Convection Heat Transfer in Manufacturing Processes P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Mode of Heat Transfer due to macro-Movements!!!

Convection Heat Transfer in Manufacturing

Some thing Happens Before Onset of Convection Heat Transfer The convective heat transfer is defined for a combined solid and fluid system. In a flow system, small layer of fluid particles close to the wall come to Mechanical, Thermal and Chemical Equilibrium With solid wall. Fundamentally this fluid layer is in Thermodynamic Equilibrium with the solid wall. Physically, the fluid packets close to a solid wall attain a zero relative velocity with the solid wall. The fluid particles will exchange maximum possible heat flux with the solid wall. A Zero temperature difference exists between wall and fluid packets at the wall.

Heat Transfer in Equilibrium Fluid Layer At Thermodynamic equilibrium The thickness of stagnant layer decides the magnitude of normal temperature gradient at the wall. And hence, the thickness of wall fluid layer decides the magnitude of rate of heat transfer form wall/to the wall. The bulk movement of fluid particles export this heat deep into fluid body duet to macro motion (convection).

At the surface, there is no fluid motion, heat transfer is only possible due to heat conduction. Thus, from the local heat flux: This is the basic mechanism for heat transfer from solid to liquid or Vice versa. The heat conducted into the fluid will further propagate into free stream fluid by convection alone. Use of Newton’s Law of Cooling: Conduction Heat Transfer in Equilibrium Fluid Layer At the edge of fluid layer :

Estimation of Heat Transfer Coefficient Estimation of heat transfer coefficient is basically computation of temperature profile. A general theoretical and experimental study to understand how the stagnant layer is developed. The global geometry of the solid wall and flow conditions will decide the structure of stagnant layer. Basic Geometry : Internal Flow or External Flow.

Structure of Internal Flows

q’’ TiTi T s (x) TiTi q’’ Hot Wall & Cold Fluid Cold Wall & Hot Fluid Temperature Profile in Internal Flow

External Flows There will be continuous growth of Solid surface affected region in Main stream direction. The extent of this region is very very small when compared to the entire flow domain. Free stream flow and thermal properties exit during the entire flow.

At the surface there is no relative motion between fluid and solid. The local momentum flux (gain or loss) is defied by Newton’s Law of Viscosity : Momentum flux of far field stream: The effect of solid boundary : ratio of shear stress at wall/free stream Momentum flux Momentum Transfer near solid Wall

Coefficient of friction:

Cold Surface Thermal Boundary Layer Plate surface is cooler than the fluid (T s < T ∞ ) Scale of temperature: Define non-dimensional Temperature as:

Empirical method How to set up an experimental test? Let’s say you want to know the heat transfer rate of an airplane wing (with fuel inside) flying at steady conditions…………. What are the parameters involved? –Velocity, –plate length, –Prandtl number, –viscosity, –Nusselt number, Which of these can we control easily? Looking for the relation: Experience has shown the following relation works well:

Experimental test setup insulation L Measure current (hence heat transfer) with various fluids and test conditions for Fluid properties are typically evaluated at the mean film temperature

Study of Convection Heat Transfer

Similarity Variables

Reynolds number : An Universal Measure Flow All Engineering Applications

Prandtl Number: The ratio of momentum diffusion to heat diffusion. Other scales of reference: Length of plate: L Free stream velocity : u oo Potential for diffusion of momentum change (Deficit or excess) created by a solid boundary. Potential for Diffusion of thermal changes created by a solid boundary.

Local convection heat transfer coefficient: For a hot horizontal flat plate

Average heat transfer coefficient:

Complex Heat Convection Geometries in Manufacturing

Cylinder in Cross Flow

The empirical correlation due to Hilpert Re D Cm