derive an expression for the thermal conductivity k(x) for these conditions

Problem 4 A cork board (k = 0.039W/m K) 3 cm thick is exposed to air with an average temperature T.. = 30°C with a convection heat transfer coefficient, h = 25 W/m².K. The other surface of the board is held at a constant temperature of 15°C. A volumetric heat generation of 5 W/m³ is occurring inside the wall. Assuming one dimensional conduction, write the governing equation and express the boundary conditions for the wall. (solve the equation is not required) Problom

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?

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Below is the dynamics of heat transfer: A container in an oven for instance dTc 1 1 ·TC+⋅ dt R+Ct -Tamb R+Ct In this equation, the container temperature Tc is the Output and the ambient temperature Tamb is the input. Thermal resistance and capacitance values are C+=7000 J/°C and R₁ = 0.0142858 W/°C. Initial condition is zero: Tc (0) = 0 °C. Obtain the transfer function of the system Create a table to compute its frequency response characteristics by considering low frequency region and high frequency region. Also consider a middle frequency. For low frequency region, consider a = 1e - 4 rad/s and w=1e-3-rad/s. For middle frequency, consider w=1e- 2 rad/s. For high frequency region, consider w = 1e-1 rad/s and w=1rad/s Using the magnitude and phase responses you tabulated, hand-sketch its Bode diagram. Clearly show low frequency and high frequency assumptions your drawing. Smoothen the diagram by considering the magnitude and phase at the middle frequency.

Do not solve this with 0 temperature BCs, instead solve with the following BCs: u(0, t) = 0, u(L, t) = -20.

You have a 1-D steady-state conduction problem, constant thermal properties, with energy generation q_dot. The material is 4.0 cm thick and has a constant thermal conductivity of k = 65.0 (W/m-k). The temperature distribution within the object is: T(x) = a + bx^2 a = 100 Celcius b = -1000 Celcius/m^2 Starting with the Heat Diffusion Equation  and using the data given above, determine the following: • Determine the heat generation rate q_dot within the wall. • Determine the heat flux q" at x=0 and at x=L.

1 . A long cylindrical shell outer radius R₂ = 2 cm is shown in cylindrical shell is temperature Ti=10 c° and outer wall at Constant temperature T₂ = 20 C° Calculate the temperature at r= 1.5 cm (Consider conduction only) Assumptions: system is Thermal in Given: The of inner and the figure. The radial + The differential The system is: J²T dr² r maintained at steady state conductivity, K = 22.5 w/mc, system follows Fourier's law of heat Heat loss in axial direction is negligible. JT dr radius Ri=1cm Length L=lom inner Wall Constant is maintained = 0 of is Ti RI R₂ constant. conduction. equation representing Tz

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Steady state temperatures at three nodes are given in K. This object generates heat itself at rate of q = 5×107 W/m³ and has a thermal conductivity of 20 W/m K. Two of its sides are maintained at a constant temperature of 300 K, while the others are insulated. Find temperatures at nodes 1, 2 and 3 in K. 5 mm 2 398.0 348.5 3 374.6 - Uniform temperature, 300 K 5 mm