HW-3-key-2012

# HW-3-key-2012 - ChE 306 HW-3 Solution(2012 PROBLEM 4.5...

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

ChE 306 HW-3 Solution (2012) PROBLEM 4.5 KNOWN: Boundary conditions on four sides of a rectangular plate. FIND: Temperature distribution. SCHEMATIC: ANALYSIS: This problem differs from the one solved in Section 4.2 only in the boundary condition at the top surface. Defining θ = T – T , the differential equation and boundary conditions are g G ± g G ² ³ g G ± G µ u U¶u·¸¹ µ u U¶º·¸¹ µ u U¶»·u¹ µ u ¼ ½¾ ½¿ À ¿ÁÂ µ Ã Ä Å (1 a, b, c, d) The solution is identical to that in Section 4.2 through Equation (4.11), U µ Æ Ç È ÉÊË ÈÌÍ Î ÉÊËÏ ÈÌÐ Î Ñ ÈÁÒ (2) To determine C n , we now apply the top surface boundary condition, Equation (1d). Differentiating Equation (2) yields ÓU Ó¸ À ¿ÁÂ µ Ô Ç È ÕÖ × ÉÊË ÕÖ² × ØÙÉÏ ÕÖÚ × Ñ ÈÁÒ ¶Û¹ Substituting this into Equation (1d) results in Ã Ä Å Ü µ Ô Ý È ÉÊË ÕÖ² × Ñ ÈÁÒ where A n = Ç È ¶ÕÖÞ×¹ØÙÉÏ¶ÕÖÚ × ß ¹ . The principles expressed in Equations (4.13) through

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

View Full Document
(4.16) still apply, but now with reference to Equation (4) and Equation (4.14), we should choose f(x) = g G u ±U ² ³ ´ µ¶· ¸ ¹º» ´¼½ ¾ ¿ ½ . Equation (4.16) then becomes À ´ ¸ g G u ± Á ¹º» ÂÃÄ Å ¿ ½ ¾ Æ Á ¹º» Ç ÂÃÄ Å ¾ Æ ¿ ½ ¸ g G u ±Ã ÈµÉÊ· ´ËÌ Í Ê Â Thus Î ´ ¸ È Ï ÐÑ u Ò µÓÌ· ÔÕÖ ËÌ ´ × ¼ ØÙÚÛ × µ´¼Ü ¾ ² · (5) The solution is given by Equation (2) with C n defined by Equation (5). PROBLEM 4.39 KNOWN: Plane surface of two-dimensional system. FIND: The finite-difference equation for nodal point on this boundary when (a) insulated; compare result with Eq. 4.42, and when (b) subjected to a constant heat flux.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern