Burstsort - Revision history

en>Mattbierner: fixed dead burstsort4j link

2014-08-04T19:44:14Z

fixed dead burstsort4j link

← Older revision		Revision as of 21:44, 4 August 2014
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	~~The '''Number of Transfer Units (NTU) Method''~~' is ~~used to calculate the rate of [[heat transfer]] in [[heat exchangers]] (especially [[Countercurrent exchange\|counter current]] exchangers) when there~~ is insufficient information to calculate the [[Log mean temperature difference\|Log-Mean Temperature Difference]] (LMTD). In heat exchanger analysis, if the fluid inlet and outlet temperatures are specified or can be determined by simple energy balance, the LMTD method can be used; but ~~when these temperatures are not available '''The NTU''' or '''The Effectiveness''' method is used.~~		Friends call her Felicidad and her husband doesn't like it at all. Kansas is where her house is but she needs to transfer because of her family. To perform croquet is the hobby I will by no means quit performing. My job is a manufacturing and distribution officer and I'm performing pretty good monetarily.<br><br>Here is my web site; extended car warranty - [http://user462.cp.Isp169.com/?document_srl=148855 This Internet page],

	~~To define the effectiveness of a heat exchanger we need~~ to ~~find the maximum possible heat~~ transfer ~~that can be hypothetically achieved in a counter-flow heat exchanger~~ of ~~infinite length~~. ~~Therefore one fluid will experience the maximum possible temperature difference, which~~ is the ~~difference of <math> \ T_{h,i}- \ T_{c,i} </math> (The temperature difference between the inlet temperature of the hot stream and the inlet temperature of the cold stream). The method proceeds~~ by ~~calculating the [[heat capacity rate]]s (i.e~~. mass flow rate multiplied by [[specific heat capacity\|specific heat]]) <math> \ C_h</math> and <math> \ C_c</math> for the hot and cold fluids respectively, and denoting the smaller one as <math> \ C_{min}</math>. The reason for selecting smaller heat capacity rate is to include maximum ''feasible'' heat transfer among the working fluids during calculation.

	~~A quantity:~~

	~~:<math>q_{max}\ = C_{min} (T_{h,i}-T_{c,i})</math>~~

	is then found,where <math> \ q_{max}</math> is the maximum heat that could be transferred between the fluids. According to the above equation, to experience the maximum heat transfer the heat capacity should be minimized since we are using the maximum possible temperature difference. This justifies the use of <math> \ C_{min} </math> in the equation.

	~~The ''effectiveness(E)'', is the ratio between the actual heat transfer rate and the maximum possible heat transfer rate:~~

	~~:<math>E \ = \frac{q}{q_{max}}</math>~~

	~~where:~~

	~~:<math>q \ = C_h (T_{h,i} -T_{h,o})\ = C_c (T_{c,o} - T_{c,i})</math>~~

	~~Effectiveness is dimensionless quantity between 0 and 1. If we know E for~~ a ~~particular heat exchanger,~~ and ~~we know the inlet conditions of the two flow streams we can calculate the amount of heat being transferred between the fluids by:~~

	~~:<math>q \ = E C_{min} (T_{h,i} -T_{c,i})</math>~~

	~~For any heat exchanger it can be shown that:~~

	~~:<math>\ E = f ( NTU,\frac{C_{min}} {C_{max}}) </math>~~

	~~For a given geometry, <math> \ E</math> can be calculated using correlations in terms of the "heat capacity ratio"~~

	~~:<math>C_r \ = \frac{C_{min}}{C_{max}}</math>~~

	and ~~the~~ '~~'number of transfer units'',~~ <~~math~~> ~~\ NTU~~<~~/math>~~

	~~:<math>NTU \ = \frac{U A}{C_{min}}</math>~~

	~~:where <math> \ U </math~~> is ~~the overall heat transfer coefficient and <math> \ A</math> is the heat transfer area.~~

