If a temperature profile in a solid flat plate is given as T(x) = -190 x³ + 40 x² +100 °C. The thermal conductivity of the plate is 5 W/m.K. Determine (a) Temperature at x = 2 cm; (b) Determine heat flux, q", at x = 2 cm; and (c) Determine the location of the maximum/minimum heat flux.
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- 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=lenthofcyclinder1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandwiched between a 2-mm-thick aluminum cladding plate on the outside and a 5-mm-thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40C when the temperature at the inside surface of the oven is 300C. Also, the air temperature in the kitchen varies from 15Cto33C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12.0W/m2K. Determine the thickness of the fiberglass insulation that is required for these conditions. What would be the outer surface temperature when the inside surface of the oven is at 475C?
- Discuss the modes of heat transfer that determine the equilibrium temperature of the space shuttle Endeavour when it is in orbit. What happens when it reenters the earths atmosphere?Using Table 1.4 as a guide, prepare a similar table showing the orders of magnitude of the thermal resistances of a unit area for convection between a surface and various fluids.A high-speed computer is located in a temperature-controlled room at 26C. When the machine is operating, its internal heat generation rate is estimated to be 800 W. The external surface temperature of the computer is to be maintained below 85C. The heat transfer coefficient for the surface of the computer is estimated to be 10W/m2K. What surface area would be necessary to assure safe operation of this machine? Comment on ways to reduce this area.
- 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 h1- A solid infinitely long cylinder, radius 2 cm, has uniform internal heat generation. The temperature distribution in the cylinder is T(r) = = 256 – 8.6 x 104 r² where r is in meters, T in °C and the thermal conductivity of the cylinder material is 16 W/ m °C. Determine: (a) The temperature at the centerline. (b) The surface temperature. (c) The heat flux at the surface. (d) The rate of heat transfer to the surrounding per unit meter of cylinder length.GChoose the right answer 1. The temperature profile for steady hest conduction through a plane wall of constant thermal conductivity is a. logarithmic b. parabolic 2. A brick wall (k-0.75 W/mK ) transmits $02 of heat loss through another wall (k-0.25 W/mK, x-100 mm). If the temperature difference across both walls is the same, the thickness of the brick wall would be a.150 mm c. linear 6T b. 240 mm c. 300 mm d. 375 mm 3. The maximum temperature at the center of the solid sphere of radius R having heat generation q (W/m') is given by g'R +9R b. T, + 4k T+9R 6k d. T+9R 8k a. 2k C. 4. The internal thermal resistance of a solid can be ignored if the Biot number is less than a. 1 b. 0.5 c. 0.1 d. Fourier number 5. The ratio of heat transfer of a fin to the heat transfer without fin is referred to as a. fin resistance b. fin efficieney efin effectiveness d. fin conductance.
- i need the answer quickly= Consider a large plane wall of thickness L=0.3 m, thermal conductivity k = 2.5 W/m.K, and surface area A = 12 m². The left side of the wall at x=0 is subjected to a net heat flux of ɖo = 700 W/m² while the temperature at that surface is measured to be T₁ = 80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary equations for steady one- dimensional heat conduction through the wall, (b) obtain a relation for the variation of the temperature in the wall by solving the differential equation, and (c) evaluate the temperature of the right surface of the wall at x=L. Ti до L XThe 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-0.3m