[cfdonline10]

Assume that there a flat oval tube (thickness T1) of 50 mm width (W1)and 8 mm height (H1)with water flowing at a rate of 2.5 liters/min. Directly below this tube, there a plate (thickness T2) of width of 35 mm (W2). I want to come up with thermal resistance for this assuming there is heat source directly below plate.
Method 1:
Direct HT Resistance = r1=(T2/(K2 *A2) +T1/(K1*A1)+ 1/(hA))
Note that here, A2=A1=A=W2*length
The remaining portion of oval tube has (behave line fins) a length of S= (W2/2) (top of oval tube) + H2 +(W2-W1)/2 on left side and the same on the right side. Assume that entire plate and tube is adiabatic.
Parallel resistance is r2 =1/(Fineff*S*T2). Where Fineff =tanh (m*S)/(m*S)
Now we can find equivalent R using 1/R = 1/R1 + 1/R2
Method 2:
Area of oval tube At= 2*(W1+H1)*L
Total resistance =(T2/(K2 *A2) +T1/(K1*A1)+ 1/(hAt))
Which one is more accurate? Any suggestion or refrerences?
Thanks

[ryaron]

Originally Posted by cfdonline10

Assume that there a flat oval tube (thickness T1) of 50 mm width (W1)and 8 mm height (H1)with water flowing at a rate of 2.5 liters/min. Directly below this tube, there a plate (thickness T2) of width of 35 mm (W2). I want to come up with thermal resistance for this assuming there is heat source directly below plate.
Method 1:
Direct HT Resistance = r1=(T2/(K2 *A2) +T1/(K1*A1)+ 1/(hA))
Note that here, A2=A1=A=W2*length
The remaining portion of oval tube has (behave line fins) a length of S= (W2/2) (top of oval tube) + H2 +(W2-W1)/2 on left side and the same on the right side. Assume that entire plate and tube is adiabatic.
Parallel resistance is r2 =1/(Fineff*S*T2). Where Fineff =tanh (m*S)/(m*S)
Now we can find equivalent R using 1/R = 1/R1 + 1/R2
Method 2:
Area of oval tube At= 2*(W1+H1)*L
Total resistance =(T2/(K2 *A2) +T1/(K1*A1)+ 1/(hAt))
Which one is more accurate? Any suggestion or refrerences?
Thanks

What are the ratios of the conductivities ?
i.e. k1/k2 ?
Here's a quick answer:
make two dimensionless parameters epsilon=k1/k2 and eta characteristic length tube/characteristic length plate, make sure they are << 1.

Denote them as epsilon and eta.
Now expand both expression you've written in powers of epsilon and eta.
The one with the higher order O(epsilon^n), O(eta^n) is the more accurate.