Question

11) An isothermal flat plate is subjected to uniform flow as shown below. Using the properties and the illustration, determine the following: a) What is the heat flux at x1 (8 Points) b) What is the heat flux at x2 (8 Points) c) A temperature profile of T(x,y) = (5x2 + 3x + 8)*y is proposed for this plate. Is this a valid temperature profile for the illustrated case with constant thermophysical properties (not changing with respect to varying temperature)? You must provide a short but accurate explanation for why or why not for full credit. (4 points) U.., X1 Constant Surface Temperature, T X2 L Pr K Р External Fluid operty Value 0.72 0.02 W/(m-K) 1.2 kg/m3 1.18 x 105 Pa-sec 1000 J/(kg-K) 1.0 m/sec 350 K 300 K M с U.. TS To L 10 m X1 X1 1 m 9 m

Answer 1

I have solved problem using basic concept of heat transfer and fluid mechanics.Each concept and step with proper reason is explained.Go through complete solution step by step and if u find it helpful then hit thumbs up and share feedback. Thanks

the Solution - This problem is bext upon concept of Heat trasffer and Heid mechanics ما ما مليوN Here How is taking place condition 7 plate When it happent x isothermal Plate Xz than layer of (To) + fluid stick to the surface of plate And if Ip To heat fronefer take place from plate to the fluid Firet heat conducted through adhered layer of fluid & then convention to next Huid layers. التیا a By making on assumption that at distance temperature profile in . fluid it I ((x,y) 9 바 Temperature gradient in adhered layer of fluid ОТ. 24

heat transfer to fluid 00 plate at from 07 = heat conducted through adhered loyer of fluid by fluid by no clip condition. o = -KASI Kafleid conductivity Tyto A = plate Area fordo. length Hux O q=k at sy 430 heat flux سلیم x = 4 әТ. -k. q= he yo & X=x, K i ong w/mk (given) q= o'oq dI he yoxd Similarly sit -0.02 DT ex he od=X © parodard temperature profile TCG4) = (5 x² + 3x+8 ) y

OC o let derivate it LOT 5.x2 + 3x+ 8 dy it i Lasly function of il at particular location along plate, profile slope cuill be conxtant. slope = OT independent of heightly) dy which is impossible every fluid particle store heat' heace of heat transfer will go on decreasing; it should be verrying in y direction generally profile 14 of exponential type giren linear ax each 2 come amount T gy but it ferill (مام) دو Or oproctical profile proboxed profile Clinear) teep) (To-Tool To-Toe Antwert G tor ab. pert heat fox = -oo0g at W/m2 dy y=0,2 =24 beat flux = -0.02 DT W/m² Jy y=0, x=X2 I Tyroix