3-3. Use the methods of vectorcalculus to derive the general heat conduction equation (Hint: Apply the first law to a volume V with surface S. and use the Gauss divergence theorem to Convert the surface integral of heat flow across S to a
volume integral over V.)
The cylindrical and spherical coordinate systems are examples of orthogonal curilinear coordinates. In general. we can denote these coordinates by ..... which are defined by specifying the Cartesian coordinates. .... as
.....
A coordinate system is orthogonal when the three families of surfaces ii Const. u, -= Consi, u3 = Const are orthogonal to one another. The figure shows an elemental paraliepiped whose faces coincide with planes u1 or or ui = Const. with edge lengths h1du h2dx,2. h1dii1 where h1. h, h are called the metric coefficseiirs. The length of a diagonal is given by
ds2 = hdu + hdu + h,du
in terms of these coordinates, the components of the temperature gradient are....

(i) Identify the metric coefficients for the cylindrical coordinate system, and hence write down V2T in cylindrical coordinates.
(ii) Repeat for the spherical coordinate system.

textbook: A F Mills, Heat Transfer, Prentice Hall, 1999

Two parallel surface with area 2000cm^2 and 5cm apart exchange heat in a vacuum. Surface A is at 125 C and surface 2 is 75 C, Emissivity is 0.9 V12 =0.9
What is the heat loss from surface 1.
What is the effective heattransfer of the surface.

A copper sphere of internal diameter 2 m and wall thickness 40 mm is insulated with 75 mm of expanded polystyrene. The thermal conductivity of copper is 380 W/mK and that of the polystyrene is 0.04 W/mK. The inside and outside surface heattransfer coefficients are 500 and 12 W/m2K respectively. The inside temperature is 280

The answers are given, but please provide solutions for these questions.
HeatTransfer Problems
1. How much heat is conducted in 1.0h through an iron plate 2.0cm thick and the 1,000cm2 in area, the temperatures of the two sides being kept at 0 and 20°C?
Answer = 4.0 x 106 cal
2. Compute the heat conducted per hour thr

The heattransfer coefficients and the fouling factors on the tube and shellside of a heat exchanger are given. The hermal resistance and the overall heattransfer coefficients based on the inner and outer areas are to be determined.
Please see the attached file for the completely formatted problem.

Show ALL your work, including the equations used to solve the problems.
An insulated Thermos contains 13cm^3 of hot coffee, at a temperature of 80.0ºC. You put in a 12.0-g ice cube at its melting point to cool the coffee. By how many degrees has your coffee cooled once the ice has melted? Treat the coffee as though it were p

Hello, I'm having difficulty figuring out how to work out a rather simple physics problem and would appreciate some guidance. The problem is as follows:
A bottle containing 5.7kg of water at a temperature of 27.3 degrees Celsius is placed in a refrigerator kept at 2.9 degrees Celsius. How much heat is transferred from the wat

Super heated steam at 500K flows through a steel pipe (outside dia. Of 15cm and a wall thickness of 0.7cm, k=54 W/mK). The pipe is insulated with a 5.3cm thick layer of an insulation (k=0.073 W/mK). The outer layer of insulation is at 27C. The sum of radiation and convective heattransfer coefficient is estimated to be 8 W/mK. C

Copper clips are sometimes used as "heat sinks." How many grams of copper must be in contact with an electric component to absorb 10.0 J of heatand not let the temperature increase by more than 40 C? The specific heat of copper is 0.385 J/g K.

Describe the differences and similarities between temperature andheat. Analyze how heattransfer occurs during the processes of conduction and convection. Provide an example of where each occurs in natural physical systems