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Both 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?
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- 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.2-88 A 1.5-mm-diameter stainless-steel rod [k = 19 W/m.°C] protrudes from a wall maintained at 45°C. The rod is 12 mm long, and the convection coefficient is 500 W/m² . °C. The environment temperature is 20°C. Calculate the temperature of the tip of the rod. Repeat the calculation for h = 200 and 1500 W/m² . °C.Determine the temperature distribution (nodal temperatures) of the structure shown in the figure using two equal-length, linear finite elements with the cross-sectional area of 1 m². The thermal conductivity is 10 W/m/°C. The left side is maintained at 300 °C. The right side is subjected to heat loss by convection with h = 1 W/m²/°C and T₁ = 30 °C. All other sides are insulated. T= 300 °C Exercise T₁ Insulated 20 m T₂ T3 T₁= 30 °C 43
- Temperature distribution along the radius of a long cylindrical shell was found to be -2596.8 W/m2; -1558.1 W/m2; all quantities in SI units. linward T(r) = 365 +21.64 ln(r) Since the temperature is only dependent on radius (r), the heat transfer in this case is radially one- dimensional. The thermal conductivity of cylindrical shell is 36 W/m-K. The shell has inner diameter of 0.5 m and outer diameter of 1 m. Find out the heat flux at r = 0.3 m and at the outer surface of the tube. Justify if the heat transfer is radially outward or radially inward.A certain material has a thickness of 30 cm and a thermal conductivity of 0.04 W/m- °C. At a particular instant in time, the temperature distribution with x, the distance from the left face, is T = 150x ^ 2 - 30x , where x is in meters. Calculate the heat-flow rates atx x = 0 and x = 30 cm . Is the solid heating up or cooling down?Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ∆T, then the rod's length approximately changes by ∆L = ∝Lo∆T, where a is the thermal expansion coefficient and ∆ T is not an extreme temperature change. For steel, ∝ = 1.24 X 10- 5 0 c- 1. (a) A steel rod has length Lo = 40 cm at To = 40°C. Find its length at T = 90°C. (b) Find its length at T = 50°C if its length at To= 100°C is 65 cm. ( c) Express length L as a function of T if Lo = 65 cm at To = 100°C.
- The composite wall of an oven consists of three materials, two of which are ofknown thermal conductivity, kA = 25 W/m ⋅ K and kC = 60 W/m ⋅ K, and knownthickness, LA = 0.40 m and LC = 0.20 m. The third material, B, which is sandwichedbetween materials A and C, is of known thickness, LB = 0.20 m, but unknownthermal conductivity kB. Under steady-state operating conditions, measurementsreveal an outer surface temperature of Ts,o = 20°C, an inner surface temperature ofTs,i = 600°C, and an oven air temperature of T∞ = 800°C. The inside convection coefficient h is known to be 25 W/m2 ⋅K. Neglecting convection transfer effect,what is the value of kB?A wall made of wood is 4.00 cm thick and has an area of 48.0 m². If the temperature inside is 25 °C and the temperature on the outside is 14 C, then at what rate is thermal energy transported through the wall by conduction? The thermal conductivity of wood is 0.080 Js ¹m¹(c)¹ 'n Muur is gemaak van hout wat 4.00 cm dik is en met 'n oppervlakte van 48.0 m². Wat is die tempo van energie oordrag as gevolg van geleiding deur die muur indien die binne temperatuur is 25 °C en die buite temperatuur 14 °C is? Die termiese geleidingskonstante van hout is 0.080 Jsm¹(C)1. Select one: a 82 W O b. 1056 W 690 W 1100 W O e. 2200 W O.C. O d. AAs shown in the sketh below, a steam pipe of 0.12-m inside diameter is insulated with a layer of calcium silicate. "2. Ta2} 1. Ta,1} Steam Insulation (a) If the insulation is 10 mm thick and its inner and outer surfaces are maintained at T, = 800 K and Ta = 490 K. respectively,. what is the rate of heat loss per unit length (q) of the pipe, in W/m? (b) Determine the rate of heat loss per unit length (d), in W/m, and outer surface temperature T,2, in K, for the steam pipe with the Inner surface temperature fixed at T = 800 K, inner radius = 0.06 m, and outer radius n = 0.18 m. The outer surface is exposed to an airflow (T 25°C) that maintains a convection coefficient of h = 25 W/m2-K and to large surroundings for which Tur = T, = 25°C. The surface emissivity of calcium silicate is approximately 0.8.
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