Lecture Objectives:

• Discuss HW3

• Introduce alternative conduction equation solution method

• Present a commercial software

eQUEST and define basic modeling

steps

Homework 3 (Similar to HW2, but unsteady, and more realistic)

East

10 m 10 m

2.5 m

North

Tair_in

IDIR

Idif

Glass

Tinter_surf ≠ Tair

Teast_i

Teast_o

Tnorth_i Tnorth_oi

Tair_out

ConcreteIDIRIdif

Surface radiation

Surfaceradiation

Top view

Insulation

Alternative: Response function methods for conduction calculation

NOTATION: θ(x,t)=T(x,)

Ts

0

T

-L / 2 L /2

h

h

h

To

T

h omogenous wa ll

L = 0.2 mk = 0 . 5 W/ m Kc = 9 20 J/kgK

= 120 0 k g/mp

2

Laplace transformation

Laplace transform is given by

Where p is a complex number whose real part is positive and large enough to cause the integral to converge.

Laplace transformation table

Principles of Response function methods

The basic strategy is to predetermine the response of a system to some unit excitation relating to the boundary conditions anticipated in reality.

Reference:

JA Clarkehttp://www.esru.strath.ac.uk/Courseware/Class-16458/or http://www.hvac.okstate.edu/research/documents/iu_fisher_04.pdf

Response functions

• Computationally inexpensive

• Accuracy ?

• Flexibility ????What if we want to calculate the moisture transport and we need to know temperature distribution in the wall elements?

Modeling

Modeling

Modeling

Modeling 1) External wall (north) node

2) Internal wall (north) node

Qsolar=solar·(Idif+IDIR) A

Qsolar+C1·A(Tsky4 - Tnorth_o

4)+ C2·A(Tground4 - Tnorth_o

4)+hextA(Tair_out-Tnorth_o)=Ak/(Tnorth_o-Tnorth_in)

C1=sky·surfacelong_wave··Fsurf_sky

Qsolar_to int surf =portion of transmitted solar radiation that is absorbed by internal surface

C3A(Tnorth_in4- Tinternal_surf

4)+C4A(Tnorth_in4- Twest_in

4)+ hintA(Tnorth_in-Tair_in)= =kA(Tnorth_out--Tnorth_in)+Qsolar_to_int_ considered _surf

C3=niort_in··north_in_to_ internal surface for homework assume ij Fiji

transmitedtotalsolarsurfconsideredenvelopetotalsurfconsideredernaLsurfconsideredtosolar QAAQ ___int_int____int_int___ )/(

A- wall area [m2]- wall thickness [m]k – conductivity [W/mK] - emissivity [0-1]- absorbance [0-1] = - for radiative-gray surface,sky=1, ground=0.95Fij – view (shape) factor [0-1]h – external convection [W/m2K]s – Stefan-Boltzmann constant [5.67 10-8 W/m2K4]

C2=ground·surfacelong_wave··Fsurf_ground

Matrix equation

M × t = f

for each time step

b1T1 + +c1T2

+=f(Tair,T1,T2

)

a2T1 + b2T2

+ +c2T3+=f(T1

,T2, T3

)

a3T2 + b3T3

+ +c3T4+=f(T2

,T3 , T4

)

a6T5 + b6T6

+ =f(T5 ,T6

, Tair)

………………………………..

M × t = f

Modeling

Modeling

Modeling steps

• Define the domain

• Analyze the most important phenomena and define the most important elements

• Discretize the elements and define the connection

• Write the energy and mass balance equations

• Solve the equations (use numeric methods or solver)

• Present the result

eQUEST

• Energy simulation software – Free: http://doe2.com/equest/– Graphical user interface (GUI) that uses DOE2– Easy to use it– Example of your HW1a

• ….