Consider a 20-cm-thick concrete plane wall
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HEAT+MASS TRANSFER:FUND.+APPL.
- Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinderarrow_forwardYou 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_forwardA heat pack can be modeled as a plane wall of thickness L=2cm. Assume that the pack has a constant thermal conductivity (4.0 W/(m*K)) and constant heat generation (800 W/m3 ) with one side (x=0) maintained at a constant temperature T1 = 80°C and the other side (x=L) cooled by moving air at T∞ = 25°C with a heat transfer coefficient of h = 20 W/(m2K).a. Reduce the heat equation with clearly stated assumptionsb. Find the steady-state temperature distribution T(x) in the pack.arrow_forward
- Q₁: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k-2.3 W/m °C, and surface area A= 20 m². The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m² °C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans: (c) 6030 Warrow_forwardQ1: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C, and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m2 C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans : (c) 6030 Warrow_forwardThe temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x) = a+ b+cx?, where T is in degrees Celsius and x is in meters, a = 200°C,b = -200°, and c = conductivity of 1 W /m · K. 30°C/m² . The wall has a thermal (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by the wall. (b) If the cold surface is exposed to a fluid at 100°C, what is the convection coefficient? k=1W/m•k T(x) =200-200x + 30x² 200°C- ĖST 142.7°C q"out | Fluid Too = 100°C,h 9"in |L-0.3marrow_forward
- Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C, and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T∞=15 oC with a heat transfer coefficient of h=24 W/m2 oC . Assuming constant thermal conductivity and no heatgeneration in the wall, (a) express the differential equation and the boundary conditions forsteady one-dimensional heat conduction through the wall, (b) obtain a relation for thevariation of temperature in the wall by solving the differential equation, and (c) evaluate therate of heat transfer through the wallarrow_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_forwardA:Find the amount of heat transferred through an iron fin of thickness 5 mm, length 10 cm and width 100 cm. Also determine the temperature difference e at the tip of the fin at: 1- adiabatic tip, 2-heat convection at the tip. Assuming the atmospheric temperature of 28°C K=50 w/mK, h=10 w/m’K, O,=80°C. B-Why is the dimensional heat flow assumption important in the analysis of fins problems? C- Why are the annular fins more efficiency than others?.arrow_forward
- It is required to perform a heat treatment for gas turbine applications, for them it is required to analyze a sample of the material to be used. The analysis will be performed using the method of a semi-infinite cylinder of stainless steel 12Awith the following thermal properties; (ρ=8700 kg/m3, Cp = 897 J/kg. °C and k = 242 W/m. °C. Of diameter D=12 cm is initially at a uniform temperature of 120 °C. Then the cylinder is placed in a furnace at a constant heat flux of 3800 W/m2, a temperature of 60 °C andh= 170 W/m2. Determine the temperature at the center of the cylinder 3.5 cm from the end surface 6 minutes after placing it in the furnace.arrow_forwardA rectangular wall of length "L" m and height "H" m is made from a thick bricklayer. The rectangular wall has a surface area as 11 m2 & Thermal conductivity as 0.53 W/mK. The wall is subjected to heat transfer due to the outside temperature 43 °C and inside temperature 24 °C. If the energy loss is 11219 kJ in 484 minutes. (HINT: 1 minute = 60 %3D seconds) Determine the following -- i) Heat transfer rate, ii) Thickness of the wall.arrow_forward3 Brass cube "p = 8530 kg/m , c= side length =9 mm, are annealed by heating them first to 813°C in a furnace and then allowing them to cool slowly to 130°C in ambient air at 28°C. If the average heat transfer coefficient is 19.9 W/m .°C, If 2204 balls are to be annealed per hour, what is the total rate of heat transfer (watts) from the balls to the ambient air? 380 J/kg.°C, k = 110 W/m.°C, a = 33.9E-6 W/m.°C",arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning