lecture 23 - Thermal and Fluids Engineering I Lecture 23...

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Thermal and Fluids Engineering I Lecture 23 Page 1 Lecture 23 – Forced Convection in Pipes (cont.) Internal Flow with Constant Wall Temperature Consider convection in a pipe with a constant wall temperature, T w : The first law for an open system is cv ii ee dE QW m h m h dt =− + & & && where h is enthalpy , not heat transfer coefficient. The flow is steady and no work is done, therefore () ei Qm h h & & For an incompressible fluid with constant specific heat pe i cT T & & pm m x xx T +∆ & & wm p m m x hAT T m c T T ∆− = &
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Thermal and Fluids Engineering I Lecture 23 Page 2 If the flow is fully-developed, only T m is a function of x. () wm p m m x xx hP x T T mc T T +∆ ∆− = & Divide by hP x and take the limit as x approaches zero. 0 lim mm pp x m x TT mc mc dT hP x hP dx ∆→ ⎡⎤ ⎢⎥ −= = ⎣⎦ && Separating variables p m mc dT dx hP T T x ⎛⎞ = ⎜⎟ ⎝⎠ & 0 e i T L p m mw T mc dT dx hP T x T = ∫∫ & ln ln ln ew iw mc mc LT T T T hP hP T T −− =− = Since the surface area is length times perimeter, an alternate form is ln p hA m c & exp p hA m c & exp ei w w p hA T T mc + &
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Thermal and Fluids Engineering I Lecture 23 Page 3 The total heat transferred between the wall and the fluid is () pe i Qm cT T =− & & p ei Q mc TT = & & Define iw i T ∆= ew e TTT ( ) p wi we i e QQ mc T T == −− && & Previously, we had ln p hA m c ⎛⎞
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This note was uploaded on 04/08/2008 for the course ENGR 2250 taught by Professor Borca-tasciuc during the Spring '08 term at Rensselaer Polytechnic Institute.

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lecture 23 - Thermal and Fluids Engineering I Lecture 23...

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