Steady State Conduction
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1 ECE309 Intrductin t Thermdynamics and Heat Transfer Spring 005 Tutrial # 7 Steady State Cnductin Prblem 1 Cnsider a naked persn standing in a rm at 0 C with an expsed surface area f 17m The deep bdy temperature f the human bdy is 37 C, and the thermal cnductivity f the human tissue near the skin is abut 03W/(m C) The bdy is lsing heat at a rate f 150W by natural cnvectin t the surrundings Taking the bdy temperature 05cm beneath the skin t be 37 C, determine the skin temperature f the persn and the cnvective heat transfer cefficient t the surrundings Slutin: Step 1: Draw a schematic diagram m Human Bdy T in T s T 0 cnd cnv Step : What t determine? The skin temperature f the persn, T s ; Cnvective heat transfer cefficient, h Step 3: The infrmatin given in the prblem statement Deep bdy temperature, T in 37 C, m temperature, T 0 0 C; Depth beneath the skin L05cm, Expsed surface Area, A17m ; Thermal cnductivity f the human tissue, k03w/(m C); Heat lss rate, 150 W Tutrial # 7 Page 1 f 5
2 ECE309 Intrductin t Thermdynamics and Heat Transfer Spring 005 Step 4: Assumptins Neglect the radiatin heat lss t the surrundings; The temperature wn t change with time(steady prblem) Step 5: Slve It s a ne-dimensin steady heat transfer prcess, and the cnductivity resistance is determined as L 05( cm) cnd 00098( C / W ) ka 03( W / m C) 17( m ) The heat lss is tatal cnd cnv 150 (W) The cnductive heat lss: cnd T cnd Tin Ts cnd Thus, Ts Tin cnd 37( C) 150( W ) 00098( C / W ) cnd The cnvective heat lss t the surrundings is calculated by cnv T cnv Ts T 1 ha S, the cnvective heat transfer cefficient, 0 355( C) h A( T s cnv T 0 ) 17( m 150( W ) ) # (355 0)( C) 569( W / m C) Step 6: Cnclusin statement The skin temperature f the persn will be 355 C and the cnvective heat transfer cefficient is 569 W/(m C) Tutrial # 7 Page f 5
3 ECE309 Intrductin t Thermdynamics and Heat Transfer Spring 005 Prblem As shwn in the figure, steam in a heating system flw thrugh ne side f rectangle plane (10cm*1cm) The plane is maintained at a temperature f 150 C ectangular aluminium ally 04-T6 s [k186 W/(m C)] with a cnstant width f 1cm and thickness f 01cm are attached t the plane The space between every tw adjacent s is 03cm The temperature f the surrunding air is 0 C and the cmbined cnvective heat transfer is 50W/(m C), Determine the verall effectiveness f the ned plane Slutin: Step 1: Draw a schematic diagram W1cm L1cm t01cm s03cm H10cm Step : What t determine? The verall effectiveness f the ned plane, Step 3: The infrmatin given in the prblem statement Tutrial # 7 Page 3 f 5
4 ECE309 Intrductin t Thermdynamics and Heat Transfer Spring 005 Plane surface temperature, T s 150 C, Atmsphere temperature, T 0 0 C; Plane gemetry: H10cm, and W1cm; Fin: cnductivity: k186 W/(m C), length: L1cm, thickness: t01cm, space: s03cm, width: W1cm The cmbined cnvective heat transfer: h50w/(m C) Step 4: Assumptins Neglect the radiatin heat lss t the surrundings; The temperature wn t change with time(steady prblem) Step 5: Slve CASE 1 With s n the plane: The efficiency f the s is determined frm Fig 8-59 t be t # ( L + ) h kt 0001 (001m + m) 50W / m C (186W / m C) (0001m) 016 which gives us the efficiency 095 the area f a is, t 0001 A W ( L + ) 01m (001m + m) 0005m S, the actual heat transfer rate thrugh the s is, # $ ha ( T s T0 ) 095 (50W / m # C) (0005m )(150 C 0 C) 15561W Fr the unned regin, the area is A un W s 01m 0003m m S, the heat transfer rate thrugh an unned area is # un haun ( Ts T0 ) (50W / m # C) (000036m )(150 C 0 C) 34W the number f the s n the plane: H n t + s 10cm 01cm + 03cm 5 Tutrial # 7 Page 4 f 5
5 ECE309 Intrductin t Thermdynamics and Heat Transfer Spring 005 Fr the ttal heat transfer rate f the whle plane: ttal, n ( + un ) 5 (1561W + 34W ) W CASE N s n the plane The area f the whle plane is and the whle heat transfer rate is A n H W 01m 01m 001m n han ( Ts T0 ) (50W / m 78W # C) (001m )(150 C 0 C) The verall effectiveness f the ned plane ttal, n 44875W 78W 575 Step 6: Cnclusin statement The verall effectiveness f the ned plane is 575, which means the heat transfer rate is enhanced 575 times when attaching the s Tutrial # 7 Page 5 f 5
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