Concept explainers
Steady-state temperatures at selected nodal points of the symmetrical section of a flow channel are known to be
- Determine the temperatures at nodes 1, 4, 7, and 9.
- Calculate the heat rate per unit length (W/m) from the outer surface A to the adjacent fluid.
- Calculate the heat rate per unit length from the inner fluid to surface B.
- Verify that your results are consistent with an over-all energy balance on the channel section.
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Fundamentals of Heat and Mass Transfer
- You are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when the temperature only depends on the radial coordinater from the centerline. The governing dT +q""=0 dr equation is written as 1 d k- r dr r = 0, dT dr =0 dT r=ro -k -=h(T-T) dr (k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r) = q"¹'r² qr qr. + 4k 2h + 4k +T , where k is thermal conductivity of tissue air (A) q" can be calculated…arrow_forwardWater at an average temperature of 23 deg C flows through a 10-cm diameter pipe that is 2.5 m long. The pipe wall is heated by steam and is held at 100 deg C. The convective heat transfer coefficient is 2.25 x 10^4 W/m^2K. Find the heat flow in W.arrow_forwardQ2/ An aluminum sphere weighting 7kg and initially at a temperature of 533K is suddenly immersed in a fluid at 283K. if heat transfer coefficient between the sphere and fluid is 50W/m?.°C. Take density=2707kg/m3, specific heat=0.9KJ/kg.°C and thermal conductivity= 204W/m °C. إجابت * Determine the Bi number 0.00696 0.000696 0.0052 0.00052 0 أخری *.Determine the time required to cool sphere to 263K 26.28min 262.8min 52.56 min 525.6 min O أخریarrow_forward
- The temperature distribution across a wall 0.25 m thick at a certain instant of time is T(x) = a + bx + cx², where T is in degrees Celsius and x is in meters, a = 200 C, b = -200 C/m, and c = 30 C/m². The wall has a thermal conductivity of 2.5 W/m.K. (a) Determine the heat flux into and out of the wall (q"in and q'out). (b) If the cold surface is exposed to a fluid at 100 C, what is the convection coefficient h? - Degree Celsius 200°C q" In- q'in q'out= h = Choose... Choose.... Choose... L₂x K = 2.5 W/m.k T(x)-200-200 x +30x² q" Out 142.7 C 11 L=0.25 m Fluid Too = 100 °C harrow_forwardConduction 1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P= 5 MW of net power production. The compressor, at an average temperature of T. = 400°C, is driven by the turbine at an average temperature of T₁ = 1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal conductivity k = 40 W/m K. Compressor min T Combustion chamber Shaft L Turbine Th out (a) Compare the steady-state conduction rate through the shaft connecting the hot turbine to the warm compressor to the net power predicted by the thermodynamics- based analysis. (b) A research team proposes to scale down the gas turbine of part (a), keeping all dimensions in the same proportions. The team assumes that the same hot and cold temperatures exist as in part (a) and that the net power output of the gas turbine is proportional to the overall volume of the device. Plot the ratio of the conduction through the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a…arrow_forwardQ3/ A stainless steel alloy has cylindrical shape (k = 25 W/m.°C), diameter is 10 cm and 25 cm long, taken to furnace. The initial temperature is 90 °C, the furnace temperature is 1260 °C and the heat transfer coefficient is h = 100 W/m2.'C. Determine the time required for a stainless steel alloy to reach 830 °C. Take thermal diffusivity (k/pc= 0.45 × 10-5 m²/s).arrow_forward
- (heat transfer ) thanks The velocity of the fluid flowing in parallel over a 500mmx500mm flat heater surface is U= 19 m/s and the inlet velocity temperature is T_∞15 C. The surface temperature of this plate is T_s140 C, the friction force is F_D=0.4 N and the surface area of the plate is A=0.32 m2. According to this;(F_D= 0.4N A=32 m2)a) Surface shear stressb) Find the coefficient of frictionc) Heat transfer coefficientd) What is the amount of heat transfer (electric power) that must be given to maintain a constant surface temperature?arrow_forwardIn a cylindrical nuclear reactor fuel rod, heat is generated internally according to the equation:Qg= local heat generation rate per unit volume in r R0= external radiusQ1= heat generation rate per unit volume in the center lineDetermine the temperature drop from the centerline to the surface, considering that the rod has a diameter of 25 mm, thermal conductivity of 26 W / (mK), and has a heat removal rate from its surface of 1570 kW / (m²). Tip 1: It is not necessary to determine the value of the constant C2. Tip 2: the volumetric rate of energy generated is such that: Q1 = 4 . Qs/ D (solve from the image equation)arrow_forwardA conductor with a diameter D= 0.8 cm, covered by an electric current, passes through an environment at T∞= 30 °C with convective heat transfer coefficient h= 120 W/(m² °C). The conductor temperature must be maintained at Ti= 130 °C. Calculate the rate of heat loss per meter of conductor length with:a) the uncoated conductor;b) the conductor covered with bakelite [k = 1.2 W/(m°C)] with a radius corresponding to the critical insulation radius.arrow_forward
- Q5/ A cylindrical storage steel tank with inside and outside diameters of 550 mm and 535 mm, respectively, filled with oil at 310° C. Estimate the heat loss rate and the temperature of the outside surface of the tank. Knowing that the outside atmospheric temperature is 35° C, the heat transfer coefficient for inside and outside of the tank are 2850 and 33 W/m² ° C, respectively, and the themal conductivity of mild steel is 43 W/m °C.arrow_forwardWater flows through a cast steel pipe ( k = 50 W/m.K ) with an outer diameter of 104 mm and 2 mm wall| thickness. (i). Calculate the heat loss by convection and conduction per metre length of un insulated pipe when the water temperature is 15 °C , the outside air temperature is -10 °C , the water side heat transfer coefficient is 30 kW/m?.K and the outside heat transfer coefficient is 20 W/m2.K. (ii). Calculate the corresponding heat loss when the pipe is lagged with insulation having an outer diameter of 365 mm, and thermal conductivity of k= 0.05 W/m.Karrow_forward10B.4. Heat conduction in an annulus (Fig. 10B.4). (a) Heat is flowing through an annular wall of inside radius and outside radius ₁. The thermal conductivity varies linearly with temperature from ko at To to k₁ at T₁. Develop an ex- pression for the heat flow through the wall. (b) Show how the expression in (a) can be simplified when (r₁-ro)/ro is very small. Interpret the result physically. Answer: (a) Q = 2πL(T₁- To T₁ T₁) ›(ko + k) (in 7.) *'; 2 "'; (b) Q = 2mr_L (ko + ki ) ( 7 2 Problems 323 Fig. 10B.4. Temperature profile in an annular wall.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning