Chemical Engineering Equations

Expression of Rate of Heat Flow Through a Composite Wall

This expression is used for calculating the rate of heat flow through the series of resistances. Here the rate is calculated as the ratio of overall temperature difference to the overall resistance of the wall. 

Expression of Rate of Heat Flow Through a Composite Cylinder

This expression is used for calculating the heat flow through a composite cylinder. Here the heat transfer area depends on the radius or the radial position.

 

Expression of Rate of Heat Flow Through a Composite Sphere

This expression is used for calculating the rate of heat flow through a composite sphere.

 

Expression for Logarithmic Mean Temperature Difference

Logarithmic Mean Temperature Difference (LMTD) is used to determine the driving force (temperature difference) for heat transfer in flow system; especially it is used for heat exchanger. However, it should not be used when overall heat transfer coefficient (U) changes appreciably or when temperature difference (ΔT) is not a linear function of q. The expression of LMTD can be written as 

Expression of Overall Heat Transfer Coefficient

For calculating the rate of heat transfer in case heat transfer from one fluid to another separated by a plane solid wall, overall heat transfer coefficient is important. The expression of overall heat transfer coefficient in such case can be written as 

Expression of Overall Heat Transfer Coefficient for the Heat Transfer in a Cylindrical Geometry

As a cylindrical geometry we can consider heat transfer from one fluid phase to another in the double-pipe heat exchanger. It consists of two concentric pipes properly fitted or welded with arrangements for pumping one of the fluids through the inner pipe and the other through the annular space. The fluids are thus brought in thermal contact in order to achieve the heat transfer.

 The overall heat transfer coefficient U_i based on the inside surface area

Overall heat transfer coefficient U₀ based on the outside surface area

Where, r_i and r_o are the inner and outer radii of the inner pipe

      h_i and h_o are the heat transfer coefficients of the inner and outer side of the pipe

      k_w is the thermal conductivity of the material of the pipe wall

 

Reference:

1.   Heat Transfer Principles and Applications, by Binay K. Dutta

2. Unit operations of Chemical Engineering, 6^th edition, by Warren L. McCabe, Julian C.                Smith, and Peter Harriott.

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