Explain how Fourier's law of conduction (in one-dimensional cartesian system) can be applied to experimentally measure the thermal conductivity of solid materials. What are the necessary conditions and assumptions?
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- We performed the experiment to measure the thermal conductivity of 2 materials (Brass & Steel) in the laboratory and measured the following tabulated values: Material 1 - BRASS (Diameter = 25mm) Power Temperature (°C) Q' (W) 2 3 4 6 7 8 1 5 9 14.6 78.9 77.5 76 50.2 46.7 42.4 36.1 34.6 33.6 Material 2 - STEEL (Diameter = 25mm) Power Temperature (°C) 7 Q' (W) 14.25 2 3 1 9 88.6 87.4 85 34.1 33.4 32.7 CALCULATE THE FOLLOWING: MATERIAL 1 - BRASS Calculation for Brass Quantities Calculated Values Power (Q') W Area of cross section (A) m2 Difference in Temperature between two points (AT) °C Difference in distance between two points (Ax) m Thermal conductivity of brass (k,) W/m'C MATERIAL 2 - STEEL Calculation for Steel Quantities Calculated Values Power (Q') W Area of cross section (A) m? Difference in Temperature between two points (AT) "C Difference in distance between two points (Ax) m Thermal conductivity of steel (k,) W/m°CWhich 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 rDetermine the heat conduction of a boiler if you are given the following data: The thickness of the boiler is 15 cm, the T1 is the temperature of the water is 25°C and the T2 of the steam is 110°C, the thermal conductivity The boiler material is iron (use presentation table), the boiler area is 4.5 m^2
- A hot water pipe is 100 mm in diameter and 80 m long. This pipe is insulated in two layers. First layer is 25 mm thick, thermal conductivity is 0.12 W/m C material, second layer is 45 mm thick It is made of material with a thermal conductivity of 0.05 W/m C. T1, T2 and T3 are the surface temperatures in the pipe. One With the acceptance of heat transfer in dimensional and continuous conditions, transfer from the pipe in case T1= 600 OC and T3= 35 C Find the amount of heat released and the temperature T2. 2.tabaka 1.tabaka 100 mm T₁ T₂ T3Consider 1D heat conduction in a Cu rod with an average temperature of 25C. Does there exist a maximum (or upper-limit value) temperature gradient for heat conduction. If so, what is that value with justification on the derivation/scientific reasoning. The thermal conductivity is k=385 W/m*K. The diameter of the rod is left in terms of d.4x 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 P
- The initial temperature distribution of a 5 cm long stick is given by the following function. The circumference of the rod in question is completely insulated, but both ends are kept at a temperature of 0 °C. Obtain the heat conduction along the rod as a function of time and position ? (x = 1.752 cm²/s for the bar in question) 100 A) T(x1) = 1 Sin ().e(-1,752 (³¹)+(sin().e (-1,752 (²) ₁ + 1 3π TC3 .....) 100 t + ··· ....... 13) T(x,t) = 200 Sin ().e(-1,752 (²t) + (sin (3). e (-1,752 (7) ²) t B) 3/3 t + …............) C) T(x.t) = 200 Sin ().e(-1,752 (²t) (sin().e(-1,752 (7) ²) t – D) T(x,t) = 200 Sin ().e(-1,752 (²)-(sin().e (-1,752 (²7) ²) t E) T(x.t)=(Sin().e(-1,752 (²t)-(sin().e(-1,752 (²) t+ t + ··· .........) t +.... t + ··· .........) …..)under steady-state conditions. If you are given T1 = 200 °C and T2 = 164 °C, determine: a) the conduction heat flux, q,.cond, in m2 W from x = 0 to x = L b) if the dimensions of the triangle ares 15 mm and h 13 mm, calculate the heat transfer due to convection, q,y, in W at x = L Finsulation T2 T T = 20°C h = 500 W/m2.K Triangular Prism x L x 0 L= 50 mm k = 100 W/m-KThe topic of total derivation is mathematics
- Thermal diffusivity is a(A) Function of temperature(B) Physical property of a substance(C) Dimensionless parameter(D) All of theseConsider 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.A J- type thermocouple is used to measure the temperature in a heating process. Sheath material used is SS316. The length of the sheath is 13mm and thickness is 0.3mm. Find the time constant of the sheath. Material QU(kg/m)s(J/Kg - °c) K(W/m-k) Platinum 21450 130 71.6 SS304 8030 500 21.4 SS316 7990 500 21.4 SS410 7750 460 24.9 Air 1.20 1005 0.025 MgO Powder 3580 877 26.8 Silicon compound3210 800 Time constant of the bare material is, T=