the book.
1. How did they decide on the temperature 437K to use in the table.

I have no idea. Maybe they meant 200 C in the problem statement insteady of 200 C, in which case the temperature would be 473K.

2. And why is the viscosity 10^-6? Not 10^6?

Look at the heading at the top of the column. It says $10^6\nu$. That means that each of the numbers in the table has been obtained by multiplying the actual $\nu$ value by $10^6$

3. I see that the description mentions something about the inverse viscosity, can anyone elaborate a little about that?

It says that the kinematic viscosity of a gas is inversely proportional to the pressure. Do you know what this means mathematically? What pressure do the values in the table apply to?

4.Last question is on the 3rd image it shows the Reynolds number is ~9000, isn't that a turbulent flow, but they say its laminar? According to wikipedia laminar flow is less than 2000 correct?

The laminar-turbulent transition depends on the specific geometry. The value of 2000 corresponds to flow in a tube. The critical Re for flow over a flat plate is much larger. Why don't you research it an get back with us?

 

[weeman203]

Thanks for the help!

It says that the kinematic viscosity of a gas is inversely proportional to the pressure. Do you know what this means mathematically? What pressure do the values in the table apply to?

Well viscosity increases with an increase in pressure. Based on the equation for kinematic viscosity, kviscosity=viscosity/density, if viscosity and pressure are both increasing, shouldn't the kinematic viscosity be increasing as well?

The laminar-turbulent transition depends on the specific geometry. The value of 2000 corresponds to flow in a tube. The critical Re for flow over a flat plate is much larger. Why don't you research it an get back with us?

OK got it, pretty simple. Re for turbulent flow over a flat plate is 10^8.

 

[Chestermiller]

Thanks for the help!

Well viscosity increases with an increase in pressure. Based on the equation for kinematic viscosity, kviscosity=viscosity/density, if viscosity and pressure are both increasing, shouldn't the kinematic viscosity be increasing as well?

For an ideal gas (and for real gases at low pressures), viscosity is independent of pressure (see Transport Phenomena, Bird, Stewart, and Lightfoot, Chapter 1) and density is proportional to pressure. So kinematic viscosity is inversely proportional to pressure.

 

[Thanh Nguyen Duc]

1. How did they decide on the temperature 437K to use in the table.
In analyzing the convection heat transfer over a plate you should have the "reference temperature" to look up, or calculate, the fluid properties such as viscosity, density, and also the thermal conductivity. Here they choose the "film temperature" to be the reference, and the film temperature is defined as the arithmetic mean of fluid temperature (573K) and the contact surface temperature (isotherm at 300K).
(573K + 300K) / 2 should yield 436.5K ~ 437K just to ignore the decimal digit.

 

[Chestermiller]

The properties need to be evaluated at an average film temperature to approximate the heat transfer coefficient. They based their calculation on the arithmetic average film temperature. It's a judgment call.