	~~For example, the effectiveness of a parallel flow heat exchanger is calculated with:~~

	~~:<math> E \ = \frac {1~~ - ~~\exp~~[~~-NTU(1 + C_{r})]}{1 + C_{r}} </math>~~

	~~Or the effectiveness of a counter-current flow heat exchanger is calculated with:~~

	:~~<math> E \ = \frac {1 - \exp[-NTU(1 - C_{r})]}{1 - C_{r}\exp[-NTU(1 - C_{r})]} </math>~~

	~~For <math> C_r \ = 1 <~~/~~math>~~

	~~:<math> E\ = \frac{NTU}{1+NTU} <~~/~~math>~~

	~~Similar effectiveness relationships can be derived for concentric tube heat exchangers and shell and tube heat exchangers~~. These relationships are differentiated from one another depending on the type of the flow (counter-current, concurrent, or cross flow), the number of passes (in shell and tube exchangers) and whether a flow stream is mixed or unmixed.

	~~Note that the <math> C_r \ = 0 </math> is a special case in which phase change [[condensation]] or [[evaporation]] is occurring in the heat exchanger~~. ~~Hence in this special case the heat exchanger behavior is independent of the flow arrangement. Therefore the effectiveness is given by:~~

	~~:<math> E \ = 1 - \exp[-NTU] <~~/~~math>~~

	=~~= References ==~~

	* [[Frank P. Incropera\|F. P. Incropera]~~] & D. P. DeWitt 1990 ''Fundamentals of Heat and Mass Transfer'', 3rd edition, pp. 658–660. Wiley, New York~~
	* F. P. Incropera, D. P. DeWitt, ~~T. L. Bergman & A. S. Lavine 2006 ''Fundamentals of Heat and Mass Transfer '',6th edition, pp 686–688. John Wiley & Sons US~~

	~~[[Category:Heat transfer]]~~

en>Gareth Jones: remove bold typeface, put reference inline

2014-02-01T12:31:59Z

remove bold typeface, put reference inline

← Older revision		Revision as of 14:31, 1 February 2014
Line 1:		Line 1:
	The ~~author~~ is ~~known as Araceli Gulledge~~. ~~He currently life~~ in ~~Idaho~~ and ~~his mothers~~ and ~~[http:~~//~~www~~.~~Carbuyingtips~~.~~com~~/~~warranty~~.~~htm fathers live] close by~~. ~~The factor I adore most bottle tops gathering and now I have time~~ ~~auto warranty to consider on new things~~. ~~Interviewing~~ is ~~what she [http~~://~~greenshelters~~.~~net~~/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/60/~~userId~~/~~96426/Default.aspx car warranty] does in~~ ~~[http~~://~~www~~.~~thelamda.com~~/~~index.php?mod~~=~~users&action=view&id=3598 extended auto warranty~~] ~~her working day~~ [~~http~~:/~~/Www~~.~~aaautowarranty.com/ auto warranty] occupation but quickly her husband~~ and ~~her will begin their own company~~.<br><br>~~Here~~ is ~~my weblog~~ [~~http~~:/~~/Bytmann~~.~~com/UserProfile/tabid/849/userId/131801/language/en-~~US~~/Default.aspx extended car warranty~~]		The '''Number of Transfer Units (NTU) Method''' is used to calculate the rate of [[heat transfer]] in [[heat exchangers]] (especially [[Countercurrent exchange\|counter current]] exchangers) when there is insufficient information to calculate the [[Log mean temperature difference\|Log-Mean Temperature Difference]] (LMTD). In heat exchanger analysis, if the fluid inlet and outlet temperatures are specified or can be determined by simple energy balance, the LMTD method can be used; but when these temperatures are not available '''The NTU''' or '''The Effectiveness''' method is used.

