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A constant-property, one-dimensional Plane slab of width 2L, initially at a uniform temperature, is heated convectively with
(a) At a dimensionless time of
(b) Letting
(e) Evaluate
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Chapter 3 Solutions
Introduction to Heat Transfer
- 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?arrow_forwardBoth ends of a 32 cm long rod are maintained a constant temperature of 100 °C. Dimensions and thermal parameters of the rod are as follows: Diameter D = 2 cm Convection coefficient h = 10 W/m2K Ambient temperature T¥ = 20 °C Thermal conductivity k = 10 W/mK What is the midpoint temperature of the rod?arrow_forwardQ2/ A thermopane window consists of two pieces of glass 7 mm thick that enclose an air space 7 mm thick. The window separates room air at 20°C from outside ambient air at -10°C. The convection coefficient associated with the inner (room-side) surface is 10 W/m? K. If the convection coeficient associated with the outer (ambient) air is 80 W/m? K, what is the heat loss through a window that is 0.8 m long by 0.5 m wide? Neglect radiation,[ kglass = 1.4 W/m-K: kair-0.024S W/m-K ] Window, 0.8 m x 0.5 m Glass 7+7+7-1 Air! Toi= 20 °C h; = 10 W/m2 K Air11 L=0.007 m To = -10 °C ho = 80 W/m2-K Airarrow_forward
- A brass plate has a circular hole whose diameter is slightly smaller than the diameter of an aluminum ball. Ifthe ball and the plate are always kept at the same temperature,(a) should the temperature of the system be increased or decreasedin order for the ball to fit through the hole? (b) Choose the bestexplanation from among the following:I. The aluminum ball changes its diameter more with temperature than the brass plate, and therefore the temperatureshould be decreased.II. Changing the temperature won’t change the fact that the ballis larger than the hole.III. Heating the brass plate makes its hole larger, and that willallow the ball to pass through.arrow_forwardQ2/ A thermopane window consists of two pieces of glass 7 mm thick that enclose an air space 7 mm thick. The window separates room air at 20°C from outside ambient air at -10°C. The convection coefficient associated with the inner (room-side) surface is 10 W/m? K. If the convection coefficient associated with the outer (ambient) air is 80 W/m? K, what is the heat loss through a window that is 0.8 m long by 0.5 m wide? Neglect radiation,f kglass = 1.4 W/m-K: kair =0.024S W/m K) -Window, 0.8 m x 0.5 m Glass Air! Tmi= 20 °C hi = 10 Wim2 K Air11 L=0.007 m To=-10 °C ho = 80 W/m2-K Airarrow_forwardQ2/A thermopane window consists of two pieces of glass 7 mm thick that enclose an air space mm thick. The window separates room air at 20°C from outside ambient air at -10°C. The 7 convection coefficient associated with the inner (room-side) surface is 10 W/m2 K. If the convection coefficient associated with the outer (ambient) air is 80 W/m2 K, what is the heat loss through a window that is 0.8 m long by 0.5 m wide? Negleet radiation,[ kglass = 1.4 W/m-K: kair =0.0245 W/m-K] トL十LトL Window, 0.8 m x 0.5 m Glass Air! Ti 20 °C h; = 10 W/m2-K Air L = 0.007 m To.o = -10 °C ho = 80 W/m2-K Airarrow_forward
- 2arrow_forwardThermal diffusivity is a(A) Function of temperature(B) Physical property of a substance(C) Dimensionless parameter(D) All of thesearrow_forwardThe nuclear fuel in cylindrical shape of length L at radius R is covered with aluminum shell at radius RC. The heat energy (Sn) that emerges as a result of splitting in nuclear fuel is per unit volume and is in the form of a parabolic function. Determine the temperature distribution in both regions for the steady state by taking the outer surface temperature of the cylinder. 1/2 Sn = Sn. [a + b(r)] "d 5. RC (cal/cm³ s) Toarrow_forward
- Three (3) bricks, specifically A, B, and C were arranged horizontally in such a way that it can be illustrated as a sandwich panel. Consider the system to be in series and in the order of Brick A, Brick B and Brick C. The outside surface temperature of Brick A is 1,500℃ and 150 ℃ for the outside surface of Brick C. The thermal conductivities for Brick A, Brick B and Brick C, are 2 ?/? °? , 0.50 ?/? °? , 60 ?/? °?. The thickness of Brick A and Brick C are 50 cm and 22 cm. The rate of heat transfer per unit area is 1,000 ?/?2 . Determine the following: The thickness of Brick B in the unit of mm. Assume that all the conditions were retain except that the thickness of Brick B was increased to 800 mm, what is the new value for the rate of heat transfer per unit area in ???/ℎ? . ??2 please explain the principles to solve thisarrow_forwardNot Ai generated answers, I need to understand please show all steps.arrow_forward2. Consider the temperature distributions associated with a dx differential control volume within the one-dimensional plane walls shown below. T(x,00) T\x,00) * dx * dx (a) (Б) Tx,1) T(x,1) * dx dx (c) (d) (a) Steady-state conditions exist. Is thermal energy being generated within the differential control volume? If so, is the generation rate positive or negative? (b) Steady-state conditions exist as in part (a). Is the volumetric generation rate positive or negative within the differential control volume? (c) Steady-state conditions do not exist, and there is no volumetric thermal energy generation. Is the temperature of the material in the differential control volume increasing or decreasing with time? (d) Transient conditions exist as in part (c). Is the temperature increasing or decreasing with time?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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