Consider fully developed constant-property laminar flow between parallel planes

Question

Consider fully developed constant-property laminar flow between parallel planes with constant heat rate per unit of length and a fully developed temperature profile. Suppose heat is transferred to the fluid on one side and out of the fluid on the other at the same rate. What is the Nusselt number on each side of the passage? Sketch the temperature profile. Suppose the fluid is an oil for which the viscosity varies greatly with temperature, but all the other properties are relatively unaffected by temperature. Is the velocity profile affected? Is the temperature profile affected? Is the Nusselt number affected? Explain.

Explanation / Answer

Given that flow is fully developed and laminar hence the Nusselt number (Nu) is constant for given flow.

As given viscosity is greatly affected by temperature the temperature profile will get affected. As viscosity varies from boundary in y direction.

As Reynolds number is dependant on viscosity the velocity profile will aslo get affected.

For oil hydrodynamic boundary layer thickness is grater than thermal boundary layer thickness.

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