			To define the effectiveness of a heat exchanger we need to find the maximum possible heat transfer that can be hypothetically achieved in a counter-flow heat exchanger of infinite length. Therefore one fluid will experience the maximum possible temperature difference, which is the difference of <math> \ T_{h,i}- \ T_{c,i} </math> (The temperature difference between the inlet temperature of the hot stream and the inlet temperature of the cold stream). The method proceeds by calculating the [[heat capacity rate]]s (i.e. mass flow rate multiplied by [[specific heat capacity\|specific heat]]) <math> \ C_h</math> and <math> \ C_c</math> for the hot and cold fluids respectively, and denoting the smaller one as <math> \ C_{min}</math>. The reason for selecting smaller heat capacity rate is to include maximum ''feasible'' heat transfer among the working fluids during calculation.

			A quantity:

			:<math>q_{max}\ = C_{min} (T_{h,i}-T_{c,i})</math>

			is then found,where <math> \ q_{max}</math> is the maximum heat that could be transferred between the fluids. According to the above equation, to experience the maximum heat transfer the heat capacity should be minimized since we are using the maximum possible temperature difference. This justifies the use of <math> \ C_{min} </math> in the equation.

			The ''effectiveness(E)'', is the ratio between the actual heat transfer rate and the maximum possible heat transfer rate:

			:<math>E \ = \frac{q}{q_{max}}</math>

			where:

			:<math>q \ = C_h (T_{h,i} -T_{h,o})\ = C_c (T_{c,o} - T_{c,i})</math>

			Effectiveness is dimensionless quantity between 0 and 1. If we know E for a particular heat exchanger, and we know the inlet conditions of the two flow streams we can calculate the amount of heat being transferred between the fluids by:

			:<math>q \ = E C_{min} (T_{h,i} -T_{c,i})</math>

			For any heat exchanger it can be shown that:

			:<math>\ E = f ( NTU,\frac{C_{min}} {C_{max}}) </math>

			For a given geometry, <math> \ E</math> can be calculated using correlations in terms of the "heat capacity ratio"

			:<math>C_r \ = \frac{C_{min}}{C_{max}}</math>

			and the ''number of transfer units'', <math> \ NTU</math>

			:<math>NTU \ = \frac{U A}{C_{min}}</math>

			:where <math> \ U </math> is the overall heat transfer coefficient and <math> \ A</math> is the heat transfer area.

			For example, the effectiveness of a parallel flow heat exchanger is calculated with:

			:<math> E \ = \frac {1 - \exp[-NTU(1 + C_{r})]}{1 + C_{r}} </math>

			Or the effectiveness of a counter-current flow heat exchanger is calculated with:

			:<math> E \ = \frac {1 - \exp[-NTU(1 - C_{r})]}{1 - C_{r}\exp[-NTU(1 - C_{r})]} </math>

			For <math> C_r \ = 1 </math>

			:<math> E\ = \frac{NTU}{1+NTU} </math>

			Similar effectiveness relationships can be derived for concentric tube heat exchangers and shell and tube heat exchangers. These relationships are differentiated from one another depending on the type of the flow (counter-current, concurrent, or cross flow), the number of passes (in shell and tube exchangers) and whether a flow stream is mixed or unmixed.

			Note that the <math> C_r \ = 0 </math> is a special case in which phase change [[condensation]] or [[evaporation]] is occurring in the heat exchanger. Hence in this special case the heat exchanger behavior is independent of the flow arrangement. Therefore the effectiveness is given by:

			:<math> E \ = 1 - \exp[-NTU] </math>

			== References ==

			* [[Frank P. Incropera\|F. P. Incropera]] & D. P. DeWitt 1990 ''Fundamentals of Heat and Mass Transfer'', 3rd edition, pp. 658–660. Wiley, New York
			* F. P. Incropera, D. P. DeWitt, T. L. Bergman & A. S. Lavine 2006 ''Fundamentals of Heat and Mass Transfer '',6th edition, pp 686–688. John Wiley & Sons US

			[[Category:Heat transfer]]

en>Profetylen at 13:43, 16 December 2011

2011-12-16T13:43:38Z

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