Thermal transport enhancement in turbulent boundary layer over a rotating non-isothermal wavy disk

Abstract The enhancement in the heat transfer process within a turbulent boundary layer by considering a rotating wavy disk heated with a non-uniform temperature distribution is reported through this communication. Applying the non-uniform disk temperature and the wavy disk configuration increases the temperature gradients inside the thermal boundary layer, thus augmenting the heat transfer process. Such an enhanced heat transport process is important in thermal management, especially in industries that require efficient cooling and precise temperature regulation. The Cebeci–Smith turbulence model, based on the eddy-viscosity concept, has been employed to incorporate the Reynolds shear stress and heat flux terms, appearing in the boundary layer form of the Navier–Stokes equations and the energy equation. These equations were reformulated with dimensionless variables and then solved numerically using the Keller-Box method based on a finite-difference approach. The impact of the amplitude-to-wavelength ratio ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>λ</mml:mi> </mml:mfrac> </mml:mrow> </mml:math> ), number of sinusoids ( N ), temperature exponent ( n ), and Prandtl number ( Pr ) on the characteristics of heat transfer has been examined. The heat transfer rate has increased by up to 8% and 29% on a uniformly heated wavy disk ( n = 0), with amplitude-to-wavelength ratio values <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>λ</mml:mi> </mml:mfrac> <mml:mo>=</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> , 0.2, compared to a flat disk. Considering the non-uniform temperature distribution with a temperature exponent n = 3 further improves thermal transport by up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>12.42</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>33.38</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:mrow> </mml:math> at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>λ</mml:mi> </mml:mfrac> <mml:mo>=</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> , 0.2, compared to a uniformly heated flat disk. The heat transfer rate shows a significant improvement up to N = 2 and remains relatively constant for N &gt; 2. The threshold values of the temperature exponent n , at which the heat transfer from the wavy disk to the surrounding fluid ceases, have been calculated. For instance, the heat transfer process stops at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>4.7878</mml:mn> </mml:mrow> </mml:math> in turbulent flow with Pr = 0.71. However, the wavy configuration appears to have a negligible effect on the threshold values. It has been observed that varying the Prandtl number ( Pr ) affects these threshold values, causing them to decrease (in magnitude) as the values of Pr increase.