Re: [TRNSYS-users] Mistake in Type 19 conduction input wall?

[Charron, Rémi <remi.charron@nrcan.gc.ca>]

Thanks Diego,

I was mistaken, and your response helped clarify how the equations for conduction input wall works.  I believe the reason you need to use equivalent temperatures comes from the energy balance:  
Q_i  + A*s = A*h_c*(T_s,i - T_z) + A*h_r_ij*(T_s,i - T_s,j)

You can solve the above equation for Q_i as follows:

Q_i=A*h_c*(T_S,i-T_eq)

so you would need to pass T_eq to the program that calculates Q_i for the above energy balance to work.

Rémi

-----Original Message-----
From: Diego A. Arias
To: Charron, Rémi
Cc: trnsys-users@engr.wisc.edu
Sent: 03/05/2006 8:58 PM
Subject: Re: [TRNSYS-users] Mistake in Type 19 conduction input wall?

Hi Rémi,

I do not think that there is an error.  The formulation of the 
conductive heat transfer in Type 19 is the result of an energy balance 
on surface i, as follows:

Energy in: 
- Q_i :  Conductive heat transfer
- A*s : Radiation absorption on the surface (absorption of solar
radiation)
Energy out:
- A*h_c*(T_s,i - T_z) : convective heat transfer to the zone
- A*h_r_ij*(T_s,i - T_s,j) : radiation exchange between surface i and 
surface j, using a linearized radiation coefficient. (For simplicity, 
let's assume that there are only two surfaces, i and j)

Energy balance yields:
Q_i  + A*s = A*h_c*(T_s,i - T_z) + A*h_r_ij*(T_s,i - T_s,j)
You can rearrange these terms as:
(Q_i/A + s)/h_c = (1 + h_r_ij/h_c )*T_s,i - h_r_ij/h_c*T_s,j - T_z

This equation is written in matrix form in equations 5.7.3.19 - 
5.7.3.22.  I guess that the confusion is given by the second part of the

paragraph, where it explains that Q_i should be evaluated using T_eq.  I

have to admit that I am not entire sure of this: if Q_i only has 
conductive heat transfer through the wall, you would only need the 
actual temperatures on the surfaces to calculate it. 
I will appreciate the comments from the experts on this list.
Best regards,

Diego

Charron wrote:
> Hello,
>
> I believe there is a mistake in the formulation of the conduction
input wall for Trnsys Type 19, can someone confirm?
>
> Equation 4.8.3.22 in the manual states that X_i=(Q_i/A_i +s_i)/hc_i
for conduction input walls and that the equivalent temperature should be
used in calculating Qi or else the effects of absorption of radiation on
the inside surface would not be correctly accounted for.  
>
> Equivalent temperature includes effects of s_i and the longwave
radiation from other surfaces.  Wouldn't including s_i in equation
4.8.3.22 be double counting of the absorbed radiation on the surface if
T_equivalent is used?  If we use zone temperature instead of equivalent
temperature, the effect of longwave radiation would not be included.
>
> Rémi
>
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-- 

Diego A. Arias
TRNSYS Coordinator
Solar Energy Laboratory
University of Wisconsin - Madison
1500 Engineering Drive
Madison, WI 53706