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A one-dimensional plane wall of thickness
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Introduction to Heat Transfer
- A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.arrow_forwardFind the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are ρ =1200 kg/m 3, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q =1000 W/m 2 is applied to the upper surface. The right and left surfaces are also kept at 0oC. Bottom surface is insulated.arrow_forwardA thermal system having a cylindrical form contains a sequence of cylindrical layers is used to cool hot gases. The thermal properties of the system materials are as follows : k = 231 W/m.K, c = 1033 J/kg.K and the density = 2702 kg/m^3. The gases to be cooled has a temperature equals to 500 C. Determine the temperature of the system that corresponds to 10 % of the maximum possible heat transfer between the gas and the system. Consider that the system has a characteristic length equals to 0.03 m. The heat convective coefficient is equal to 50 W/m^2.K. The initial temperature of the system is equal to 20 C. Select one: О а. 370 К O b. 489 K С. 341 К d. 410 Karrow_forward
- Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are p=(1200*32)kg/mº, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux 9" =1000 W/m² is applied to the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated. 9" (W/m) T=0°C T=0°C W=(10*32)cm B=(30*32)cmarrow_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_forwardDerive the general heat conduction equation in Cartesian coordinates. b) Electric heater wires are installed in a solid wall having a thickness of 8 cm and k =2.5W/m ◦C.The right face is exposed to an environment with h=50W/m2◦C and T∞ = 30°C, while the left face is exposed to h=75W/m2◦C and T∞ =50◦C. What is the maximum allowable heat-generation rate such that the maximum temperature in the solid does not exceed 300◦C?arrow_forward
- 1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature distribution has the form T = a + bx + cx² °C. The surface at x=0 has a temperature of To = 120 °C and experiences convection with a fluid for which T.. surface at x= 50 mm is well insulated (no heat transfer). Find: (a) The volumetric energy generation rate q. (15) (b) Determine the coefficients a, b, and c. 20 °C and h 500 W/m² K. The To: = 120°C T = 20°C h = 500 W/m².K 111 Fluid T(x)- = q, k = 5 W/m.K L = 50 mmarrow_forwardThe heat flow per unit length of a thick cylindrical pipe is 772 W per meter. The pipe has radii ri = 12 cm, ro = 24 cm, outside surface temperature, To = 95 deg C and k = 0.05 + 0.0008T where T is in deg C and k is in W/(m K). Find the inside surface temperature of the pipe, assuming steady state conditions and accounting for the variation of thermal conductivity with temperature. Also determine the temperature of a point midway to the inside and outside radius.arrow_forwardQ1/ Consider a large plane wall of thickness L=0.03 m. The wall surface at x =0 is insulated, while the surface at x =L is maintained at a temperature of 30°C. The thermal conductivity of the wall is k=25 W/m °C, and heat is generated in the wall at a rate of g = 9oe0.5x/L W/m³ Where g, = 8 x 10 W /m². Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) determine the temperature of the insulated surface of the wall.arrow_forward
- 2.1 i. ii. 2.2 2.3 A plane wall with thermal conductivity of 10.2 W/m °C, thickness of 100mm, and area of 3m². The steady surface temperatures are 170 °C and 100 °C, as shown in the figure below. Determine: rate of heat flow across the plane wall and, temperature gradient in the flow direction. ( An oven whose thickness of side wall is 82.5mm has a thermal conductivity of wall insulation of 0.044 W/m °C. The temperature on inside of the side wall is 175 °C and the energy dissipated by the electric coil within the oven is 40.5 W. Determine the area of wall surface so that temperature on the other side of wall does not exceed 75 °C. (4) A 2-kW resistance heater wire whose thermal conductivity is k = 15 W/m - °C has a diameter of D = 4 mm and a length of L = 0.5 m, and is used to boil water. If the outer surface temperature of the resistance wire is Ts = 105°C, determine the temperature at the centre of the wire. (.arrow_forwardA uniform internal energy generation occurs in a plane wall with a thickness of 60 mm and a constant thermal conductivity of 3W / m. K. For these conditions, the temperature distribution has the form T (x) = a + bx + c x?. The surface at x = 0 has a temperature = T = 110 ° C and experiences convection with a fluid for which To = 25 ° C and h = 300 W / m². K. The surface at x = L is well insulated. For one - dimensional, steady - state conduction (a) calculate the volumetric energy generation rate. (b) determine the coefficients a, b, and c by applying the boundary conditions to the prescribed temperature distribution.arrow_forward4x F2 # 3 E 4, F3 54 $ R F4 Ac = 1m² ▬ H DII x= 1 m (4) Consider a wall (as shown above) of thickness L-1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h= 1 W/m²K and an ambient temperature T. 1 K. There is no heat generation inside the wall. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). % To,1 = 1 K h₁ = 1 W/m²K 5 Q Search F5 T T₁ A 6 x=0 F6 à = 0 W/m³ k= 1W/mK L=1m Y 994 F7 & 7 T₂ U Ton2 = 1 K h₂ = 1 W/m²K1 PrtScn F8 Page of 7 ) 0 PgUp F11 Parrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning