Chapter 5, Problem 5.5P

Interpretation Introduction

Interpretation: The rise in the temperature of the oil in the previous question is to be calculated due to viscous dissipation.

Concept introduction: The rise in temperature is generally calculated from the heat balance equation. The rise or increase in the temperature is generally due to the physical factors involved in the system or surroundings. The equation for the heat balance to calculate the rise in temperature is,

  $\text{Q}\text{=}{\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover><mo> ×c</mo>}}_{\text{p}}\text{×ΔT}\mathrm{.......}\text{(1)}$

The notations used in this equation are,

  $\begin{array}{l}\text{Q =}\text{Amount of heat supplied}\\ \text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{Mass flow rate of the oil}\\ {\text{c}}_{\text{p}}\text{=}\text{Specific}\text{heat}\text{of}\text{the}\text{oil}\\ \text{ΔT}\text{=}\text{Rise}\text{in}\text{temperature}\end{array}$

The mass flow rate of the oil can be given as,

  $\begin{array}{l}\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}\text{=}\text{ρ×q}\mathrm{.......}\text{(2)}\\ \text{ρ}\text{= Density}\text{of}\text{oil}\\ \text{q}\text{=}\text{Flow rate of the oil}\end{array}$

On combining equation (1) and equation (2) and rearranging,

  $\text{ΔT}\text{=}\frac{\text{Q}}{\text{ρ}\text{×}\text{q}\text{×}{\text{c}}_{\text{p}}}\mathrm{.......}\text{(3)}$