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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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_forward(a) Consider nodal configuration shown below. (a) Derive the finite-difference equations under steady-state conditions if the boundary is insulated. (b) Find the value of Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k = = W 3 m. k . Ay m-1, n m, n | Δx=" m, n+1 m, n-1 The side insulatedarrow_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_forward
- Q2/ 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_forwardDon’t use Heissler charts to answer this question Heat sterilization of lumber, timbers, and pallets is used to kill insects to prevent their transfer between countries in international trade. This is analogous to food sterilization by heat. A typical requirement here is that the slowest heating point of any woodconfiguration be held at 56 °C for 30 minutes. Consider hot air heating of wooden boards that maintains their surface temperature at 70 °C. The boards are stacked outside and in the winter time they can be considered to be at 0 °Cwhen theyare brought in for heating. The thermal diffusivity of the wood is 9*10-8m2/s. a.Calculate the time from the start of heating for a 2.5 cm thick board to reach a sterilization temperature of 56 °C at its slowest heating point .b.Calculate the heating time when four such boards are stacked together. c.Calculate the ratio of the two heating times (for a single board versus when they are stacked), and explain the ratio. Note: You’re free to…arrow_forwardTo avoid overheating, natural convection analysis is to beconsidered. If the minimum allowable heat transfer due tonatural convection is 30 W, find the maximum angle at whichthe TV can hang off the wall (0 < θ < 60). Some temperatureswere collected; Back panel surface: 45 °C, ambient: 32 °C. A typical 55-inch TV screen measures (122 cm x 69 cm). please answer and show all detailed calculationsarrow_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
- A piece of beef steak 5 cm thick will be frozen in the freezer room -30 ° C. This product has a moisture content of 73%, a density of 970 kg / m³, and a thermal conductivity (frozen) of 1.1 W / (m K). Estimate the freezing time. using the Plank equation. This product has an initial freezing temperature of -1.75 ° C, and the movement of air in the freezing room gives a convective heat transfer coefficient of 10 W / (m² K). t f =arrow_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_forwardThree (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_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning