# ch03 - PROBLEM 3.1 KNOWN: One-dimensional, plane wall...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PROBLEM 3.1 KNOWN: One-dimensional, plane wall separating hot and cold fluids at T and T ,1 ,2 , respectively. FIND: Temperature distribution, T(x), and heat flux, q x , in terms of T T h ,1 ,2 1 , , , h 2 , k and L. SCHEMATIC: ASSUMPTIONS: (1) One-dimensional conduction, (2) Steady-state conditions, (3) Constant properties, (4) Negligible radiation, (5) No generation. ANALYSIS: For the foregoing conditions, the general solution to the heat diffusion equation is of the form, Equation 3.2, ( ) 1 2 T x C x C . = + (1) The constants of integration, C 1 and C 2 , are determined by using surface energy balance conditions at x = 0 and x = L, Equation 2.23, and as illustrated above, ( ) ( ) 1 , 1 2 , 2 x=0 x=L dT dT k h T T 0 k h T L T . dt dx = = (2,3) For the BC at x = 0, Equation (2), use Equation (1) to find ( ) ( ) 1 1 , 1 1 2 k C h T C C + = + (4) and for the BC at x = L to find ( ) ( ) 1 2 1 2 , 2 k C h C L C T . + = + (5) Multiply Eq. (4) by h 2 and Eq. (5) by h 1 , and add the equations to obtain C 1 . Then substitute C 1 into Eq. (4) to obtain C 2 . The results are ( ) ( ) ,1 ,2 ,1 ,2 1 2 , 1 1 1 2 1 2 T T T T C C T 1 1 L 1 1 L k h h h k h h k = = + + + + + ( ) ( ) ,1 ,2 ,1 1 1 2 T T x 1 T x T . k h 1 1 L h h k = + + + + < From Fouriers law, the heat flux is a constant and of the form ( ) ,1 ,2 x 1 1 2 T T dT q k k C . dx 1 1 L h h k = = = + + + < PROBLEM 3.2 KNOWN: Temperatures and convection coefficients associated with air at the inner and outer surfaces of a rear window. FIND: (a) Inner and outer window surface temperatures, T s,i and T s,o , and (b) T s,i and T s,o as a function of the outside air temperature T ,o and for selected values of outer convection coefficient, h o . SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional conduction, (3) Negligible radiation effects, (4) Constant properties. PROPERTIES: Table A-3 , Glass (300 K): k = 1.4 W/m K. ANALYSIS: (a) The heat flux may be obtained from Eqs. 3.11 and 3.12, ( ) ,i ,o 2 2 o i 40 C 10 C T T q 1 L 1 1 0.004 m 1 h k h 1.4 W m K 65 W m K 30 W m K = = + + + + ( ) 2 2 50 C q 9 6 8 W m 0.0154 0.0029 0.0333 m K W = = + + . Hence, with ( ) i , i , o q h T T = , the inner surface temperature is 2 s,i ,i 2 i q 9 6 8 W m T T 40 C 7.7 C h 30 W m K = = = < Similarly for the outer surface temperature with ( ) o s,o ,o q h T T = find 2 s,o ,o 2 o q 9 6 8 W m T T 10 C 4.9 C h 65 W m K = = = < (b) Using the same analysis, T s,i and T s,o have been computed and plotted as a function of the outside air...
View Full Document

## This note was uploaded on 11/02/2009 for the course CHEM 378 taught by Professor Corti during the Spring '09 term at Purdue University-West Lafayette.

### Page1 / 225

ch03 - PROBLEM 3.1 KNOWN: One-dimensional, plane wall...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online