Thermodynamics: Control Volume flow through radiatior

In summary: It's all just a guess since this problem is flawed anyway.In summary, the problem involves calculating the temperature of air as it leaves a car radiator based on given values for air and water flow rates and temperatures. The equations used include an energy balance for air and water, assuming ideal gas behavior for air and standard conditions for pressure. The specific volume and mass flow rate of air are calculated using the ideal gas equation, and the change in enthalpy is determined using the specific heat at constant pressure. However, due to inconsistencies in the given values, the results may not be accurate.
  • #1
aznkid310
109
1

Homework Statement



Air enters a car radiator at 50 km/hr, 25 C. The radiator is 1 m2 facial area. 2 kg/s of water enters the radiator from the engine at 10 bar, 200 C and leaves at 10 bar, 180 C. What is the temperature of the air as it leaves the radiator?

Homework Equations



I did an energy balance for air and then for water, but I am not sure which terms can be ignored. After i obtain these eqns, i can set them equal to each other and solve for T (from
Q =m(c_p)(Change in T))?

The Attempt at a Solution



For Air: W = Q + (m)(h_in + [(v_in)^2]/2 +g*z_in - h_out - [(v_out)^2]/2 -g*z_out)

m = mass flow rate
Q = heat flow rate
W = work flow rate
h = enthalpy
v = velocity

I assume W, z_in, z_out are zero and also that m_in = m_out

So i get Q = m(h_in - h_out + [(v_in)^2]/2)

For water:

Q = m(h_out - h_in) = (0.2)(762.8 - 2827.9) = -2065.1 kW
 
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  • #2
Hi aznkid. You've almost got it. On the right track anyway.

The problem gives you air velocity into the radiator but not out of the radiator. From that I'd simply assume the velocity out is equal to the velocity in, so your velocity terms in your equation:
Q = m(h_in - h_out + [(v_in)^2]/2)
also drop out and you're left with the change in enthalpy for the air.

Now the only part of the problem you really haven't resolved is how to determine mass flow rate of air. How do you think you can determine mass flow rate of air? Note the variables you're given:
- Velocity
- cross sectional area
- Inlet temp
 
  • #3
Can i assume its an ideal gas?

Then i can use the ideal gas eqn to get specific volume v: pv = RT, where R = 8.314/MW

Next, m = VA/v [(velocity*area)/specific volume]?
 
  • #4
aznkid310 said:
Can i assume its an ideal gas?

Then i can use the ideal gas eqn to get specific volume v: pv = RT, where R = 8.314/MW

Next, m = VA/v [(velocity*area)/specific volume]?

You sure can.
 
  • #5
You can assume ideal gas in order to calculate specific volume, or just look up density for air at standard conditions.
 
  • #6
So can i assume standard air pressure of 101.325 kPa?

Then once i find Q, i can use Q = mc(change in T) to find T?

What would my c be?
 
  • #7
aznkid310 said:
So can i assume standard air pressure of 101.325 kPa?
Sure... If they don't give you atmospheric pressure, just assume it's standard conditions.

aznkid310 said:
Then once i find Q, i can use Q = mc(change in T) to find T?

What would my c be?
I think you're asking whether to use Cv or Cp.

Consider it this way.

mCp(dT) calculates a change in enthalpy.

mCv(dT) calculates a change in internal energy.

Do you know which one is applicable here?
 
  • #8
Since it's constant pressure, would it be C_p?

v = RT/p = (8.314)(298)/(101.325) = 0.8458 m^3/g = 845.8 m^3/kg

m = (13.89 m/s)(1 m^2) / (845.8 m^3/kg) = 0.0164 kg/s

Then Q = m*c_p*(T_2 - T_1), where Q = 2065.1 kW (from h20 calculated before)

2065.1 kW = (0.0164 kg/s)*(1.005 kJ/kg k)*(T_2 -298K)

T_2 = 125592.26 K

This seems wrong
 
Last edited:
  • #9
For water at 10 barg, saturation temp is 184 C which means the water is going in superheated and coming out subcooled.

For water at 10 bara, saturation temp is 179.4 C which means the water is going in and coming out superheated.

Let me guess... this problem was made up by a grad student, right? lol

Let's just assume the person that created this problem meant for the water to be liquid in and out. I'll use 170 C inlet and 150 C outlet at 10 barg.. You should get an energy removal of roughly 177 kW. (or 237 hp) so the power removed his HUGE. A very large truck might approach this much heat rejection at full tilt, but that’s way more than a car.

Also, I’m getting an air mass flow rate of 16.5 kg/s and an outlet temperature of roughly 35.7 C.

Give it another shot.
 
  • #10
Was there a particular reason you chose 170C and 150C?
 
  • #11
aznkid310 said:
Was there a particular reason you chose 170C and 150C?
um... yea. because it's less than the saturation pressure of water at 10 barg, and because specific heat is roughly constant over the range of pressure and temperature you're looking at so I would want to maintain the 20 degree C dT.
 

Related to Thermodynamics: Control Volume flow through radiatior

What is thermodynamics?

Thermodynamics is the branch of science that deals with the relationship between heat, energy, and work. It studies how energy is transferred between different forms and how it affects the properties of matter.

What is a control volume?

A control volume is an imaginary boundary that encloses a specific region of space in which mass, energy, and momentum can be analyzed. It is commonly used to study the flow of fluids or gases through a system.

How does heat transfer through a radiator?

Heat transfer through a radiator occurs through a process called convection. As hot water or steam flows through the tubes of a radiator, it transfers heat to the metal fins, which then transfer the heat to the surrounding air. The warm air rises and is replaced by cooler air, creating a convection current that allows for efficient heat transfer.

What is the purpose of a radiator in a thermodynamic system?

The purpose of a radiator in a thermodynamic system is to transfer heat from one medium (such as hot water or steam) to another medium (such as air) to regulate the temperature of the system. This is essential in maintaining the efficiency and functionality of many industrial and mechanical processes.

What factors affect the flow through a radiator?

The flow through a radiator can be affected by several factors, such as the temperature difference between the hot and cold mediums, the surface area and design of the radiator, the flow rate of the fluid, and the properties of the fluids involved (such as viscosity and density).

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