The convection coefficient for flow over a solid sphere may be determined by submerging the sphere,...

The convection coefficient for flow over a solid sphere may be determined by submerging the sphere, which is initially at 25 °C, into the flow, which is at 75 °C, and measuring its surface temperature at some time during the transient heating process. If the sphere has a diameter of 0.1 m, a thermal conductivity of 20 W/(m·K), and a thermal diffusivity of 4.0×10-5 m²/s, at what time will a surface temperature of 60 ºC be recorded if the convection coefficient is 300 W/(m²·K)?

a) When deciding if the lumped capacitance method can be used, what is the value of the Biot number?

Bi c= 0.2505 ( correct)

b) When using the one-term approximation for transient 1-D conduction, what is the value of the applicable Biot number? Use Table 5.1.

Bi=??

c) Using the one-term approximation, if Bi in Table 5.1 were equal to 0.5, what would be the value of C1 for this problem?

C1=??

d) Use the one-term approximation method to solve for the Fourier number.
F0=??

e) Solve for the time required for the surface of the sphere to reach 60 ºC, in sec.

t=?? sec

Solutions

Expert Solution

samet mamat answered 1 year ago

Next > < Previous

Related Solutions

The local convection coefficient on a plate decreases as the thickness of the boundary layer grows...

The local convection coefficient on a plate decreases as the thickness of the boundary layer grows along the plate. After transition from laminar to turbulent flow, the local convection coefficient becomes much larger, even though the boundary layer is much thicker. Explain why this is so. Explain with a paragraph in a clear and straightforward manner, please.

A solid sphere, a follow sphere, and a ring (a hollow cylinder) of uniform density, each...

A solid sphere, a follow sphere, and a ring (a hollow cylinder) of uniform density, each with radius 0.24m and mass 2.6kg roll without slipping on a flat surface at an angular speed of 6.1 rad/s. They then roll without slipping up an incline. 1. What is the linear speed of the center of mass of the ring when it is rolling on the flat surface? 2. What happens as the objects roll up the incline? 3. How high up...

A solid sphere has a temperature of 674 K. The sphere is melted down and recast...

A solid sphere has a temperature of 674 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cube's temperature in kelvins?

The correlation coefficient is: the range of values over which the probability may be estimated based...

The correlation coefficient is: the range of values over which the probability may be estimated based upon the regression equation results. the proportion of the total variance in the dependent variable explained by the independent variable. the measure of variability of the actual observations from the predicting (forecasting) equation line. the relative degree that changes in one variable can be used to estimate changes in another variable.

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder...

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder of radius R all have the same mass, and all three are rotating with the same angular velocity. The sphere is rotating around an axis through its center, and each cylinder is rotating around its symmetry axis. Which one has the greatest rotational kinetic energy? both cylinders have the same rotational kinetic energy the solid cylinder the solid sphere they all have the same...

Rotational Inertia –Rolling Kinetic Energy. A solid sphere, a hollow sphere, a hollow cylinder, and a...

Rotational Inertia –Rolling Kinetic Energy. A solid sphere, a hollow sphere, a hollow cylinder, and a solid cylinder, all of with same mass (M=0.25 kg ) and radius(R= 0.20 m) – are placed at the top of an incline at height (h= 1.5 m ). All the objects are released from rest at the same moment to roll down without slipping. Hint: search for the rotational inertia formula for each of the rolling object first. Then calculate each of them...

Consider the following schematic for an experiemental methodology to measure the convection heat transfer coefficient distrubution...

Consider the following schematic for an experiemental methodology to measure the convection heat transfer coefficient distrubution on an airfoil. The metal sheathing is supplied with a heat generation rate of 20 * 106 W/m3. The thickness of the metal sheathing is t = 30 um, and the sheathing's thermal conductivity is k=25 W/mK. The 30 surface locations where the temperatures are measured are spaced evenly at 2mm apart. The measured temperatures are listed in the table below. Location Temperature (degrees...

A solid is bounded by the sphere centered at the origin of radius 5 and the...

A solid is bounded by the sphere centered at the origin of radius 5 and the infinite cylinder along the z-axis of radius 3. (a) Write inequalities that describe the solid in Cartesian coordinates. (b) Write inequalities that describe the solid in cylindrical coordinates. (c) Why is this solid difficult to describe in spherical coordinates? Which of the variables ρ, θ, φ are difficult to describe? Explain.

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius....

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius. They both roll without slipping, have the same linear speed and approach the same inclined plane. As they roll up the inclined plane, they continue to roll without slipping. Which object will reach the greatest height on the inclined plane? A: solid homogeneous cylinder B: solid homogeneous sphere C: they both reach the same maximum height If you could explain why in your answer...

A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r,...

A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r, and a hollow cylinder of radius r are all allowed to roll down an incline. Derive a general relationship for the linear acceleration of each object depending on the angle of the ramp and the rotational inertia. You may assume that the frictional force is small enough that it is only causing rotation in each case.

Subjects