Use the alternative conduction analysis of Section 3.2 to derive an expression relating the radial heat rate, q,, to the wall temperatures Ts,1 and Ts,2, for the hollow cylinder show in the figure below. Cold fluid Too,2, h₂ Ts,1 Hot fluid Too,1, h₁1 Ts,1 Ts2 r1 12 Ts.2 Use your expression to calculate the heat transfer rate, in W, associated with a L = 1.25 m long cylinder of inner and outer radii of r₁ = 50 mm and r₂ = 75 mm, respectively. The thermal conductivity of the cylindrical wall is k 2.5 W/m-K, and the inner and outer surface temperatures are Ts,1 100°C and Ts2 = 67°C, respectively. = 9r = i W
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- Consider a wall of thickness 50 mm and thermal conductivity 14 W/m.K, the left side (x-0) is insulated. Heat generation (q,) is present within the wall and the one dimensional steady-state temperature distribution is given by T(x) = ax +bx+c [°CJ, where c 200 °C, a = -1144 °C/m is the heat fluxes at the right side, x L, (kW/m)? b= needs to he determined, and x is in meters. What 9, K 4L) Insulation10B.4. Heat conduction in an annulus (Fig. 10B.4). (a) Heat is flowing through an annular wall of inside radius and outside radius ₁. The thermal conductivity varies linearly with temperature from ko at To to k₁ at T₁. Develop an ex- pression for the heat flow through the wall. (b) Show how the expression in (a) can be simplified when (r₁-ro)/ro is very small. Interpret the result physically. Answer: (a) Q = 2πL(T₁- To T₁ T₁) ›(ko + k) (in 7.) *'; 2 "'; (b) Q = 2mr_L (ko + ki ) ( 7 2 Problems 323 Fig. 10B.4. Temperature profile in an annular wall.number 1 A food product containing 82% moisture content is being frozen. Estimate the specific heat of the product at -8 ° C when 82% of the water is frozen. The specific heat of the dry product is 2.5 kJ / (kg ° C). It is assumed that the specific heat of water at -10 ° C is the same as the specific heat of water at 0 ° C, and that the specific heat of ice follows the function Cp es = 0.0062 T Frozen + 2.0649. Cp of frozen product = kJ / kg ° C.
- A certain ideal gas (unknown) inside a close piston-cylinder assembly undergoes a set of processesthat composed of Isothermal expansion from State point 1 to state point 2, Isometric heat rejectionfrom state point 2 to state point 3, and Isentropic compression from state point 3 back to the initialcondition. If the maximum pressure is 3000kPa and maximum and minimum volume is 200cm3and50cm3, analyze the problem and perform the following:a. Draw and label the graph of this set of processes in the P-V and T-S diagram showing the statepoint numbers and energy directions.b. From the known ideal gases as shown in Table 1.0, select the best suited ideal gas to attain theprocesses stated if the lowest pressure is limited to 629.8kPa. Assume a constant specific heat.c. For the selected ideal gas from b, compute the work of compression (kJ/kg), work of expansion(kJ/kg), and heat rejected (kJ/kgA certain ideal gas (unknown) inside a close piston-cylinder assembly undergoes a set of processesthat composed of Isothermal expansion from State point 1 to state point 2, Isometric heat rejectionfrom state point 2 to state point 3, and Isentropic compression from state point 3 back to the initialcondition. If the maximum pressure is 3000kPa and maximum and minimum volume is 200cm3and50cm3, analyze the problem and perform the following: a. Draw and label the graph of this set of processes in the P-V and T-S diagram showing the statepoint numbers and energy directions. b. From the known ideal gases as shown in Table 1.0, select the best suited ideal gas to attain theprocesses stated if the lowest pressure is limited to 629.8kPa. Assume a constant specific heat. c. For the selected ideal gas from b, compute the work of compression (kJ/kg), work of expansion(kJ/kg), and heat rejected (kJ/kg)number 1 A food product containing 75% moisture content is being frozen. Estimate the specific heat of the product at -10° C when 85% of the water is frozen. The specific heat of the dry product is 2 kJ / (kg ° C). It is assumed that the specific heat of water at -10 ° C is the same as the specific heat of water at 0 ° C, and that the specific heat of ice follows the function Cp es = 0.0062 T Frozen + 2.0649. Cp of frozen product = kJ / kg ° C.
- The heat flow per unit length of a thick cylindrical pipe is 772 W per meter. The pipe has radii ri = 12 cm, ro = 24 cm, outside surface temperature, To = 95 deg C and k = 0.05 + 0.0008T where T is in deg C and k is in W/(m K). Find the inside surface temperature of the pipe, assuming steady state conditions and accounting for the variation of thermal conductivity with temperature. Also determine the temperature of a point midway to the inside and outside radius.Heat Transfer question In order to cool down a hot steel sphere (its diameter is 5 cm), CO2 gas is blown over it through a pipe with a diameter of 10 cm. The CO2 gas is kept at atmospheric pressure while moving through a smooth pipe at a speed of 6 m/sec. The gas temperature entering the pipe is 300K and exiting the pipe is 340 K. The pipe temperature at the entrance is 350K and at the exit is 550K. The sphere is located just about the pipe exit. Find the convective heat transfer coefficient of the gas moving in the pipe, the heat transfer rate at the pipe and the pipe length. What is the surface temperature of the sphere if the heat transfer rate between the sphere and the gas is 7W and its surface temperature is higher than the gas?Qi: (50 marks) Find the total heat flux of the composite wall when: B KA = KC = KF = 15 m. K KB = KD = 10 m. K KE = KG = 20 %3D m. K D. Height of B = C = D 4 cm 3 cm 4 cm 6 cm Height of F = G AT = 30 K
- Q2/ A plane wall generates heat internally at the rate of 0.2 MW/m' with 8.0 cm thick. One side of the wall is insulated, and the other side is exposed to an environment at 60°C. The convection heat-transfer coefficient between the wall and the environment is 520 W/m2. °C. The thermal conductivity of the wall is 34 W/m.°C. Start from principle to calculate the maximum temperature in the wall.A plane wall of thickness 2L = 30 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a rate q, while convection heat transfer occurs at both of its surfaces (x = − L, + L), each of which is exposed to a fluid of temperature T = 20°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx² where a = 82.0°C, b = -210°C/m, c = -2x 10°C/m², and x is in meters. The origin of the x-coordinate is at the midplane of the wall. (a) What is the volumetric rate à of heat generation in the wall? (b) Determine the surface heat fluxes, q" (L)and q ( + L). (c) What are the convection coefficients for the surfaces at x = - Land x = + L? The volumetric rate of heat generation in the wall, in W/m³: q = i W/m³ The surface heat flux, in W/m²: qx ( - L) = i The surface heat flux, in W/m²: q (+ L) = i W/m² W/m² The convection coefficients for the surface at x = - L, in W/m²-K: h(- L) = i W/m².K The convection…Continuous temperature distribution in a semi-permeable material with laser radiation on it, thickness L and with a heat conduction coefficient k, T(x)=-A/k.a^2.e^-ax+Bx+C It is given by equality. Here A, a, B and C are known constants. For this case, the radiation absorption in the material manifests itself in a uniform heat generation term in the form q (x). a) Obtain a relationship for the type that gives the conduction heat fluxes on the front and back surfaces. b) get a correlation for q(x) c) Obtain a relation that gives the radiation energy produced per unit surface area in the whole material.