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The heat flux that is applied to the left face of a plane wall is
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Chapter 1 Solutions
Introduction to Heat Transfer
- Plaster Insulation Brick Inside Outside Air Air R/2 R3/2 G R/2 A particular house wall consists of three layers and has a surface area A. The inside layer is made of plaster board, the middle layer is made of fiberglass insulation, and the outside layer is made of brick. The thermal conductivity of all three layers is known, and the thickness of the plaster board and siding are also known. The convection coefficient for the inside and outside wall surfaces are known: System_Parameters - (h; = 40.0 h, = 60.0 k = 0.2 k = 0.04 k3 = 0.3 A= 30.0) System_Parameters = (L = 10.0 L2= unknown L3 = 100.0 cp1 = 950.0 c p2 = 10.0 cp3= 800.0 P1 = 700.0 Pz = 0.5 P3= 2000.0) W - mm; A ~ m²; k ~. m °C ;p~ 8: T ~ °C kg °C L m² °C m- a) If the thermal capacitances of the walls is ignored, How thick must the insulation layer be so that the heat loss is no greater than 400W if the outside temperature is -15-C? b) Now consider the situation where the thermal capacitance is also considered. Develop the state…arrow_forward1-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_forwardGiven the illustration and data below. Determine the heat lost per day. T1 = 1000°C T2 T3 = 80°C A = 1 m²2 5 cm 10 сm W k = 0.09 т-к %3D W k = 1.64; т-кarrow_forward
- please provide answers with step-by-step calculations and explanationarrow_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_forwardQ2. Steam pumped through a long- insulated pipe at a temperature of T= 500 K and provides a convection coefficient of h, = 100 W/m?K at the inner surface of the pipe. The inner and outer radius of the pipe and insulation material are r1 = 10, r2 = 12 and r3 = 17 cm, respectively. The thermal conductivity of the pipe is 100 W/mK. The insulation material is glass fiber and its outer surface is exposed to ambient air at 300 K. If the ambient air provides a convection coefficient of ho = 20 Internal flow Ambient air W/m?K, determine the followings: a. What are the thermal resistance coefficients for convections and conductions b. What is the heat transfer rate per unit length of the pipe c. If the pipe is 30 m long, what will be total heat transfer rate from the pipe. t00 noints)arrow_forward
- Consider a plate whose thickness is 2L=20 cm and thermal conductivity is 44 W/mK. Heat generation inside the plate (5x105 W/m³) is uniform. The surface of the plate is maintained at Ts=10°C. Find the temperature at the center of plate. T Ts -L L X O a. 45 °C ОБ.75 °С О с. 67 оС O d. 90 °C O e. 85 °Carrow_forwardWhich formula is used to calculate the heat conduction in the AXIAL direction in a vertically located pipe segment whose inner and outer surfaces are perfectly insulated. Here r, is inner radius, r, outer radius, Tri pipe inner surface temperature, Tro pipe outer surface temperature, L is the length of the pipe, T the temperature on the lower surface, Ty the temperature on upper surface. Tu r; Tro rarrow_forwardConsider a plate whose thickness is 2L=20 cm and thermal conductivity is 20 W/mK. Heat generation inside the plate (104 W/m³) is uniform. The plate is placed in an environment at T=20°C and convective heat transfer coefficient is h=16 W/m²K. Find the temperature at the center of plate. h To -L O a. 45 °C O b. 75 °C O c. 67 °C O d. 85 °C О е. 90 °Сarrow_forward
- Calculate the heat transfer rate per unit area of a 200 mm thick concrete wall when the surface temperatures are 27 ° C and 70 ° C, respectively. The thermal conductivity of concrete is 0.935 W / (m ° C). Heat transfer rate per unit area = Answer watts / m2arrow_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_forwardConsider a copper plate that has dimensions of 3 cm x 3 cm x 7 cm (length, width, and thickness, respectively). As shown in the following figure, the copper plate is exposed to a thermal energy source that puts out 126 J every second. The density of copper is 8,900 kg/m³. Assume there is no heat loss to the surrounding block. 126 J Copper Insulation Ⓡ What is the specific heat of copper (in J/(kg K))? J/(kg. K) What is the mass of the copper plate (in kg)? kg How much energy (in J) will be consumed during 11 seconds? J Determine the temperature rise (in K) in the plate after 11 seconds.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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